*Review* **The Metal Content of the Hot Atmospheres of Galaxy Groups**

**Fabio Gastaldello 1,\* , Aurora Simionescu 2,3,4, Francois Mernier 2,5, Veronica Biffi 6,7, Massimo Gaspari 8,9, Kosuke Sato <sup>10</sup> and Kyoko Matsushita <sup>11</sup>**


**Abstract:** Galaxy groups host the majority of matter and more than half of all the galaxies in the Universe. Their hot (10<sup>7</sup> K), X-ray emitting intra-group medium (IGrM) reveals emission lines typical of many elements synthesized by stars and supernovae. Because their gravitational potentials are shallower than those of rich galaxy clusters, groups are ideal targets for studying, through X-ray observations , feedback effects, which leave important marks on their gas and metal contents. Here, we review the history and present status of the chemical abundances in the IGrM probed by X-ray spectroscopy. We discuss the limitations of our current knowledge, in particular due to uncertainties in the modeling of the Fe-L shell by plasma codes, and coverage of the volume beyond the central region. We further summarize the constraints on the abundance pattern at the group mass scale and the insight it provides to the history of chemical enrichment. Parallel to the observational efforts, we review the progress made by both cosmological hydrodynamical simulations and controlled highresolution 3D simulations to reproduce the radial distribution of metals in the IGrM, the dependence on system mass from group to cluster scales, and the role of AGN and SN feedback in producing the observed phenomenology. Finally, we highlight future prospects in this field, where progress will be driven both by a much richer sample of X-ray emitting groups identified with eROSITA, and by a revolution in the study of X-ray spectra expected from micro-calorimeters onboard XRISM and ATHENA.

**Keywords:** galaxies:abundances; galaxies:clusters:intracluster medium; X-rays:galaxies

#### **1. Introduction**

Two major astrophysical discoveries have provided key answers to the fundamental question of the origin of the chemical elements in the past century: the discovery that stellar nucleosynthesis is responsible for the production of all the heavy elements from lithium to uranium [1–3] and the detection of line emission due to highly ionized iron in the X-ray spectra of the intra-cluster medium (ICM) [4,5]. The impact of these two

**Citation:** Gastaldello, F.; Simionescu, A.; Mernier, F.; Biffi, V.; Gaspari, M.; Sato, K.; Matsushita, K. The Metal Content of the Hot Atmospheres of Galaxy Groups. *Universe* **2021**, *7*, 208. https://doi.org/10.3390/universe 7070208

Academic Editor: Francesco Shankar

Received: 31 March 2021 Accepted: 16 June 2021 Published: 24 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

discoveries was extraordinary. The first one demonstrated that all the elements (with the exception of hydrogen, helium, and traces of lithium and berillium produced by the Big Bang nucleosynthesis) are forged in the cores of stars and in supernovae (SNe) and that when a star explodes as a supernova it enriches the surrounding interstellar medium with freshly created elements. The second one showed that galaxies lost part of their synthesized elements and that there has been a considerable exchange of chemical elements between stars, galaxies and the hot plasma surrounding them. This also means that the chemical elements trace the formation and evolution of structure which is shaped by the physical processes occurring on a very wide range of spatial scales, from the size of single supernova remnants to cosmological volumes.

The improvements in the stellar and supernova nucleosynthesis theory and modelization (e.g., References [6,7] and references therein) established that the major astrophysical sources of the chemical elements are: (i) Core-collapse supernovae (SNcc) and their massive progenitors ( 8–10 *M*) synthesize most of the O, Ne, and Mg of the Universe and a considerable fraction of Si and S (collectively called *α* elements as they are the result of fusion process involving the capture of *α* particles); (ii) Type Ia supernovae (SNIa), whose progenitors are generally believed to be exploding white dwarfs in binary systems, synthesize Ar, Fe, and the other Fe-peak elements, such as Cr and Ni, and the remaining fraction of Si and S; (iii) Asymptotic giant branch (AGB) stars produce mainly C, N which are ejected through stellar winds.

In astrophysics, the term "metals" refers to all the elements heavier than helium, in contrast to the terminology adopted in other scientific disciplines, in part because all these elements make up a small contribution in number and mass with respect to H and He. A considerable fraction of the metals (and most of the iron) do not reside in the galaxies of groups and clusters and they have been expelled in their surrounding X-ray emitting hot atmospheres (for the purpose of this review, we will define the hot atmosphere of groups as intra-group medium, IGrM). Indeed, the iron share, i.e., the ratio of iron in the hot atmosphere and the iron locked up in stars in the galaxies, ranges from 1 up to 10 (see, for recent measurements, References [8,9]). Therefore, the key question is to understand the main transport mechanisms responsible for that unbalance (see, for a more detailed discussion, References [10,11]). There are two broad categories of mechanisms: (i) extraction by ram pressure stripping and galaxy-galaxy interactions; (ii) ejection by galactic winds powered from inside the galaxies themselves either by SNe (stellar feedback) or by the supermassive black hole (SMBH) at their center (in the so-called active galactic nucleus, AGN, feedback). Other important processes redistributing the metals within the hot atmospheres are the central AGN uplift of metals (see the reviews by References [12–15] and the companion review by Eckert et al.) and sloshing, i.e., the offset of the bulk of central part of the hot atmosphere from its hydrostatic equilibrium in its gravitational potential and the subsequent oscillations that may broaden the original distribution at larger scales (see the reviews by References [16,17]). Another source of metals could be the diffuse stellar component not associated to any single galaxy but to the global halo of the cluster or group (also know as intra-cluster light, ICL) polluting the ICM and the IGrM in situ [18].

The purpose of this paper is to review the status of the metal abundance measurements in the IGrM and the progress made by simulations to reproduce and interpret those measurements. It is a companion of the other reviews in this series addressing the scaling relations of these systems (Lovisari et al.), the impact of AGN feedback (Eckert et al.), the overall insight provided by simulations (Oppenheimter et al.), and the properties of the particular class of fossil groups (Aguerri et al.).

Groups of galaxies (which can be defined as objects with total masses *M*<sup>500</sup> in the range 1013–1014 *<sup>M</sup>*, though see Lovisari et al. for the unavoidable ambiguity of the definition of a galaxy group) bridge the mass spectrum between L\* galaxies and galaxy clusters. They are known to host a significant fraction of the number of galaxies in the Universe (e.g., References [19,20]), they form in the filaments of the cosmic web and not only in the nodes (e.g., Reference [21]), and they are bright enough to be relatively easily observable in

X-rays, while having low enough masses such that complex baryonic physics (e.g., cooling, galactic winds, AGN feedback) begins to dominate above gravity, making these objects more than simple scaled down versions of galaxy clusters (e.g., References [22,23] and the aforementioned reviews in this series). Groups of galaxies appear as critical systems to understand the process of structure formation, the dynamical assembly of baryons in the dark matter halos, and the complex physical processes affecting both the gas and the stellar components. For all the above reasons, it is important to study metals in groups: if, for example, it is more controversial with respect to clusters that they can be considered as "closed box", they can provide key information on the processes, resulting in the redistribution and loss of metals, and it is clearly instructive to investigate the metal budget in different types of systems (see the interesting discussion in the review by Reference [24]).

Many excellent reviews exist already focusing either on the more general topic of X-ray spectroscopy, mainly of the ICM, or directly on metal abundances both observationally and theoretically [10,11,25–32] that ease our work which will then focus on the topics more directly related to the recent updates about metal abundances in galaxy groups. In this respect the only reviews of the topic are about the early history of the metal abundance measurements in the IGrM described in Reference [19] and a more recent update including the *Chandra*and XMM-*Newton* data can be found in Reference [33]. A comparison of the metal budget in groups compared to the one in clusters and elliptical galaxies has been discussed in Reference [31].

The review is organized as follows. In Section 2, we review the observational measurements, from the early *ROSAT* and *ASCA* results to the more recent *Chandra*, XMM-*Newton* and *Suzaku* CCD and high spectral resolution (with the RGS instrument on board XMM-*Newton*) results. In Section 3, we discuss the theoretical framework and the insight from numerical simulations. In Section 4, we discuss the most relevant upcoming missions which will provide a key contribution to the field, and ,in Section 5, we present our final remarks.

#### **2. X-ray Observations**

#### *2.1. The Observational Signatures of Metals in the IGrM*

The X-ray spectra of the hot, diffuse gas that fills the dark matter halos of galaxies, galaxy groups, and galaxy clusters, is typically described as an optically thin plasma in collisional ionization equilibrium (CIE), composed mainly of primordial hydrogen and helium gas but containing trace amounts of heavier elements from C up to Ni. These approximations usually provide a sufficient description of the bulk of the emission, although subtle effects due to various deviations from a simple thermal model can sometimes become relevant—we refer the reader to Gu et al. [34] for a review.

There are two noteworthy differences between the X-ray emission from the ICM and IGrM. Firstly, in the hot ICM of clusters of galaxies, the free-free bremsstrahlung continuum is the dominant radiation process (see, e.g., Reference [35]). Conversely, for plasma temperatures around and below 1 keV, which are typical of galaxy groups, increasing contributions to the continuum level come also from (i) recombination radiation, caused by the capture of an electron by an ion, leading to a spectral shape characterized by sharp ionization edges, and (ii) the slow transition from the 2 s to the 1 s state, which is forbidden by angular momentum conservation but can happen as a very slow two-photon process giving rise to continuum emission (see, e.g., Figure 6 of Reference [28]). This makes it more difficult to determine the equivalent width of a given spectral line (EW1), a quantity that serves as a main diagnostic of the abundance of the chemical element from which that line originates.

Secondly, at higher plasma temperatures (∼4 keV and above), abundance measurements are typically driven by the signal obtained from the Fe XXV He-*α* line at 6.7 keV (rest frame). By comparison, below temperatures of around 2 keV, i.e., in the low-mass cluster and group regime, the most prominent diagnostic of the metallicity comes instead from the Fe-L line complex at 0.7–1.2 keV. This blend of emission lines originating from the L-shell transitions of Fe XVII–Fe XXIV is completely unresolved at the spectral resolution

of CCD cameras; the lines are so closely spaced together that, in many cases, they remain blended even for the XMM-*Newton* RGS and the upcoming high-spectral resolution microcalorimeter onboard *XRISM*. Next to the dominant Fe-L lines, emission from Ne X and the L-shell of Ni at similar energies is also blended within the same spectral structure.

In practice, elemental abundances are usually estimated by fitting the X-ray spectra with models of CIE emitting plasma, that account for the presence of various emission lines within the Fe-L blend (as well as the recombination and two-photon continua). The two plasma radiation codes most commonly used today in X-ray astronomy are AtomDB [36,37] and SPEXACT [38,39]. These models have evolved considerably over the last 4 decades, since the Fe-L emission was first discovered with the Solid-State Spectrometer onboard the *Einstein* satellite [40,41].

In Figure 1, we illustrate the historic development of these two model 'flavors' over time, using the specific example of a 1 keV plasma with Solar elemental composition, folded through the spectral response of a CCD camera. Simply and perhaps simplistically put, transitions belonging to lower ionization states of Fe (whose emission lines lie at lower energies within the Fe-L 'bump') require more complex computations and were, therefore, not fully accounted for in earlier models. This is why, both for AtomDB and SPEX, the shape of the lower energy wing of the Fe-L blend particularly appears to evolve significantly, and great care must be taken when discussing results obtained with older precursors of these plasma emission codes. It is encouraging that the models seem to be converging in recent years and, at least at CCD-level spectral resolution, the latest versions of AtomDB and SPEX only differ at about the ∼5–10% level for a 1 keV plasma. Nevertheless, larger differences still remain for lower temperatures (up to 20% at kT < 0.4 keV when folded through a CCD response), and when viewing the models at higher spectral resolution, where the brightest lines in the Fe-L complex can be distinguished from the blend (for a general and up-to-date discussion of the discrepancies of the two plasma codes, see the discussion in Reference [42]).

**Figure 1.** Historic evolution of the two most commonly used plasma emission models. For illustration, we focus on the specific case of a 1 keV plasma with Solar composition (following the Solar abundance units of Asplund et al. [43]). All models have the same emission measure *nenHdV* and have been folded through the XMM-Newton MOS detector response. (**Left**) AtomDB [37] can be viewed as the replacement for/development of the Raymond-Smith code [44]. (**Right**) SPEXACT originated from the 'meka' model developed by Rolf Mewe and Jelle Kaastra, which later became the 'mekal' model; the addition of the final 'l' comes from Duane Liedahl who calculated the atomic parameters for a large number of Fe L-shell ions [35,45,46].

Observationally speaking, the Fe-L complex is both a blessing and a curse. On one hand, as mentioned above, it involves modeling the emission of Fe ions with many re-

maining electrons, which is significantly more difficult than H- or He-like transitions. On the other hand, because these lines are very bright, the total 0.5–2.0 keV flux of a kT = 0.6–0.8 keV IGrM plasma with a Solar composition is *more than three times brighter* than a 4 keV ICM plasma with the same emission measure (defined as *nenHdV*). Quite literally, metals make the IGrM shine, and emission from Fe, in particular, is crucial for detecting what would otherwise be extremely faint and diffuse plasma in galaxy groups. However, this also means that, unlike the case of the ICM, a knowledge of the metallicity in the IGrM is indispensable for converting the observed X-ray flux into a particle number density. Furthermore, since the total flux and shape of the Fe-L bump are extremely sensitive to the plasma temperature (e.g., see the difference between the Fe-L model for a 0.6 versus a 1.2 keV plasma in Figure 2), significant biases arise when a spectrum containing multiple temperature components (for instance due to projection effects or radiative cooling in the core of a group) is approximated by a single-temperature model. This effect, dubbed 'the Fe bias', is discussed in detail already in References [47,48] using ASCA data of elliptical galaxies and galaxy groups. In that work, and many subsequent references thereto, it is consistently shown that, if the abundance measurements are driven by the Fe-L signal, a two-temperature model can yield best-fit metallicities more than twice higher than a single temperature approximation. Although this conclusion was originally reached with old versions of the Fe-L plasma emission, it remains true today, as we illustrate in Figure 2. It is also worth mentioning in passing that, at least at CCD spectral resolution, multi-temperature models can only be constrained if the abundances of the two components are coupled to each other, which need not be true in nature. In addition, beside the IGrM being intrinsically multi-phase, the unresolved emission from low-mass X-ray binaries (LMXB) may be an important spectral component, at least near the center of the brightest group galaxy (BGG) (e.g., Reference [49]); if unaccounted for, this may lead to biases in the measured abundances as well.

As a last cautionary note in terms of interpreting various metal abundance measurements quoted in the literature, it is important to remember that these are customarily reported with respect to the Solar number ratio of that element compared to H; however, this reference point, too, has evolved over the past few decades. While the Solar photospheric units of Reference [50] are still the default in the Xspec fitting package and, therefore, widely used, this reference value for Fe/H is between 43 and 48% higher than reported by the more recent work of References [43,51], respectively. Hence, the Fe abundances reported by various groups can be considerably different depending on the Solar units assumed, and care must be taken when comparing the results. Here, we choose to normalize all quoted abundances to the units of Reference [43].

Moreover, the absolute values of, e.g., O/H (often assumed to be Solar, with the implied variations/uncertainties just stated above), also affect the way that absorption edges from our own Milky Way influence the spectrum; since most of the emission from the IGrM is in the soft band, using the correct Galactic *n*<sup>H</sup> (see, for example, the discussion in Reference [52]), as well as the correct chemical composition of the absorbing gas, is important for obtaining a robust characterization of the spectral properties of the IGrM.

Armed with this overview of the spectral characteristics and potential pitfalls of modeling the IGrM, in the following sub-sections, we discuss how our observational picture of metals in galaxy groups has evolved over the past several decades.

**Figure 2.** Simulated XMM-*Newton* MOS observations of a multi-temperature plasma, illustrating the effect of the Fe bias. A mix of 0.6 and 1.2 keV plasmas with emission measures in a proportion of 1:10, Solar abundances in the units of Asplund et al. [43], and a total flux similar to that of NGC5846 (integrated within 0.05r500), was simulated using SPEXACT v3.0.6. Despite the fact that the low temperature component has only 1/10th of the emission measure of the hotter gas, a single temperature fit results in a best fit metallicity that is half of the value input to the simulation. The bottom panel shows the fit residuals for a 1T and 2T model for the 10 ks observation; while there is still a hint that the 1T model does not perfectly describe the data (given the positive residuals around 0.7 keV), this could easily be missed for fainter/more distant targets or when using smaller extraction regions for creating radial profiles or maps.

#### *2.2. The Early Measurements of Global Metallicity*

The first milestone discoveries of a true detection of the IGrM in the two galaxy groups NGC 2300 [53] (see Figure 3) and HCG 62 [54] done with *ROSAT* pointed to a surprisingly low abundance of the plasma of 0.09 Solar for NGC 2300 and 0.22 Solar for HCG 62, assuming the RS thermal plasma model [44]. The entire detectable extent of the emission was fitted in a single aperture (25 for NGC 2300 and 18 for HCG 62, in the case of the analysis of NGC 2300 excluding the emission around the central galaxy itself). The *ROSAT* observation of NGC 5044 [55] made it possible to measure spatially resolved temperatures and abundances, with super-Solar abundances in the inner 6 and beyond that radius consistent with a uniform distribution of 1.2 Solar. Very low abundance, <0.12, was reported in the NGC 4261 group from a fit with a RS model to a spectrum extracted from 40 [56]. In the first sample of HCGs [57], a solid detection of extended emission in 3 of them (the already mentioned HCG 62, HCG 92, and HCG 97) and a possible detection in another 3, were all well fitted by a RS model with very low metal abundances. Additional *ROSAT* observations allowed spatially resolved measurements for NGC 2300 confirming the low abundance, less than 0.16 Solar [58]. In a more complete survey of 85 HCGs with either deeper pointed (in 32 cases) or survey *ROSAT* PSPC observations, extended

emission from an IGrM was detected in 22 of them, including in the group emission also the emission spatially located on the dominant central elliptical [59]. The metallicity derived for the 12 spectra of enough quality within an aperture of 200 kpc (in their cosmology) all pointed to a low abundance with a weighted mean of 0.27 Solar. Interestingly enough, Ponman et al. [59] commented to treat these results with caution because the inferred low metal abundances rely heavily on the isothermal assumption: when temperature variations in the gas are taken into account, metallicities several times higher can be inferred [60], extending the search for *ROSAT* observation of galaxy groups beyond HCGs with other optical catalogues in a sample of an additional 14 groups, finding emission from 4 of them, and extending the census of the IGrM to 25 of the 48 groups analyzed at that time. Some conclusions were starting to be made, with the general lower abundance of the IGrM with respect to the ICM, despite the more equal share between gas and stellar mass, possibly suggesting that the IGrM may be largely primordial.

**Figure 3.** The *ROSAT* X-ray spectrum of the group NGC 2300 plotted together with the beat-fit Raymond-Smith model (**a**) and residuals from the best fit model (**b**). Figure reproduced with permission from Reference [53].

However, concerns were starting to increase about the ability to model the dominant Fe-L emission in the IGrM by the available plasma codes. The first *ASCA* CCD spectra (with the SIS instrument) of the cores of cool core clusters, Perseus, Abell 1795, and the Centaurus cluster exposed the limitations of both the RS and MEKA [35,45] models [61], causing a major revision of the modeling of the Fe-L shell emission [46] which later was incorporated in the MEKAL code. These concerns were reinforced by the discrepancy between the low metallicity found also in the inter-stellar medium of elliptical galaxies and the super-Solar abundances expected just by stellar mass loss [62,63].

*ASCA* measurements also reported a great scatter in the metallicity of the IGrM. The *ASCA* study of NGC 5044 and HCG 51 reported metal abundances significantly higher than those of NGC 2300 and HCG 62 (also performed with *ASCA*) and more similar to clusters [64]. Ref. [65] analyzed *ASCA* data for 17 groups with single apertures ranging from 4 to 30 , finding, in general, low abundances in the range 0.15–0.6 Solar. The higher

temperature and mass objects with *ASCA* measurements reported by Reference [66] showed an average abundance of 0.44 Solar consistent with that observed in rich clusters and, therefore, clearly highlighting the 1 keV regime as the one showing the spread to lower values of the abundance measurement.

The overall summary as done by Mulchaey [19] is that of a surprising scatter in the measured metallicities in groups, from low (0.15–0.3 Solar) to higher than the values determined in clusters in those days (0.7–0.9) with *ROSAT* and *ASCA*.

A key insight was provided by a series of papers showing the biases introduced by fitting with a single isothermal model complex spectra with multi-temperature components. In the spectra extracted from large apertures in the bright cores of galaxy groups and ellipticals, temperature and abundance gradients are present [47,48,67,68]. The very sub-Solar abundances obtained from previous studies were an artefact of fitting isothermal models and two-temperature models provided better fits to the data and higher metallicities. This is the Fe-bias also described in the previous section and demonstrated by means of simulations of *ASCA* spectra [48]. The discovery of the Fe bias highlighted the importance of the ability of performing spatially resolved spectroscopy and the difficulties in the modelization of the thermal and abundance structure in the cores of galaxy, groups and clusters, as it was shown at those times by the early results of M87 with XMM-*Newton* [69].

The last influential paper dealing with single measurements of metal abundances is Baumgartner et al. [70], presenting an analysis of the *ASCA* spectra of 273 groups and clusters with the largest possible aperture collecting all the detectable flux and stacked in bins of temperature. That work found a constant Fe abundance value of 0.3 Solar for hot clusters and for groups with an increase up to a factor of 3 with respect to the average value in the range 2–4 keV. This is a manifestation of the "inverse" Fe-bias [71–73] which overestimates the abundances in multi-temperature plasma (ranging from about 1–2 keV to about 5 keV) resulting in a mean global temperature in the range 2–4 keV as found by Baumgartner et al. [70]. Although, in practice, when this occurs, the spectra show the presence of both Fe-L and Fe-K lines, the inverse Fe-bias is essentially weighted by the higher statistics of the Fe-L complex. In this regime, the fitting procedure increases the estimated Fe abundance to overcome the weaker Fe-lines expected in the single temperature plasma (for more details, see Reference [73]).

#### *2.3. The Spatial Distribution of the Metals in the IGrM*

Succeeding the *ROSAT* and *ASCA* eras, which allowed to set a first light on global metallicities of the IGrM, the advent of CCD instruments offered by the generation of early 2000s X-ray observatories (*Chandra*, XMM-*Newton*, *Suzaku*) brought a significant progress. They allowed not only to reveal the spatial distribution of metals across galaxy groups, but also to focus on elements other than Fe—hence exploring groups' chemical history with respect to its SNIa *and* SNcc components. In the following sub-sections, we tackle these two aspects in more detail.

#### 2.3.1. Radial Profiles of Iron Abundance

The essence of this sub-section is summarized in Figure 4, where we show a few recent radial metallicity (i.e., Fe) profiles of galaxy groups (from both individual and sample measurements), with comparison with typical cluster profiles. These profiles, along with a number of other ones reported in the literature, are further discussed below.

Radial metallicity profiles of individual sources have been in fact investigated by many authors using either XMM-*Newton*, *Chandra*, or *Suzaku* (or even earlier with *ROSAT* [48]). This is the case for systems, such as NGC 5044 [74,75], RX J1159+5531 [76,77], AMW 4 [78], HCG 62 [75,79–81], MKW 4 [75,82], NGC 1399 [83–85], and UGC 03957 [86].

The vast majority of these studies show a gradual metallicity increase towards the core of the systems, with the maximum value spanning from half a Solar to slightly super-Solar values. This picture is qualitatively in line with the centrally peaked Fe abundance profiles that are typically found in relaxed clusters (e.g., References [9,52,87–89]). Quantitatively,

samples including groups *and* clusters are valuable to provide comprehensive comparisons. For instance, Johnson et al. [90,91] studied 28 galaxy groups and concluded that (i) systems with lower level of feedback impact are on average more metal rich within ∼0.03*R*500, and (ii) systems classified as "cool-cores"<sup>2</sup> are, on average, more enriched in their cores (∼0.1*R*500) than clusters. Similar conclusions were reached for 43 *Chandra* groups (re-) analyzed by Sun [33], although a significant increase of average metallicity with group temperature (hence, mass) was also reported. More recently, results from the CHEERS sample—consisting of 21 "groups/ellipticals" and 23 "clusters"3—suggest for instance a similar decreasing profile for both types, with the former being on average slightly less enriched than the latter [89]. On the other hand, Lovisari and Reiprich [52] analyzed a sample of 207 systems and concluded that, despite their scatter, on average "groups/ellipticals" (defined in the same way) have a slightly higher metallicity than clusters within 0.1*Rr*500. A recent re-analysis of the CHEERS sample within 0.1*R*<sup>500</sup> using an updated SPEX version (v3.0.4, also more consistent with the apec v3.0.9 version used in Lovisari and Reiprich [52]) find more consistent results, with groups being at least as enriched as clusters within that limit [92]. More detailed discussions and interpretations on the absolute metallicities in groups versus more massive systems is addressed in Section 2.4 (observations) and Section 3.2.1 (cosmological simulations).

In addition, quite remarkably, Figure 4 suggests that the sample-averaged metallicity gradient measured from these different authors all have a similar slope. One notable exception (not shown here) is perhaps the sample of 15 nearby groups observed with *Chandra* by Rasmussen and Ponman [93,94], whose average profile exhibits a significantly sharper central peak (as already pointed outby Reference [33]). This difference might originate from spectral modeling (including outdated atomic data and/or multi-temperature biases), instrumental calibration, or subtle background effects, which were all less understood at that time.

It is worth noting that the metallicity does not always increase with decreasing radius. In fact, for a number of systems, the Fe abundance was found to peak a few kpc outside of the core while *decreasing* towards its very center. Although historically discovered and investigated in the Centaurus cluster [95], these drops are more commonly found in lowermass systems (e.g., References [79,80,89,93,96]). Whether the presence of these drops is truly related to mass of the system (and/or the strength of their cool core) is not clear yet. Indeed, abundance drop detections might be affected by selection biases—originating from either the usually larger distance of clusters (resulting in a poorer spatial resolution, hence no detected drop), or the selection itself of the currently most studied systems.

Such low abundances are in fact surprising and intriguing, as they cannot be easily explained by classical models of IGrM formation and enrichment. Although, in some cases, drops were found to be the result of spectroscopic biases (e.g., multi-temperature bias [97]), no evidence points toward the latter as being the sole explanation. Similarly, resonant scattering seems to be excluded from the culprit list in at least a few specific cases [98], and possible helium sedimentation—leading to an incorrect estimate of the continuum should provide limited effects only, if not largely inhibited by thermal diffusion [99,100] and references therein). Interestingly, however, probing the *chemical composition* in the central low-Fe regions of these systems may provide an interesting hint toward the physical nature of these drops. This is further discussed in Section 2.3.2.

Another important open debate concerns the comparison of clusters' and groups' metallicities in their outskirts (∼*R*<sup>500</sup> and beyond). Whereas there is now striking evidence for clusters having their metallicity flattening with radius and converging toward an universal value of ∼0.3 Solar [9,101,102], groups and elliptical galaxies have sometimes been measured with an uninterrupted decrease of metallicity down to at most 0.1–0.2 Solar (e.g., References [77,84,103,104]). The trend seems to be followed by the sample results of Rasmussen and Ponman [93,94] and of Sun [33]. These results, however, should be interpreted with caution, given how recent atomic codes improvements changed our view on the Fe-L complex, its modeling at moderate resolution, and its associated abundance

(Section 2.1). Moreover, some past measurements may have been affected by the Fe-bias discussed above, as moderate exposures available per source did not necessarily allow to model outer regions with more than one temperature. We note, for instance, that the more recent sample measurements of Mernier et al. [89] and Lovisari and Reiprich [52] show hints of a flattening beyond ∼0.3*R*<sup>500</sup> that remains formally consistent with the 0.3 Solar value reported in clusters (References [9,102]; see Figure 4). These results are in agreement with Thölken et al. [86], who reported that the metallicity profile of the group UGC 03957 does not decrease further below 0.3 Solar, even at distances *beyond R*200. Other measurements, on the other hand, show in-between results, with evidence of a flattening though around 0.2 Solar, i.e., *below* the universal value. This is the case for the galaxy group RX J1159+5531 [77], as well as (perhaps even more intriguingly) for the Virgo cluster [105].

**Figure 4.** Fe abundance radial profiles in various galaxy groups (and clusters) from the literature. (**Left**) The recent average profiles of (Reference Mernier et al. [89], the 21 CHEERS groups) and (Reference Lovisari and Reiprich [52], 13 groups excluding systems overlapping with the CHEERS observations) are compared with those of (Sasaki et al. [75], 4 groups) and (Sun [33] 27 groups—below *kT*<sup>500</sup> = 1.9 keV), as well as with independent measurements of UGC 03957 [86] and RX J1159+5531 (Reference [77], azimuthally averaged). (**Right**) The same two average group profiles are compared with measurements of more massive systems—i.e., the XCOP sample (Reference [9], 12 clusters), the Fe abundance in cluster outskirts (Urban et al. [102], with averaged and single measurements shown, respectively, below and beyond *r*500—also including the outermost Perseus value from Werner et al. [101]), as well as the (azimuthally averaged) profiles of the Virgo cluster [105]. For consistency, the scatter envelope of the samples of Urban et al. [102] and Lovisari and Reiprich [52] have been computed following that of the CHEERS sample Mernier et al. [89]. All measurements have been re-scaled into radial units of *r*<sup>500</sup> (following the values given in the corresponding papers and/or the conversion proposed by Reference [106]) and into Solar units of Asplund et al. [43].

The question of whether groups and clusters have their outskirts enriched at similar levels is of crucial importance. Besides the fact that outskirts represent by far the largest volume of these systems (hence, the bulk of their metal masses), they are direct witnesses of freshly accreted gas through the gravitational potential of these systems and, thus, constitute a fossil record of the enrichment of these systems at their formation epoch. In fact, the (radially *and* azimuthally) uniform metallicity distribution measured in clusters outskirts constitutes by far our best evidence in favor of an "early-enrichment" scenario, in which supermassive black hole feedback played a fundamental role in ejecting and mixing freshly produced metals out of their galaxy hosts during or before their assembly into larger scale structures and the formation of their hot ICM, i.e., at *z* 2–3 (for recent reviews, see, e.g., References [31,107]). Quite remarkably, this redshift range also corresponds to the peak of star formation activity (for a review, see, e.g., Reference [108]), as well as to an epoch of enhanced AGN accretion and activity—not only at cosmic scale (for a review, see, e.g., Reference [109]) but also (and especially) in clusters and groups (e.g., References [110–112]), naturally leading to the picture of their higher feedback to efficiently stir the freshly produced metals. Robust measurements revealing a uniform metal distribution in the IGrM as in the ICM will constitute decisive evidence towards this scenario and its "universal" 0.3 Solar value. On the contrary, significantly lower abundances measured in the IGrM outside ∼*R*<sup>500</sup> would challenge this scenario and would require to rethink our global picture of chemical enrichment at galactic scales and beyond. High resolution spectroscopy coupled to high throughput will be essential to bring our current measurements up to the required accuracy (Section 4).

#### 2.3.2. Chemical Composition and Its Radial Dependence

Since Fe has the strongest emission lines in the IGrM, it typically dominates the abundance measurements reported in the literature. For low-statistics spectra, it is common to assume that the abundances of other elements with respect to Fe follow the Solar ratio. However, important information about the metal enrichment history of the IGrM is encoded in its chemical composition, in particular since the O/Fe, Mg/Fe, and/or Si/Fe ratios are good tracers of the relative contribution of SNcc and SNIa. This relative contribution is expressed in various ways throughout the relevant literature, for example as the ratio between the numbers of different supernova explosions (either *Ncc*/*NIa* or *fIa* = *NIa*/*NIa*+*Ncc*); or as the fraction of Fe supplied by SNIa, *f*Fe,Ia = *NIa* ∗ *yIa*,*Fe*/(*Ncc* ∗ *ycc*,*Fe* + *NIa* ∗ *yIa*,*Fe*), where *ySN*,*<sup>i</sup>* represents the mass of element *i* produced by a supernova of type *SN*. The details of this decomposition depend on the exact model yields *ySN*,*i*, which are subject to remaining uncertainties in stellar astrophysics, and furthermore rely on various assumptions about the initial metallicity and mass function of the supernova progenitors. Nevertheless, the general trend wherein light-*α* elements are almost exclusively produced by SNcc, while Fe-group elements are mainly supplied by SNIa is robust among the current chemical evolution models, lending credibility to this type of analysis.

Back to the *ROSAT* and *ASCA* era, Finoguenov and Ponman [113] reported from a sample of four galaxy groups that SNcc products (i.e., Si and Mg) were found to be more uniformly spread, while SNIa products (namely, Fe) showed a more peaked distribution. These results were naturally interpreted as the bulk of SNcc having exploded, gotten mixed with, and enriched their surroundings earlier than the bulk of SNIa (the latter being more likely to originate from long-lived low-mass star populations in the red-and-dead central dominant galaxy). That interpretation was later supported by Rasmussen and Ponman [93,94] who measured a radial increase of the Si/Fe ratio with *Chandra* observations of 15 groups.

However, these initial conclusions do not appear to have stood the test of time. Some early XMM-*Newton* data already provided results that conflicted with the initial paradigm of a relatively uniform *α*-element and peaked Fe distribution in the IGrM: no gradient in Si/Fe was seen in NGC5044, comparing the regions within and beyond 48 kpc from the BGG [74]; a constant and close to Solar *α*/Fe out to at least 100 kpc was reported in NGC507 [114]; and Xue et al. [115] found that *all* measured abundances (O, Mg, Si, S, and Fe) in the group RGH80 showed a monotonic decrease with radius. In all these three cases, *f*Fe,Ia was inferred to be in the range of 70–85%, assuming a model consisting of simple linear combinations of SNIa and SNcc. Therefore, although most Fe is being supplied indeed by SNIa, there did not appear to be a significant change in *f*Fe,Ia with radius, or from system to system. Similar conclusions were starting to be reached in galaxy clusters, as well (e.g., Reference [72,97,116,117]).

The low instrumental background of *Suzaku*, and the superior low-energy response of the XIS CCDs particularly in the first few years after launch, shed additional light on this topic: the radial profiles of Mg/Fe, Si/Fe, and S/Fe were consistently shown to remain uniform (i.e., all four elements showed a radially decreasing profile) in HCG 62 [118], NGC 5044 [119], NGC 507 [120], and NGC 1550 [121] over the entire area probed by the *Suzaku* observations. A sample of 4 groups consisting of MKW4, HCG62, NGC1550, and NGC5044, was covered by *Suzaku* out to as far as 0.5 *r*180, confirming that the Mg/Fe and Si/Fe ratios remain nearly constant and close to the Solar ratio (assuming the units of Reference [122]) out to a significant fraction of the virial radius [75]. All these measurements are consistent with an *Ncc*/*NIa* of 3–4 [119,121,123]. For the supernova yields assumed in these works, *Ncc*/*NIa* = 3 corresponds to a *f*Fe,Ia of 80%, in line with the XMM-*Newton* results discussed in the previous paragraph. A point of contention in the *Suzaku* results remained the O abundance, that seemed to have much shallower radial gradients than all other *α*-elements (a conclusion shared by all references mentioned earlier in this paragraph). This would imply increasing O/Mg and O/Si ratios as a function of radius; since all these three elements are predominantly produced by SNcc, it is impossible to reconcile these measurements with a simple model where the relative contribution from SNIa and SNcc varies with distance from the BGG. It is likely that residuals in modeling the Galactic absorption and/or OVIII foreground emission, or issues related to Solar Wind Charge Exchange (whose strongest emission also comes from O), may have affected the measurements.

More recently, results from the XMM-*Newton* CHEERS sample reported similar radial distributions of the O, Mg, Si, S, Ar, Ca, and Fe abundances in clusters *and* groups separately. While the covered radial range does not extend as far as that from *Suzaku* studies, the agreement between the radial trends of all measured elemental abundances, together with the larger sample size, provides solid and cohesive evidence for a lack of significant spatial variation of the SNcc versus SNIa contributions to the enrichment across the mass scale [89].

With the latest advancements in our knowledge of spectral modeling, multi-temperature biases, and/or instrumental calibration, current measurements, thus, favor a uniform chemical composition over the entire volume of clusters and groups, as early suggested for the cores of both systems (and ellipticals) by de Grandi and Molendi [124]. Interestingly, in both regimes the chemical composition is also remarkably close to that of our own Solar System. Indeed, *Hitomi* confirmed that all the investigated X/Fe ratios of the Perseus Cluster are consistent with Solar at very high precision [125,126] and detailed investigations of the CHEERS sample found the same trend for groups and ellipticals, as well [127,128]. This is further illustrated in Figure 5, where we compiled the average chemical composition of the 21 CHEERS low-mass systems.

It is worth noting that the chemical composition of the ICM/IGrM must, therefore, be markedly different than that of the stars in the BCG/BGG: as shown by References [129,130], massive early-type galaxies (ETGs) with a velocity dispersion above 200 km/s typically have high *α*/Fe ratios up to twice the Solar value, which is inconsistent with the abundance pattern of the hot diffuse gas in their immediate vicinity (see Figure 5). High values of *α*/Fe are usually associated with a very short starburst: BCG/BGGs may have made most of their stars before SNIa had time to explode, so that very few Fe-group elements are incorporated into the stars themselves. Nearly all SNIa later polluted the central ICM/IGrM instead, gradually lowering its *α*/Fe ratios.

But although the SNIa contribution cannot have come too quickly (else the stars in the central galaxy would not have such a high *α*/Fe), it also cannot have happened too slowly, or else the observed radial distribution of Fe should follow the present-day stellar light, which is not observed (Section 2.4). A significant late-time input of SNIa products would also modify the radial trends of *α*/Fe in the ICM/IGrM, contradicting the constant near-Solar *α*/Fe ratios measured throughout the volumes of clusters and groups.

This suggests that most (if not all) SNIa contributing to the enrichment exploded not much later than the peak of cosmic star formation (*z* 2–3 [108]). Several studies of the SNIa delay-time distribution in fact support this picture, finding that a significant number of such explosions occur as early as 100 Myr after a star formation event (Totani et al. [131], Maoz et al. [132]; for a review on SNIa delay-time distribution and its interpretations, see Maoz et al. [133]).

**Figure 5.** Average chemical composition (expressed as X/Fe abundance ratios in units of Reference [43]) within the central 0.05*r*<sup>500</sup> of the 21 galaxy groups and massive ellipticals from the CHEERS sample (defined as *kT*mean < 1.7 keV). The O/Fe and Ne/Fe ratios (including their intrinsic scatter) were measured using the XMM-*Newton* RGS instruments, while the other ratios are measured using the XMM-*Newton* EPIC MOS and pn instruments. To be conservative, the EPIC "combined" measurements cover the entire MOS-pn discrepancies, which fully accounts for the intrinsic scatter, as well. Comparison with the average chemical composition of clusters shows values that are similar and near-Solar in both regimes. For comparison, Solar uncertainties are also shown, as well as stellar abundances in ETGs measured for different bins of stellar velocity dispersion *σ* [129]. Adapted from Mernier et al. [128].

Nevertheless, the confirmation (or rejection) of this new paradigm will be crucial to achieve with future missions. Metal abundances determined with CCD spectrometers in clusters of galaxies are still subject to systematic uncertainties in the range of ∼20% [124,126]; given the still ongoing challenge to derive accurate abundances from unresolved line complexes, these uncertainties may be even more important for the IGrM. Ultimately, the stellar population histories of typical central dominant galaxies are fundamentally different from that of the Milky Way. Future measurements using high-resolution spectroscopy will reach percent-level accuracy in determining the abundance of numerous chemical elements in gaseous halos of varying mass; it would be nothing short of a stunning cosmic conspiracy if, as smaller and smaller spatial scales start to be probed at such a level of precision, the central abundances in groups and clusters remain in agreement with the Solar composition.

Besides quantifying the relative contribution of SNIa and SNcc to the enrichment of the IGrM, elemental abundance ratios may also reveal the nature of the so far unexplained abundance drops that are sometimes observed (see Section 2.3.1) in the very inner centers of groups and clusters. Under the assumption that these abundance drops have an astrophysical origin, an interesting scenario proposed by Panagoulia et al. [80,134] considers that IGrM-phase metals may deplete into dust and then become invisible to the X-ray window. As a second step, AGN jets and buoyantly rising bubbles may contribute to move this dust mass away, before eventually re-heating it to the X-ray phase outside of

the very core. If true, an interesting corollary of this scenario concerns the Ne and Ar abundance. As these two elements are noble gases, they cannot be incorporated into dust; hence, they should *not* exhibit any central decrease. Although a few authors have investigated this issue [89,135,136], no real consensus is established yet given the sensitivity of the measurements to systematic effects. Ar and Ne lines should be easily measurable with future micro-calorimeters (Section 4). Provided that atomic codes continue to converge (Section 2.1) in the years to come, *Athena* (and possibly *XRISM* for very nearby systems) will provide a definitive answer to this question.

Clarifying these outstanding issues will allow us to identify which combinations of theoretical supernova yield models, *ySN*,*i*, provide the best fit to the observations of the ICM and IGrM (avoiding regions affected by dust depletion if applicable), offering important clues about open aspects of stellar astrophysics. For instance, it was realized very early on that abundance ratios measured from X-ray spectra of the ICM could be used to distinguish between various SNIa explosion mechanisms, preferring a deflagration over a delayed detonation model [137]. Similar conclusions were tentatively reached for the IGrM [74,123]. It is becoming clear, however, that both an improvement in the data quality and increased accuracy in the yield models are necessary before robust conclusions can be drawn (de Grandi and Molendi [124], Mernier et al. [138], Hitomi Collaboration [125], Simionescu et al. [126]; for a review, see Mernier et al. [31]). Significant progress is expected to be driven in this sense by upcoming high-resolution X-ray spectroscopy studies.

#### 2.3.3. 2-Dimensional Metallicity Maps

In addition to the radial dependence of the metal abundances, important information can be inferred also from the azimuthal substructure revealed by 2D maps; typically, these are of course only available for very deep observations of the brightest systems. Early work by Finoguenov et al. [139] presented a systematic analysis of the metallicity distribution in NGC5846, NGC4636, and NGC5044 using XMM-*Newton*. It was shown that, while the profiles are consistent with a linear decrease with radius, the scatter of the data points was as high as 30–50%. This pointed towards a patchiness of the 2D metal abundance using typical spatial resolution elements of 2–10 kpc, which cannot be explained solely by the satellite subhalos. Later studies revealed that, very generally speaking, the main physical mechanisms responsible for such a 2D metallicity substructure are related either to AGN feedback or to ongoing mergers.

In terms of AGN feedback, in the case of clusters of galaxies, it is now well established that the buoyantly rising bubbles produced by the activity of the supermassive black hole in the BCG are able to uplift metals in their wake, leading to an abundance enhancement along the axis corresponding to the radio jets compared to the perpendicular direction [72,140–142]. Given the shallower gravitational potential wells of galaxy groups, one might expect this effect to be even more pronounced, and even more important for the physical evolution of the IGrM, as metals produced in the BGG may even escape the group halo through the action of the AGN. However, to our knowledge, a systematic study of the metal asymmetry in groups (i.e., an equivalent to the sample study of References [141,142] which focused primarily on galaxy clusters) is still lacking. The main impediment is likely related to the fact that the region of uplift is also generally expected to be multi-phase (see, especially, Reference [140]) which, as discussed in Section 2.1, significantly complicates the determination of an exact Fe budget in a given spatial region.

Nonetheless, hints that the relativistic radio lobes of the central AGN do have an impact on the metallicity distribution in groups have been obtained in a few objects. Perhaps the clearest example so far is that of AWM 4, where O'Sullivan et al. [143] found a metal enhancement along the inner jet of the central dominant galaxy, NGC6051, corresponding to an excess mass of iron in the entrained gas of <sup>∼</sup>1.4 <sup>×</sup> 106 <sup>M</sup>. Another case is that of NGC4636, where O'Sullivan et al. [144] report a plume of cool, metal-rich gas extending beyond a known AGN lobe to the southwest of the galaxy center, and interpret this to be the product of metal entrainment by past AGN activity. Less clear is the scenario in NGC4325; here Laganá et al. [145] reported an elongated Fe-rich filament to the south/southeast of the central galaxy which could be due to metal entrainment by the AGN; however, no X-ray cavity is found in this system that would confirm this interpretation. Finally, there are the interesting examples of rather clearly detected *anti*correlations, i.e., a low metallicity corresponding to the radio lobes in NGC5813 [146] and inner radio lobes of M49 [96]—although, in both cases, only a single-temperature fit was used to create the 2D maps; hence, the Fe bias may be the reason for these results.

Mergers on the other hand typically result in tails and arcs of enhanced metallicity in the IGrM, depending on the merger stage and geometry. In a simple case where a subgroup is falling towards a larger cluster of galaxies, a ram-pressure stripped tail exhibiting an orderly head-tail morphology is often seen; as metals are stripped from the central group galaxy, the elemental abundances in this tail are expected to be higher than those of the surrounding diffuse medium. This has been confirmed by X-ray spectral mapping of the metallicity in a handful of cases. One of the clearest examples is that of the M86 group falling into the Virgo Cluster; this is a very rare case where a metal abundance map from a *twotemperature* model is available for the IGrM [147], showing a long, 100–150 kpc tail of near-Solar abundance (in units of Grevesse and Sauval [148]) trailing M86. The abundance in the ram-pressure stripped tail is about twice higher than the off-tail regions, demonstrating how infalling groups contribute to the metal budgets of the ICM. Another remarkable system is the northeastern group falling into Abell 2142, which exhibits a long, straight, narrow tail that flares out after about 300 kpc from the BGG. The metallicity map published in Eckert et al. [149] shows a significant enrichment along most of the narrow tail, with the transition between the straight tail and the irregular diffuse tail corresponding to a marked abundance drop. Recent spectral maps by O'Sullivan et al. [150] also show tails of cooler, lower entropy, metal-enriched gas behind both cores in a group-group (as opposed to group-cluster) merger in NGC 6338.

In later merger stages, after the first pericenter passage of the sub- and main halo, internal gas sloshing or tidal (also known as 'slingshot') tails [151,152] can instead be recognized as arc-shaped high metallicity 'fronts'. Internal gas sloshing is likely responsible for the high abundance arc in HCG 62 [79,81,153,154] and for the abundance map asymmetry in NGC5044 [155]; although no 2D metal abundance map is available, radial profiles of an azimuthally resolved wedge in the NGC 7618–UGC 12491 pair [156] suggest a metal enhancement that was originally attributed to ram-pressure stripping but later recognized as rather due to a slingshot tail [152].

Of course, mergers and AGN feedback can work in unison. For instance, in M49, the 2D Fe abundance map derived by Su et al. [157] using XMM-Newton (covering a significantly larger field than that in Reference [96] discussed above) suggests both the presence of a metal enriched tail to the southwest, and a metal enhancement aligned with two outer ghost X-ray cavities along the NE-SW axis on smaller spatial scales (see Figure 6). The authors conclude that the tail gas can be traced back to the cooler and enriched gas uplifted from the BGG center by buoyant bubbles, implying that active galactic nucleus outbursts may have intensified the stripping process. On the other hand, Sheardown et al. [152] argue instead that M49 may host a slingshot rather than a rampressure tail. A similar case may be that of NGC507; again, no 2D metal abundance map is available, but Kraft et al. [158] report a gradient in the elemental abundance across a sharp arc-like X-ray surface brightness discontinuity with opening angle of 125 deg. Because that discontinuity is aligned with a low surface brightness radio lobe, the authors conclude that this 'abundance front' can be explained by the transport of high-abundance material from the center of the galaxy due to the transonic inflation of the radio lobe; however, it was subsequently realized (e.g. see previous paragraph) that classical cold fronts are likely to produce such abundance arcs as well. The abundance feature in NGC507 is therefore not unusual and could be simply due to classical sloshing, or to an interaction between AGN feedback and past merging activity.

**Figure 6.** XMM-*Newton* spectroscopic map of the Fe abundance in M49 in units of the Solar abundance of Reference [43], derived assuming a single temperature model. X-ray contours in the 0.7–1.3 keV energy band are overlaid in black. The Fe distribution is elongated in the direction of the AGN ghost cavities (denoted by white dashed circles), with an additional extension towards the west/southwest on larger scales, likely related to a ram-pressure or slingshot tail as the galaxy is falling into the Virgo Cluster. Figure reproduced with permission from Reference [157].

#### *2.4. Metal Budgets*

In the previous sections, we reviewed the measurements of the abundances probing a fraction of the IGrM volume. As pointed out early by Arnaud et al. [159], the physically meaningful quantity for the study of the IGrM (and of the ICM) are the metal (iron or other chemical elements) mass and stellar mass present in the groups (and clusters). The ratio of the iron mass and stellar mass is directly linked to a fundamental quantity in chemical evolution models, the iron (or other chemical elements when measured) yield which is the ratio of the total iron mass released by stars to the total stellar mass formed for a given stellar population (see References [8,9,160] and references therein):

$$\mathcal{Y}\_{\text{Fe}} = \frac{M\_{\text{Fe,SO}0}^{\text{star}} + M\_{\text{Fe,500}}}{M\_{\text{star,500}}(0)},\tag{1}$$

where *M*Fe,500 is the iron mass enclosed within *r*<sup>500</sup> in the ICM/IGrM, *M*star Fe,500 is the iron mass locked into stars, *M*star,500(0) is the mass of gas that went into stars whose present mass is reduced to *M*star,500 by the mass return from stellar mass loss, i.e., *M*star,500(0) = *roM*star,500, where *ro* is the return factor. We take *ro* = 1/0.58 following Renzini and Andreon [8] and Maraston [161]. A caveat should be made that the iron yield can be matched to a theoretical prediction only if we are able to make a full inventory under the assumption of a closed

system. If iron can leave the system or just does not reside within the radius used to make the estimate, we cannot draw a conclusive inference. This is particularly the case at the scale of groups as we discuss further in this section.

One can then measure *M*Fe,500 either by multiplying a representative deprojected gas-mass weighted iron abundance times the total gas mass of the system within *r*<sup>500</sup> [8] or by taking fully into account the radial dependence of the deprojected iron abundance and gas mass [9,162]:

$$M\_{\rm Fe}(<\mathcal{R}) = 4\pi A\_{\rm Fe} m\_{\rm HI} Z\_{\odot} \int\_{0}^{R} Z\_{\rm depro}(r) \, n\_{\rm H}(r) \, r^{2} dr,\tag{2}$$

where *Z*depro is the deprojected abundance profile, *A*Fe is the atomic weight of iron, and *m*<sup>H</sup> is the atomic unit mass. The hydrogen density *n*<sup>H</sup> is derived from the gas density *n*gas through the usual relation *n*gas = (1 + *ne*/*n*H)*n*<sup>H</sup> = 2.21*n*H, where *ne* is the electron density; *n*gas is obtained through deprojection. In the latter case *M*Fe,500 = *M*Fe(< *r*500). For the measurement of *M*star Fe,500 it is usually assumed that the average iron abundance in clusters and groups stars is solar (for the validity and limitations of this assumption, see, for example, Reference [163] and references therein). This iron abundance of the stars is then multiplied by the total stellar mass enclosed within *r*500. The latter value can again be estimated through two approaches. The first one performs a flux measurement for each galaxy in a given optical band and calculates the mass of the galaxy through the Spectral Energy Distribution (SED) fitting, the mass of the galaxies are then summed together [9,164]. The second approach calculates the total luminosity in a given optical band by integrating the luminosity function of the red cluster galaxies, summing the contribution of the BCG and possibly of ICL and then multiply for an assumed stellar-mass-to-light ratio in the same optical band (see, for example, Reference [8] and references therein). Both quantities are deprojected assuming a generalized or a simple Navarro-Frenk-White (NFW) distribution for the galaxy and optical light distribution. These observational estimates can be compared with the expected theoretical estimate based on the current understanding of stellar nucleosynthesis. We take the values reported in Ghizzardi et al. [9] for the YFe based on the derivation by Renzini and Andreon [8] and Maoz and Graur [165]. YFe is computed as the product of the Fe mass produced by a SN explosion, *y*, and the number of SN events produced per unit mass of gas turned into stars, *k*. Both contributions from Ia and CC SN are considered. Thus, YFe can be written as:

$$
\mathcal{Y}\_{\text{Fe}} = y\_{\text{la}} \cdot k\_{\text{la}} + y\_{\text{CC}} \cdot k\_{\text{CC}'} \tag{3}
$$

where Ia and CC subscripts refer to the two different SN types. For Ia, we assume *<sup>y</sup>*Ia <sup>=</sup> 0.7 *<sup>M</sup>* and *<sup>k</sup>*Ia <sup>=</sup> 1.3 <sup>×</sup> <sup>10</sup>−<sup>3</sup> *<sup>M</sup>*−<sup>1</sup> . Renzini and Andreon [8], as well as Greggio and Renzini [166], suggest a possible higher *<sup>k</sup>*Ia value of 2.5 <sup>×</sup> <sup>10</sup>−<sup>3</sup> *<sup>M</sup>*−<sup>1</sup> . For CC SN we assume *<sup>y</sup>*CC <sup>=</sup> 0.074 *<sup>M</sup>* and *<sup>k</sup>*CC <sup>=</sup> 1.0 <sup>×</sup> <sup>10</sup>−<sup>2</sup> *<sup>M</sup>*−<sup>1</sup> . Substituting the above values in Equation (3) and dividing by the solar abundance we get YFe, = 0.93 *Z*. An higher estimate can be obtained by assuming that SNIa rate is higher in clusters with respect to the field [165,167,168]. If, following Freundlich and Maoz [168], we assume a SNIa rate per unit mass of *<sup>k</sup>*Ia <sup>=</sup> 3.1 <sup>±</sup> 1.1 <sup>×</sup> <sup>10</sup>−<sup>3</sup> *<sup>M</sup>*−<sup>1</sup> , we derive <sup>Y</sup>Fe, <sup>=</sup> 2.34 <sup>±</sup> 0.62 *<sup>Z</sup>*.

We report in Figure 7 the effective iron yield for the sample of clusters studied in Ghizzardi et al. [9], for the sample of groups studied in Renzini and Andreon [8] with iron abundance measurements in the IGrM derived by Sun [33] and for the objects in Sasaki et al. [75]. This plot seems to show apparently that for groups there is no discrepancy with the theoretical expectations as it is dramatically the case at the cluster scale. The large amount of intra-cluster iron is difficult to reconcile with the metal production of stars seen in clusters today and it is posing a long standing challenge, with several unconventional solutions proposed, such as a very different IMF in clusters or a significant contribution by pop III stars or pair-instability supernovae (see the review by Reference [31] and references therein). However, these results should be treated with caution as not only the measurement of YFe, is prone to systematic errors (see the exhaustive discussion in Reference [9]) but also the different trends of stellar and gas mass as a function of total mass play a fundamental role. In particular, the low baryonic fraction of groups within *r*<sup>500</sup> with respect to the cosmic baryon fraction does not allow to draw strong conclusions. Clearly, this plot should be more populated, particularly at the mass scale of groups with robust measurements of the iron abundance consistently out to *r*500.

**Figure 7.** Effective iron yield YFe, for the clusters in the sample of Ghizzardi et al. [9] (circles), for the groups in the sample of Renzini and Andreon [8] (squares) and for the additional objects (NGC 1550, MKW 4, Hydra A, Perseus, and Coma in order of increasing mass) in the sample of Sasaki et al. [75] (triangles) as a function of the total mass of the system. We estimated stellar masses for the objects of Sasaki et al. [75] converting their *LK* optical luminosities to stellar masses, assuming a stellar mass-to-light ratio in the K-band of 1 consistent with stellar population models for a Kroupa IMF [161] and with observational results [169–171]. The yellow band shows the expected value computed through the SN yields derived from Maoz and Graur [165] and Renzini and Andreon [8]; the brown band represents the expected value derived assuming a higher SNIa rate in galaxy clusters than in the field, following Freundlich and Maoz [168].

Indeed, both the iron abundance and to a lesser extent the total iron mass in the IGrM do not depend only on the total amount of iron produced, but also on its dilution with pristine gas, its ejection due to non-gravitational feedback by AGN and SN and the different phases in the gas. All these effects should be taken into account (e.g., Reference [172]).

Another related quantity exploits directly the luminosity of the system either in the optical (B) or infrared (K) bands: it is the ratio of the iron mass to the total light of the cluster/group (IMLR [62,173]). If different metals in addition to iron are measured then the specific element MLR can be estimated, like, for example, O and Si MLRs. These quantities are even more important to consider given the trends of stellar and gas fractions (and their sum, the baryon fraction) as a function of total mass which clearly mark the scale of groups as a crucial one in comparison with clusters. The derived baryon fraction for rich clusters is consistent with the cosmic baryon fraction, Ω*b*/Ω*<sup>M</sup>* ∼ 0.15 [174] as obtained with X-ray, optical and infra-red observations (e.g., References [175–181]; also see the companion reviews by Lovisari et al. and Eckert et al.) On the other hand, groups are characterized by higher stellar mass and lower IGrM mass fractions than rich clusters, and the number of baryon fraction tends to be lower with smaller groups (e.g., References [8,182–184]). Explanations of this discrepancy are suggested in the above references as follows: 1. different physical

processes depending on the system mass, like, for example, a different efficiency of baryonto-stars conversion; 2. observational data missing for fainter sources (as, for example, the intra-cluster light component) and for the IGRM at large radii; 3. systematic errors for the mass estimations; 4. non-gravitational heating and metal mixing by AGN feed back (e.g., Reference [172,185]; see Eckert et al.), but a definitive solution has not been reached yet. As for the non-gravitational effect, such as AGN feedback, the entropy profiles are a good probe to estimate for each group and cluster, and we describe it in the following paragraph.

Historically, Arnaud et al. [159] found that the total iron mass in the ICM is proportional to the total luminosity of the early type galaxies in the clusters. And the IMLR in the B-band had larger values in clusters than in groups, mainly caused by the biased low early global abundance measurements (see Section 2.2) at the group scale (e.g., References [186,187]). The current state of the art of measurements of the IMLRs is achieved by combining near-infrared (K-band) luminosities (more directly related to the bulk of the stellar mass in early type galaxies [171,188]) obtained with the two micron all sky survey (2MASS) and the measurements performed by Suzaku extending to the outer regions of nearby clusters and groups (e.g., References [120,121,189]). Figure 8 reports the IMLRs thus obtained: there is a general increase with radius and poorer clusters and groups also have lower IMLRs within the 0.2 *r*<sup>180</sup> region. On the other hand, the IMLRs of groups and clusters in the outer region at *r* > 0.5 *r*<sup>180</sup> seem to be closer to each other. Figure 8 suggests that poorer systems (groups and clusters with fewer member galaxies) could not hold the gas including metals due to the relatively shallower potential in their assembly process. In a following work, Sasaki et al. [75] showed that the same systems have lower IMLRs and larger entropy excess, which is a signature of the non-gravitational energy input in the central regions of groups during the assembly stage.

**Figure 8.** (**Left**) Radial IMLR profiles with Suzaku X-ray observations and K-band luminosity of the member galaxies from 2MASS data [75,120,121,189–191]. (**Right**) Temperature dependence of the IMLRs for groups and clusters in 0.2 or 0.5 *r*<sup>180</sup> with Suzaku.

Abundance ratios of silicon to iron in clusters and groups look similar to each other in *r* < *r*<sup>500</sup> (see Section 2.3.2), and the silicon mass in poorer systems has a lower value than those in larger systems (the same trend as for the iron mass, caused by the lower gas mass). Because significant fractions of oxygen and silicon are mainly synthesized by SNcc, they are good indicators to estimate the amount of massive stars in the past. Renzini [192] calculated the oxygen and silicon MLRs under the assumption of the Salpeter initial mass function with the slope of the power-law shape to be −2.35. If we assumed the silicon to iron abundance ratios to be ∼1 up to the virial radius (e.g., References [89,189]), the expected silicon mass to light ratios (SiMLR) in rich clusters agree with the estimate derived by Renzini [192], as shown in Matsushita et al. [189] and Sasaki et al. (2021). However, for groups, neither iron nor silicon have been observed yet out to and beyond *r*<sup>500</sup> with the exception of a handful of systems. To study the metal enrichment history of the ICM and IGrM, we need to measure oxygen profile, mainly produced by SNcc, to the virial radius and beyond since the whole clusters and group include the metals synthesized in the cluster and group formation phase. To summarize, in order to progress in the understanding of the chemical enrichment of both groups and clusters, we need to measure the gas and metal MLRs to the virial radius for both clusters and groups to high redshift of *z* ∼ 2 with the next generation of X-ray instruments (see Section 4).

#### *2.5. High Resolution Spectroscopy: Current Observational Results with RGS*

Undoubtedly, the need for high spectral resolution (particularly the capability to resolve the Fe-L complex) is absolutely crucial to provide accurate constraints on chemical abundances (and the physics of the enrichment) in groups and elliptical galaxies. While waiting for the exploitation of micro-calorimeters onboard *XRISM* and *Athena*, one should keep in mind the valuable potential of the Reflection Grating Spectrometer (RGS) instrument onboard XMM-*Newton* to deliver high resolution spectra. Formally, the RGS has a spectral resolution of ∼3 eV. In the case of extended sources, however, the slit-less characteristic of this instrument induces a convolution of a given line profile with the spatial distribution of its surface brightness along the dispersion direction of the detector. Although this makes the RGS abundance measurements of extended clusters rather challenging (yet still feasible, e.g., Reference [126]), groups are by definition more compact and are less affected by this instrumental broadening. The spectral window of the instrument (typically <sup>∼</sup>6–30 A˚ , corresponding to <sup>∼</sup>0.4–2 keV) is both an advantage—as it covers the O VIII (and O VII), N VII, and even C VI lines which are difficult or impossible to detect with CCD instrumental responses—and a drawback—as the continuum is challenging to constrain within this band. Consequently, the power of RGS resides less in the measurements of the IGrM absolute abundances than in the measurements of their (relative) N/Fe, O/Fe, Ne/Fe, and Mg/Fe ratios. Although discrepancies of absolute Fe measurements between RGS and CCD-like instruments may in principle lead to discrepancies in their respective X/Fe ratios, we note a generally good agreement in the latter case (e.g., Reference [127]).

Abundances measured using RGS have been, for instance, reported on individual poor systems [193–195], as well as in larger samples [196–198]. The CHEERS sample, which was constructed specifically to ensure a >5*σ* detection of the O VIII line in each system, provided interesting measurements in this respect. Mao et al. [199] obtained reliable constraints (>3*σ*) on the N/Fe ratio in six galaxies (M 49, NGC 4636, NGC 4649) and groups (NGC 5044, NGC 5813, and NGC 5846), as well as in M 87 and one cluster (A 3526). Unlike all the other ratios known in the IGrM which are typically close to Solar (Section 2.3.2 and Figure 5), the average N/Fe is clearly super-Solar. This strongly suggests that the bulk of nitrogen originates from an enrichment channel that is separate from the usual SNcc and SNIa contributions—very likely AGB stars. The O/Fe ratio was investigated (in groups and ellipticals, but also in more massive systems) by de Plaa et al. [200], and was found to be consistent with Solar, thus being in line with the picture of the hot gas chemical composition remaining uniform with mass (Section 2.3.2), despite a significant scatter from system to system.

Despite the valuable ability of RGS to measure accurately important ratios (particularly N/Fe and O/Fe, see Figure 9), its limited spectral window—coupled to its sensitivity to the spatial extent of the source and the difficulty to perform spatial spectroscopy (see, however, Reference [201,202])—makes this instrument taken at its best advantage when combined with CCD measurements. Nevertheless, RGS offers the unique advantage to reveal a glimpse of the main transitions populating the Fe-L complex at groups (and clusters) temperature regime(s). This is particularly essential, not only to refine our science prediction expected with micro-calorimeter instruments, like Resolve onboard *XRISM* (Section 4.2), but also to pursue the improvement of our spectral models in this crucial spectral band

even before the release of *XRISM*, particularly by comparing updated atomic calculations with (i) laboratory measurements and (ii) state-of-the-art observational data [203,204].

**Figure 9.** An example of RGS spectrum from a deep observation of NGC 5846, with indication of its main emission lines (and the stellar origin of their corresponding element). Spectra from the RGS 1 and RGS 2 instruments were combined before successive fits assuming models with one temperature (1 CIE), two temperatures (2 CIE), and a Gaussian-like multi-temperature structure (GDEM). Residuals are shown in the right panels. Figure reproduced with permission from de Plaa et al. [200].

#### **3. Theoretical Framework and Simulations**

#### *3.1. High-Resolution Hydrodynamical Simulations and Small-Scale Astrophysics*

While Section 3.2 focuses on the large-scale metal origins and evolution from the high-*z* universe via cosmological particle simulations, here we discuss the metal abundance evolution in terms of small-scale (astro)physics and tracer advection by means of highresolution (HR) hydrodynamical (HD) grid simulations in single halos. Resolutions in such simulations can reach down to the pc scale and often employ adaptive/static mesh refinement, together with finite-volume Godunov methods with third-order (or higher) accuracy. Given the high resolution (and small timesteps), such simulations are mainly focusing on the cores of galaxy groups (*r* < 0.1 *R*500) and are well suited to track the turbulence mixing, shocks, entrainment, and detailed feedback/feeding imprints, such as AGN cavities and thermal instabilities. We note that, in this section, Section 3.1, we take a more physically-oriented approach, rather than following an historical sequence.

Before tackling typical HD simulation results, it is worth to review a few common physical and numerical properties of metals leveraged by investigations of different groups. A key small-scale feature of metals is that they are passive tracers of the hydrodynamical evolution; thus, they can be used akin to dyes/pollutants in fluid dynamics studies (e.g., Reference [205]). In hydrodynamics (e.g., Reference [206]), the equation describing the temporal rate of change of the metal tracer density is given by (in the Eulerian/grid framework):

$$\frac{\partial \rho\_Z}{\partial t} + \nabla \cdot (\rho\_Z \mathbf{v}) = \mathbf{S}\_{Z, \prime} \tag{4}$$

where *SZ* is a general metal abundance source term; in Equation (6) and the related paragraph below, we will unpack such a source term, which, in the IGrM, is mainly shaped by stellar feedback processes, such as supernovae and stellar winds. In fluid dynamics, Equation (4) is also known as a conservation equation. In the weak compressibility case, the metals are purely advected along the Lagrangian stream, reducing Equation (4) to

$$\frac{d\rho\_Z}{dt} \equiv \frac{\partial \rho\_Z}{\partial t} + \mathbf{v} \cdot \nabla \rho\_Z = \mathbf{S}\_Z. \tag{5}$$

We note that, in localized IGrM regions with *∇ · v* <sup>=</sup> 0, the pollutants may also experience compressions or rarefactions, hence tracing not only smooth bulk processes (subsonic turbulent eddies) but also nonlinear in-situ features (shocks and cold fronts). In the HD grid simulations, such iron density is implemented via a normalized scalar *Z* ∈ [0, 1] tied to each cell gas density, such as *ρ<sup>Z</sup>* = *Z ρ* (see Reference [207]). Ought to high-order Godunov schemes, such as the Piecewise-Parabolic Method (PPM; Colella and Woodward [208]), numerical diffusion is kept at low levels compared with physical diffusion, e.g., due to turbulence. Further, despite the large diversity of elements, IGrM HR numerical studies often use the approximation *Z* ≈ *Z*Fe, since iron has one of the strongest line emissions among heavy elements—especially in hot plasma halos—which can be robustly constrained via X-ray spectra (Section 2). We note that, while metals are a dynamical passive tracer, they contribute significantly to the line cooling of the gas below *T* < 1 keV (e.g., Reference [209]), hence accelerating the IGrM condensation cascade.

Typical HR HD simulations focus on the group core, where the central galaxy contributes to a substantial amount of metals later dispersed in the diffuse IGrM, which are mainly produced via supernovae (SN) explosions and winds from red giant stars (SWs). An exemplary and well modeled system is the nearby galaxy group NGC 5044, with the homonymous central galaxy dominating over the many smaller satellites. In several ETGs/BGGs analytic studies and non-cosmological HD simulations (e.g., Loewenstein and Mathews [210], Ciotti et al. [173], Renzini and Ciotti [62], Brighenti and Mathews [211], Brighenti and Mathews [212], Mathews and Brighenti [213], Gaspari et al. [214], Gaspari et al. [215], Pellegrini et al. [216]), a common implementation of Equation (5) is to recast it in terms of the astrophysical IGrM abundance of the *i*th-element (by mass in Solar unit):

$$\frac{dZ\_i}{dt} = \left(\underbrace{N\_\*\,a\_\*}\_{\text{stellar wirds}} + \underbrace{N\_{\text{SN}}\,a\_{\text{SN}}}\_{\text{supernovae}}\right)\frac{\rho\_\*}{\rho}\,'\,\tag{6}$$

where the two normalization factors related to stellar winds and supernovae are, respectively, *N*<sup>∗</sup> = *Z*∗,*<sup>i</sup>* − *Zi* (with *Z*∗,*<sup>i</sup>* the stellar abundance) and *N*SN = *y*SN,*i*/(*Zi*,*M*SN) (with *y*SN,*<sup>i</sup>* the SN yield in *M* and *M*SN the ejected supernova mass). The BGG stellar density *ρ*<sup>∗</sup> is usually modeled via a de Vaucoulers profile [217]. The specific injection rates due to SWs and SN are *<sup>α</sup>*<sup>∗</sup> <sup>≈</sup> 4.7 <sup>×</sup> <sup>10</sup>−20(*t*/*t*now)−1.3 <sup>s</sup>−<sup>1</sup> and *<sup>α</sup>*SN 3.2 <sup>×</sup> <sup>10</sup>−<sup>20</sup> *<sup>r</sup>*SN(*t*)(*M*SN/*M*) <sup>Υ</sup>−<sup>1</sup> *<sup>B</sup>* <sup>s</sup><sup>−</sup>1, where Υ−<sup>1</sup> *<sup>B</sup>* is the optical stellar mass-to-light ratio in the B band (e.g., References [213,218–220]), respectively. As introduced above, iron is one of the best metals to leverage as dynamical tracer in HR simulations: in BGGs/ETGs (which have star-formation histories peaked at early times) SNII are mostly consumed at high redshifts, while SNIa—exploding in binary systems with a white dwarf—drive the BGG long-term iron enrichment. The local SNIa rate is *<sup>r</sup>*SNIa <sup>∼</sup> 0.1(*t*/*t*now)−1.1 SNU (per 100 year and stellar luminosity 1010 *<sup>L</sup>*B,, e.g., Greggio [218], Mannucci et al. [219], Humphrey and Buote [220]). The iron normalization values for the SNIa (*M*SNIa = 1.4 *M*) are *y*SNIa,Fe = 0.7 *M* ∼ 10 *y*SNII,Fe and *<sup>Z</sup>*Fe, <sup>=</sup> 1.83 <sup>×</sup> <sup>10</sup><sup>−</sup>3.

We now review the results of HD simulations leveraging the metal tracing framework. In HR HD simulations, metals are a crucial tool to unveil and understand the kinematics of major physical processes, such as AGN feedback, SMBH feeding, and IGrM turbulence. While the detailed AGN self-regulation thermodynamics (cooling and heating cycle) is tackled in the companion Eckert et al. review (also see the unification diagram

in Gaspari et al. [221]), here, we focus on the main IGrM cores kinematics features. The SMBH/AGN at the center of each BGG or ETG is fed recurrently via chaotic cold accretion (CCA [222]), i.e., the filamentary/cloudy condensation rain that is generated via *nonlinear* turbulent thermal instability in the IGrM hot halo (Gaspari et al. [223], Voit [224]; also see McCourt et al. [225], Sharma et al. [226] for linear thermal instability simulations). Such frequent CCA clouds trigger the AGN feedback response by re-ejecting substantial amount of mass and energy via ultrafast outflows and relativistic jets (e.g., References [227,228]). At the macro scale of tens kpc, such entrained outflows/jets use their mechanical ram pressure to generate a diverse range of astrophysical phenomena (buoyant X-ray cavities, weak transonic shocks, turbulent eddies), which recurrently reheat the IGrM halo and quench cooling flows/star formation throughout the several Gyr evolution (e.g., Churazov et al. [229], Brüggen [230], Brighenti and Mathews [231], McNamara and Nulsen [12], McNamara and Nulsen [13], Gitti et al. [15], Gaspari et al. [232], Barai et al. [233], Yang et al. [234]).

The macro-scale AGN feedback deposition channels are difficult to disentangle through simple temperature or surface brightness maps. The metal tracers are instead able to unveil in a clear manner such feedback features. Indeed, while the BGG produces a continuous reservoir of metals/iron in the core of the galaxy group, the self-regulated AGN outflows uplift them (Equation (4)) outwards, on top of the low-*Z* background, thus creating key contrast patterns and imprints. Figure 10 exemplifies this during a typical HR HD simulation [215] of AGN feedback—self-regulated via CCA—in a galaxy group akin to NGC 5044 (with a central BGG *<sup>M</sup>*<sup>∗</sup> 3.4 <sup>×</sup> 1011 *<sup>M</sup>*). In the right panel, the meso AGN outflows have just uplifted the iron generated in the core of the BGG (magenta) up to several tens kpc. The pattern is highly anisotropic and the enhancement can reach up to ∼2× values compared with the pristine background (<0.3 *Z*, e.g., Ghizzardi et al. [9]). Inhomogeneities are also visible, particularly the thin metal-rich rim that envelopes the inflated buoyant bubble. At variance, in the left panel, as the AGN outflows subside and CCA feeding is quenched via the previous AGN outburst, the cascading subsonic turbulence drives mixing, eventually washing out the inhomogeneities (cavity, cocoon, jet channel) and restoring the azimuthally symmetric IGrM halo 'weather'. Subsequently, this enables another phase of gradual IGrM precipitation and, hence, boosted accretion, with the triggering of another AGN feedback cycle via the condensed material. Both the above-shown anisotropic metal outflows and turbulent distributions have been found by a wide range of hot halo observations involving mechanical AGN feedback (Section 2.3.3) and a diverse range of HD numerical studies and groups [207,235–240]. We note that galactic SN-driven outflows, albeit weaker and difficult to spatially detect, can enhance the anisotropic enrichment, especially in low-mass halos (e.g., References [241,242]).

Metal maps not only give us constraints on the effects of AGN feedback, but can also constrain different AGN feeding modes. Figure 11 shows two HR HD simulations testing two different models of AGN self-regulation and feeding in a massive galaxy group with extended IGrM (*L*<sup>x</sup> ∼ <sup>10</sup><sup>43</sup> erg s<sup>−</sup>1). In the left panel, CCA feeding/cold mode selfregulation drives a very intermittent duty cycle tightly related to the recent cooling rate in the group core (typically with pink-noise time power spectrum; Gaspari et al. [223]). The rapid flickering of the AGN enables the formation of characteristic AGN feedback imprints, such as buoyant bubbles and cocoon shocks that are encased by metal-rich rims (cyan) protruding on top of the low abundance background. In addition, the buoyant bubble can dredge out trailing filaments of metals via the hydrodynamical Darwin [243] effect (*V*trail ∼ 0.5 *V*b, where *V*<sup>b</sup> is the bubble volume). Conversely, hot-mode feeding (e.g., Bondi or ADAF; Bondi [244], Narayan and Fabian [245]) drives a continuous AGN feedback evolution with a perennial, monolithic, wide and uniform cylinder of metals, without any signs of cavities or shocks. As for the thermodynamics (cf. the companion Eckert et al. review), observational constraints favor the former intermittent bubble duty cycle (via cold mode/CCA), rather than the latter quasi-continuous triggering mode (Bondi

or hot-mode feeding)—Simionescu et al. [140], Hlavacek-Larrondo et al. [246], McNamara and Nulsen [13], Gitti et al. [15], Liu et al. [247], Gaspari et al. [248].

**Figure 10.** Emission-weighted iron abundance during a typical HR HD 3D simulation of self-regulated AGN feedback in a median 1 keV galaxy group akin to NGC 5044 (adapted from Gaspari et al. [215]), showing two typical stages. The black regions denote the diffuse, primordial iron background (*Z*Fe < 0.3 *Z*). (**Left**) turbulence-driven period, during which mixing dominates, gradually washing out the anisotropic features and restoring azimuthal symmetry. (**Right**) the meso-scale (sub-kpc) AGN outflows have inflated a common X-ray cavity in the IGrM, generating a thin metal-rich rim (coincident with the compressive cocoon shock) and anisotropic iron uplift from the BGG outwards in the extended IGrM.

**Figure 11.** The iron abundance projected maps can differentiate between different models of AGN feeding triggering and self-regulation, here in a common HR HD simulation of a massive galaxy group (adapted from Gaspari et al. [214]). (**Left**) CCA feeding mode, driving intermittent and frequent AGN features, such as cavities with metal-rich rims and trailing filaments. (**Right**) Bondi feeding mode, driving a perennial, wide monolithic cylinder of metals into the group core (with no bubbles or cocoons).

As introduced above, a key component of the metal circulation is turbulence, either generated by the AGN feedback or by the large-scale cosmological evolution (Section 3.2), which is worth to further dissect. Remarkably, turbulent motions generate two (seemingly) contrasting effects, but on different scales. On the one hand, turbulent motions promote the diffusion of metals, tending to equalize the radial abundance profile from a negative to null gradient (e.g., References [249,250]). On the other hand, turbulence induces local chaotic relative density fluctuations *δρ*/*ρ*. As per the above Equation (5), metals can be considered on average akin to passive tracers of the HD density field; thus, *δρZ*/*ρ<sup>Z</sup>* ∼ *δρ*/*ρ*. As shown by numerical and analytic studies (e.g., References [251,252]), such stratified hot-halo fluctuations are linearly tied to the turbulent Mach number Mat; hence, the relative metal abundance can help us to constrain the level of turbulence in the IGrM too, *δρZ*/*ρ<sup>Z</sup>* ∝ Mat, with the slope of the Fourier spectrum constraining plasma processes, such as thermal conduction [253]. In the IGrM, the inferred 3D sonic Mach number of

turbulence is Mat ∼ 0.3–0.5 [254,255], i.e., *<sup>σ</sup><sup>v</sup>* of a few 100 km s<sup>−</sup>1. This can complement upcoming spectral X-ray IFU studies carried out via *XRISM* and *Athena* (see Section 4), with detailed synthetic observations already highlighting unprecedented features of metals and turbulence in hot halos [256–259]. Moreover, constraining the turbulent metal evolution in the IGrM plasma phase enables to assess the kinematics of the top-down multiphase rain, since the condensed warm (H*α*+[NII]) filaments and cold (CO, HI) clouds share analogous ensemble velocity dispersion [260–263].

While the large-scale cosmological evolution is discussed in the upcoming Section 3.2, it is worth to note here that at *<sup>r</sup>* <sup>&</sup>gt;<sup>∼</sup> 100 kpc (and with Gyr frequency), the infalling substructures and interacting galaxies (particularly dry dark matter halos; see the HD simulation review by Zuhone and Roediger [17]) can induce significant amount of sloshing in the IGrM, hence creating large-scale metal anisotropies and tails that are often correlated with cold fronts/contact discontinuities or ram-pressure stripping features [149,155,264–269]. For the observational insights on related metallicity maps, we refer the interested reader to Section 2.3.3.

#### *3.2. Cosmological Simulations and Large-Scale Evolution*

The metal content of cosmic structures has been addressed via complex large-scale cosmological hydrodynamical simulations, as well [32]. Cosmological simulations [270] allow us to study and predict the formation and evolution of galaxies and galaxy systems, such as groups and clusters, within the large-scale cosmological framework [271,272], while consistently accounting for a large variety of physical processes shaping the baryonic matter component—from gas cooling, to star-formation and BH evolution, to energy feedback. In particular, chemical evolution models are needed to consistently follow the production and evolution of the metal content in the stellar and gaseous components, which has important consequences on the cooling properties of the gas, on the conversion of gas into stars, and, therefore, is linked to the thermo-dynamical structure of galaxy systems. Given the large dynamical ranges spanned in simulations of cosmological volumes, chemical evolution is typically treated via a sub-resolution model, similarly to other small-scale physical processes (like star formation or energy feedback).

Chemical evolution models have been introduced in cosmological simulations starting from the 1990s [273,274]. While early studies including chemical enrichment mainly focused on galaxies [273,275], soon Smoothed-Particle Hydrodynamics (SPH) simulations of large-scale structure and galaxy clusters started to include chemical evolution models as well [276–278]. Despite different level of complexity, already in the early implementations, the metal production associated to both SNIa and SNcc was included, and the metal content of the gas was taken into account in the cooling process (e.g., References [279,280]). In Reference [278], the contribution to chemical enrichment due to low- and intermediatemass stars undergoing the AGB phase, as well as the treatment of metallicity-dependent stellar yields and mass-dependent stellar life-times were also included [281]. Starting from the initial models that focused on total metallicity or iron abundance, an increasing level of detail has been reached over the years, with modern simulations typically following the production and evolution of several metal species separately (e.g., oxygen, silicon, etc.). Chemical enrichment models are typically based on three fundamental pillars: the initial mass function (IMF) (e.g., References [282–284]), and mass-dependent stellar lifetimes (e.g., References [285–288]) and metal yields (e.g., References [6,289–292]). In SPH simulations [293], in particular, chemical evolution models are coupled directly with the star formation model, where every stellar particle is representative of a simple stellar population (SSP), that is a population of stars all characterized by the same age and metallicity. The assumptions on the IMF and on the stellar yields are required to predict the amount of metals generated by each SSP and the time-scale on which different enrichment channels (primarily SNIa, SNcc and AGB stars) release the metal mass into the surrounding gas elements (e.g., References [294,295], for more details on the principal equations that describe the stellar evolution and metal production).

Results from cosmological hydrodynamical simulations on the chemical enrichment of cosmic structures, from galaxies to groups and clusters, can be very sensitive to the specific assumptions on the IMF or of stellar yields. In particular, these can affect the normalization of metallicity profiles and the value of global abundances. Changes in the underlying IMF functional form, affect directly the final ICM metallicity and abundance ratio profiles, for instance, due to different relative amounts of low- and high-mass stars [281,288,296]. The yield tables are also an important source of uncertainty [289] in the predicted integrated level of enrichment, as well as the supernova rates (see a recent investigation based on the Illustris Simulations by Reference [297]). More importantly, the complex interplay with other gas thermal and dynamical processes treated in the simulations, such as energetic feedback or merging processes, can substantially impact the spatial distribution of metals and, therefore, the gradients of the radial profiles, as further discussed in Section 3.2.1 (also see Section 3.1).

In the last decade, more and more cosmological simulation codes have combined chemical enrichment models with many other important physical processes describing the evolution of gas and stars, with the principal aim of reaching an increasingly detailed and realistic picture of cosmic structures, from galaxies to galaxy clusters and cosmic filaments, to be compared against observational findings [172,297–303].

Nonetheless, most of the numerical studies based on cosmological simulations so far have concentrated on the case of (massive) galaxy clusters, for which the impact of resolution, feedback processes and interplay with the member galaxy population can be better constrained. Given their special position at the crossroad between smaller-scale physics and cosmic evolution, galaxy groups represent in fact a rather challenging, albeit crucial, target: capturing correctly the effects of feedback from central galaxies and BHs, given the shallower potential wells of groups compared to clusters, is of great importance. This has been in fact the main source of discrepancy in the comparison with observational findings, and consequently one of the crucial testbeds for cosmological simulations and the physical models therein included (for a thorough discussion, see the companion review by Oppenheimer et al.).

#### 3.2.1. Results from Cosmological Simulations

Cosmological simulations can be extremely powerful resources to study and predict the detailed enrichment history of the gas in cosmic structures, as well as to investigate the expected spatial distribution of metals. It is, therefore, crucial to assess their reliability by comparing simulated results to observational findings.

As a consequence of the interplay of different physical and dynamical processes, especially energetic feedback, simulations allow us to explore the expected observable signatures on the resulting distribution of metals in the IGrM gas. Numerical investigations showed, for instance, that feedback from AGNs is crucial to reproduce the large-scale homogeneous enrichment observed in the outer periphery of galaxy systems, such as groups and clusters [107]. In such simulations, metallicity profiles show a relatively flat trend out to large distances from the center in clusters, and a very similar enrichment level in smaller structures, as well. Consistent findings emerge from recent observational studies, as discussed in detail in Section 2.3.1 [31].

This effect of early AGN feedback promoting a more homogeneous enrichment and shallower radial profiles, was already observed in the simulations by Reference [172], for both massive clusters and lower temperature systems. At the group regime (*T* - 3 keV), they found that the flat profile of iron abundance in the outskirts of the simulated groups was in contrast with the observational results by Reference [93], employed for comparison (also see Reference [300]). The simulation results are instead more in line with recent observational data, e.g., by Reference [52,89]. Already in Reference [172], it was shown that also the the silicon-to-iron abundance ratio in simulations was found to be flat out to large distances from the center in groups, as well as in clusters, indicating also a similar contribution of SNIa and SNcc to the gas metal enrichment. A relatively flat silicon-to-iron

ratio was also confirmed by independent results obtained by Reference [23] on a set of simulated galaxy groups extracted from the OverWhelmingly Large Simulations (OWLS) project [304], despite finding typically more pronounced radial gradients of the IGrM metallicity. Several independent simulation studies converge on the idea that energy feedback solely due to supernova winds typically produces clumpier distributions of *α*-elements, like oxygen or silicon, and steeper, decreasing radial metallicity profiles. The reason for the different metal distribution can be related to the origin of the *α*-elements, mostly produced by SNcc and, therefore, confined in the vicinity of star-formation sites, where they can be efficiently locked back into newly formed stars unless an efficient mechanism intervenes to quickly distribute them far enough. The steeper profiles in absence of AGN feedback was also mildly noted in Reference [305], although the galactic outflow model used in their cosmological simulations was able to reproduce the global iron content in group-size halos, together with various observations of cosmic chemical enrichment. Those authors concluded, as well, that an efficient outflow mechanism, able to displace pre-enriched gas out of galaxies, must be in place already at early times, in order to explain the observed chemical enrichment of the inter-galactic medium at *z* ∼ 6 (also see Reference [280]).

These general trends have been also confirmed by following simulation campaigns [297,298,306]. In addition to consistent results on the relation between AGN feedback effects and the enrichment level at large distances from the center (i.e., beyond ∼0.3 *R*500), these recent simulations also finally reproduced the diversity of thermal and chemical properties found in the core (-0.1 × *R*500) of observed systems [303,306]. Some differences, e.g., on the metallicity profile normalization and, thus, on the global enrichment level, is nonetheless still present depending on the specific set of simulations analyzed [301], and consequently on the set of stellar yields and supernova rates adopted. In addition, the modeling of dust and metal spreading within cosmological simulations can further impact the details of the spatial distribution of metals that remain in the gaseous phase, for which further dedicated studies are needed.

When comparing simulation results with observations, it is important to pay attention to the way quantities are evaluated in simulations. In particular, estimates of metallicity (as well as other thermal properties) can be derived in different ways depending on the weight *w* used to compute the average *Z* value, that is *Zw* = *wZ*d*V*/ *w*d*V*. Typical weights are the mass of the gas or its emissivity in the X-ray band. In general, flatter metallicity profiles in simulations are better reproduced when a projected emission-weighted estimate is pursued, whereas the mass-weighted three-dimensional metallicity typically shows a somewhat steeper decrease with radius [107]. In this perspective, the issue of a fair comparison between gas properties in simulations and observations has also been tackled via the generation of detailed X-ray synthetic observations out of numerical simulations, properly taking into account the specific characteristics of X-ray telescopes. With such techniques, Ref. [71] showed that an observational-like reconstruction of the iron and oxygen abundances with mock XMM-*Newton* observations of simulated clusters and groups is in good agreement with the intrinsic simulation value. More recently, Ref. [257] employed synthetic observations of the X-ray Integral Field Unit (X-IFU) on board the next-generation European X-ray observatory Athena to reconstruct chemical properties of the ICM from simulated galaxy clusters. The authors showed that the metallicity values obtained from X-IFU spectra match well the emission-measure-estimate computed directly from the simulations.

The homogeneous enrichment of the intra-cluster and intra-group gas on large scales, as indicated by the little scatter around very shallow radial profiles in the outskirts, is also strongly connected to the history of the chemical enrichment. The so-called pre-enrichment scenario implies that the gas enriched within proto-groups and proto-cluster galaxies has been displaced beyond their shallower potential wells by some efficient mechanism at early times (*z* 3)—while stellar feedback alone is not sufficient, many recent state-of-the-art cosmological simulations identify the responsible mechanism with early AGN feedback. This allows the bulk of the diffuse inter-galactic gas to be pre-enriched and then re-accreted

into the assembling galaxy group or cluster. This further supports the idea that a significant fraction of the gas chemical enrichment happens at those early times, as confirmed by the little evolution of the gas metallicity below *z* ∼ 2, especially on the large scales, found in observations (e.g., References [307–309]) and also in simulation studies [107,297,298]. At the group scale, cosmological simulations predict a gas metallicity evolution below *z* - 1–2 that is very similar to the one found, and observed, in more massive clusters. Consistently with the results discussed above, simulations including AGN feedback find a shallow dependence on redshift, especially when the global metallicity within *R*<sup>500</sup> or the enrichment level in the outer regions ( 0.3 × *R*500) is concerned. Ref. [299] show that the evolution of the metallicity in different radial range is similarly mild at groups scales, as well, unless only stellar feedback is included in the simulations. In that case, they note again an effective reduction of the gas iron and oxygen content which is more severe particularly in the group regime. This is interpreted as a more substantial, unsuppressed, star formation activity which efficiently, and preferentially, consumes metalrich gas. In the galactic-outflow model by Reference [305] a higher growth rate, with respect to observations, was in fact observed in the simulated groups.

The similarities between chemical enrichment of the IGrM in lower-temperature groups and the ICM in massive objects is further supported by the shallow dependence of gas global metallicity on the system mass (or temperature). In contrast to observational findings, where lower iron abundances were typically observed in group-size systems compared to clusters, Ref. [310] report a shallow, mildly anti-correlating, metallicitytemperature relation, employing semi-analytic models of galaxy evolution. Simulation results, like those presented in References [297,302], also predict a shallow anti-relation between metallicity and temperature, that extends without breaks from clusters down to groups. More recently, Reference [299] compared the relation between temperature and iron abundance in the core (i.e., <0.1 *R*500) of simulated groups and clusters with recent results from the CHEERS sample [92], also finding a shallow anti-correlation overall, with a mass-invariance of the IGrM and ICM iron abundance in cool-core clusters, as shown in Figure 12. In the figure, in particular, the simulated data (star symbols) are reported together with the best-fit relation for the whole sample, and for the CC and NCC subsamples, with the former in better agreement with the CHEERS results (also see Reference [31]).

Ref. [302] show that a flat relation with temperature applies, as well, when abundance ratios relative to iron are investigated (e.g., O/Fe, Si/Fe, S/Fe, etc.). Interestingly, this is also in line with recent observational findings (e.g., Reference [128]; also see discussion in Section 2.3.2).

So far, the main limitation to study simulated groups of galaxies in more detail has been the lack of simulations within cosmological context able to consistently resolve and match the stellar and gas properties of massive galaxy clusters and galaxies, simultaneously. Groups, in this respect, have often rather served as crucial testbed for assessing the prediction power of physical models embedded into cosmological simulations, especially related to feedback from central galaxies (see the companion reviews by Oppenheimer et al. and Eckert et al.). Nonetheless, given the recent encouraging results obtained on the chemical and thermal properties of the diffuse gas in various cosmic structures, especially with improvements in the description of chemo-energetic feedback from galaxies in group and cluster cores, more dedicated studies specifically focusing on the group regime in cosmological simulations are definitely needed to explore the details of their formation and evolution.

**Figure 12.** Relation between gas iron abundance and temperature in the core (*r* < 0.1*R*500) of groups and clusters. Comparison between cosmological simulations (empty stars) and X-ray observational results from the CHEERS sample (filled circles). We also report best-fit relations for the whole simulated sample (solid grey line), and for the CC and NCC subsamples (blue dot-dashed and red dashed lines, respectively), as well as the relation determined from the CHEERS data (turquoise line and shaded area, for the associated 68.3% confidence region). Consistently with previous sections, iron abundances, relative to hydrogen, are reported with respect to the Solar reference value by Reference [43]. Adapted from Reference [299].

#### **4. Future X-ray Missions**

Beyond the impressive observational efforts provided by the community to best characterize metals in the IGrM using the past and current fleet of X-ray observatories (Section 2.2 and 2.3), it is clear that the next generation of X-ray missions is essential to overcome the current limitations and to advance our knowledge. As we further discuss in this section, higher spectral resolution, higher throughput, and larger sky coverage will be key factors.

#### *4.1. eROSITA*

The present knowledge of the physical properties of the IGrM, both thermodynamical and chemical, is limited to archival studies with known systems mainly at the high end of the mass and luminosity ranges. X-ray selection provides a more reliable way than optical selection of identifying virialized groups with a bona fide IGrM, but groups are typically at the limit sensitivity of the *ROSAT* All Sky Survey (RASS) and their detection is biased towards peaked surface brightness objects (the X-ray cool-core bias [311,312]). Even though the advent of XMM-*Newton* and *Chandra* made available deep surveys of limited areas providing less biased samples of groups, these systems are typically at moderate redshifts and they lack even global abundance measurements (e.g., References [313,314]). Optically selected systems with a dedicated X-ray follow-up can circumvent some of the biases of the RASS X-ray selection and provide some partial answer to the characteristic of the general population of groups (see, for example, Reference [315] and the interesting discussion therein).

*Spectrum Roentgen Gamma* (SRG, launched in 2019) hosts the eROSITA instrument, a set of seven co-aligned soft X-ray telescopes covering the 0.2–10 keV band, with a field of

view of 1◦ and ∼15 spatial resolution equipped with CCDs with spectral resolution of 60–80 eV in the 0.5–2 keV band [316]. At the end of 2023, after four years surveying the whole sky once every 6 months, eROSITA will build up an all-sky survey 25× deeper than RASS in the 0.5–2 keV band [316,317].

eROSITA will, therefore, provide for the first time a large, homogeneously selected Xray sample of groups for detailed studies with future generations of X-ray instruments (Reference [315,317,318], and also see the companion reviews, particularly Eckert et al.) detailed in the next sections and for the pointed phase of eROSITA itself, in a similar fashion as *ROSAT*. In particular, given the large field of view, pointed observations of eROSITA will provide valuable information for the outer regions of groups and their metallicity. These upcoming data sets are all the more interesting in the context of the expected spectral model improvements driven by microcalorimeter data, which will further ensure that the results derived from lower-spectral resolution CCD observations are robust.

#### *4.2. XRISM*

Non-dispersive, high-spectral resolution X-ray micro-calorimeters will enable a giant leap in our understanding of the metal content of the diffuse IGrM. The next such detector slated for launch is the *Resolve* instrument onboard the X-ray Imaging and Spectroscopy Mission (*XRISM*), a JAXA-led satellite with contributions from NASA and ESA [319] with a launch expected around 2023. The *XRISM*/*Resolve* instrument, covering a 3 × 3 arcmin field of view with 35 micro-calorimeter pixels, will carry forward the seminal observations begun by the *Hitomi*/*SXS* on the ICM of the Perseus Cluster [125]. With each pixel delivering a spectral resolution of <7 eV, more than 10 times better than conventional CCDs, and given its non-dispersive nature meaning that the spectra of extended sources are not blurred by the size of the target, *XRISM*/*Resolve* will reveal emission lines from various chemical elements in the IGrM with unprecedented sharpness (see, for example, Figure 13). Due to the relatively modest spatial resolution (with a HPD of 1.7 arcmin) and effective area, *XRISM* observations are ideally suited for studying the centers of nearby clusters and groups. Using these targets, together with dedicated laboratory measurements driven by these new observations (e.g., Reference [204,320]), it is expected that remaining uncertainties and differences between AtomDB and SPEXACT in modeling the Fe-L line emission will be ironed out early during the lifetime of the mission, whose expected launch is currently set for Japanese fiscal year 2022.

For the bright, line-rich cores of galaxy groups, 100 ks observations with *XRISM*/ *Resolve* can determine the abundances of Fe, O, Ne, Mg, Si, and S with statistical precisions of 5% and systematic uncertainties that are far reduced compared to those from fitting CCD spectra. Weaker lines from other elements like N, Al, Ar, Ca, and Ni (based on the Ni L-shell emission) may also be detected in the IGrM. This will provide a fantastic and stringent test of the current picture that the chemical composition of the ICM/IGrM is consistent with the Solar values (see Section 2.3.2).

Furthermore, precise measurements of the metal abundance patterns of the ICM and IGrM are expected to offer new tests of stellar astrophysics. Elemental abundances in the Sun and in the stars in the Local Group have so far been the most commonly used points of comparison in order to check whether or not current theoretical nucleosynthesis yields provide a self-consistent picture that can appropriately describe Galactic chemical evolution (see, e.g., Reference [7,321]). High-resolution X-ray spectroscopy with *XRISM*, followed by the *Athena* X-IFU (see Section 4.3) will provide complementary measurements of the enrichment history of the hot-diffuse gas, with a precision rivaling optical and infrared stellar spectroscopy, ushering in a new era of extra-galactic archaeology.

**Figure 13.** A comparison between existing archival XMM-*Newton* data of the central regions of the galaxy group NGC1550, and predictions for *XRISM*/*Resolve* using a similar exposure time and spectral model. (**Top panel**) The RGS spectrum extracted from a 3.4 arcmin-wide stripe in the cross-dispersion direction; spectra from RGS1 and RGS2 and from the three different existing observations have been stacked for display purposes (for details of the data reduction, see Reference [322]). The blue curve shows the best-fit 2T model using SPEXACT v3.0.6, including the effect of line broadening due to the extent of the source. (**Bottom panel**) The XMM-*Newton*-MOS1 spectrum from the central 0.05 *r*<sup>500</sup> region of NGC1550 (adapted from Reference [128]) is shown in blue. This region roughly corresponds to the FoV of *XRISM*/*Resolve*. In red, we show the predicted model obtained by re-scaling the 2T RGS model from the top panel to match the XMM-*Newton*-MOS1 flux, and folding this through the *XRISM*/*Resolve* response. This re-scaling is necessary because the absolute flux determined by XMM-*Newton*-RGS for an extended source is uncertain, since technically a region up to 10 arcmin along the dispersion direction can contribute to the observed count rate. A simulated 100 ks *XRISM*/*Resolve* spectrum using this model is shown in black. The 5 brightest Fe lines, and lines from all elements other than Fe with a line flux exceeding <sup>5</sup> <sup>×</sup> <sup>10</sup>−<sup>17</sup> photons/s/cm3, are labeled.

#### *4.3. Athena*

In the continuation of the high resolution spectroscopy era to be settled by *XRISM*, the future European mission *Athena* will be a game changer for our understanding of the chemical enrichment of hot halos pervading large-scale structures, from individual galaxies to rich clusters. Currently planned to be launched around 2033, *Athena* will embark two revolutionary instruments: the Wide Field Imager (WFI [323,324]) and the X-ray Integral Field Unit (X-IFU [325,326]). The former consists of a DEPFET (depleted p-channel fieldeffect transistor) camera able to perform imaging and moderate-resolution spectroscopy over an impressive field of view of 40 × 40 , whereas the latter is a cryogenic spectrometer made of a ∼5 diameter array of more than 3000 TES (transition edge sensors)—each of

which offering an exquisite spectral resolution of 2.5 eV over a required spatial resolution of 5 arcsec half energy width (thus allowing to probe the spatial substructure if the IGrM at levels comparable to XMM-*Newton*). Concretely, both instruments will be nicely complementary. While the WFI is expected to discover a large number of high-redshift clusters and groups, the X-IFU will be able to investigate them spectroscopically with unprecedented resolving power. The promises of the latter have been thoroughly demonstrated in the case of clusters, in terms of spatial distribution of metals (Reference [257]; also see Section 3.2.1) but also of chemical composition and underlying stellar sources [259].

The outstanding scientific potential offered by *Athena* for exploring the metal content of the IGrM is illustrated in Figure 14, where we simulated 100 ks of WFI and X-IFU exposures (in comparison to that of XMM-*Newton*/pn) for the core (<0.05 *r*500) of a typical NGC 1550-like group assumed at various redshifts. Whereas, for this specific case, pn cannot provide significant metal constraints at *z* = 0.5 and beyond, we calculate that the WFI and the X-IFU should be able to track the overall metallicity up to *z* = 1 within ∼40% or less. An interesting feature immediately visible from this figure is the possibility of performing spectroscopy on high-redshift groups with the WFI. As the effective spectral resolution of any instrument naturally tends to deteriorate with decreasing flux (in order to keep enough meaningful statistics per spectral bin), at *z* = 1 typical WFI and X-IFU spectra of groups are expected to deliver very similar spectral information. Combined with its ability to detect and image several groups simultaneously over a large region of the sky (more than 10,000 systems at *<sup>z</sup>* <sup>&</sup>gt; 0.5 with *<sup>M</sup>* <sup>≥</sup> 1013*M* over the nominal four years of the mission [327]), this will make the WFI a highly valuable instrument to trace the metal content of *many* (local and distant) groups at once. This actually provides a unique synergy with the X-IFU, as the latter will be invaluable to resolve a plethora of metal lines at low and moderate redshifts (in order to derive absolute and relative abundances with exquisite accuracy, but also to further refine atomic calculations and make the available spectral codes further converge).

**Figure 14.** Simulated (100 ks) spectra of the core of a typical NGC 1550-like group (*L*0.3−2keV 2.1 <sup>×</sup>10<sup>42</sup> erg/s, *kT* 1.3 keV, Fe 0.6 Solar) set at various redshifts, as seen by the XMM-*Newton*/pn, *Athena*/WFI, and *Athena*/X-IFU instruments. Each spectrum has been appropriately re-binned for clarity.

Another particularly interesting possibility offered by the X-IFU instrument resides in the determination of the abundances ratios. By giving us access to even more metals with even fainter lines than *XRISM*, the X-IFU will offer the best diagnostics of the SN explosion mechanisms, initial metallicity of the progenitor stars contributing to the enrichment of the cosmos, and especially the slope of the IMF, with the aim to contribute in a significant way to the debate about its universality. Higher line emissivities of a few key elements (e.g., O, Mg) at the groups regime are critical for constraining the IMF and will nicely complement the case of clusters, which will be thoroughly studied, as well (see, e.g., Reference [259]).

Although more tailored WFI and X-IFU predictions (including, e.g., cosmological evolution of groups, the effects of the background and its reproducibility and/or other instrumental effects) are left for future dedicated work, it is clear that *Athena* will push our understanding of the chemistry of large-scale structures to the next level, even at and below groups scales.

#### *4.4. HUBS and Super DIOS*

While *XRISM* and *Athena* will lead to significant advancements in our understanding of the precise chemical make-up of the centers of galaxy groups and its redshift evolution, the high spectral resolution IFUs onboard both of these future missions have a limited field of view. This means that studies of the metal abundance ratios in the outskirts of groups and clusters would be very expensive in terms of observing time: nearby objects would be too large on the sky, and require mosaics composed of an unwieldy number of pointings, while high-redshift objects whose outskirts do fit within the FoV would be significantly dimmer. To give a concrete example, covering the entire area between 1–1.5 *R*<sup>500</sup> of NGC 5846<sup>4</sup> would require no less than 423 observations with the *Athena*/X-IFU.

Two future missions currently under study promise to address this issue by offering capabilities that are complementary to those of *Athena*: the Hot Universe Baryon Surveyor (*HUBS*) [329], which is a project of the Chinese National Space Administration (CNSA), and the JAXA-led *Super DIOS* ("Diffuse Intergalactic Oxygen Surveyor", Sato et al. [330]) mission. Both have expected launch dates in the 2030s. By prioritizing a shorter mirror focal length (which implies a smaller on-axis effective area) but using larger pixels and covering a larger field of view (of order ∼1 deg2), these future satellites will be able to survey a wider area of the sky more efficiently while maintaining a high spectral resolution (Δ*E* - 2 eV). Due to the shorter focal length and their planned deployment in low-Earth orbit which both help to minimize the detector background, these missions are optimized to enable detailed high-resolution spectroscopy of the faint outskirts of nearby groups and clusters of galaxies, among several other science topics. In Figure 15, we summarize the capabilities and advantages of planned X-ray IFUs over the next ∼decade. Remarkable to note is that the *Super DIOS* concept plans to employ nearly an order of magnitude more TES pixels than *Athena* with developments of a new TES readout system, enabling a 10–15 arcsec resolution over 0.5–1 deg2; while HUBS has a similar number of pixels as *Athena* (and, therefore, a poorer spatial resolution of ∼1 arcmin over a 1 deg2 FoV), it carries a central 12 by 12 arcmin sub-array with an energy resolution of 0.6 eV, that will be the first detector to reach a resolving power of *E*/Δ*E* > 1000 around the Fe-L complex.

**Figure 15.** Summary of the capabilities of future missions and mission concepts carrying highspectral resolution X-ray integral field unit detectors, using the *XMM-Newton* EPIC/pn as a reference value of 1 along each axis. The grasp is defined as the effective area *Aeff* integrated over the field of view; plotted along the 'low NXB' axis are the non-dimensional figures of merit *FNXB* for detector-background-limited observations (also known as non-X-ray background), expressed as *FNXB* = *Aeff* /(*F*2*B*) with F the mirror focal length and B=1 in low-Earth orbit and 4 for high orbits, as defined by, e.g., Reference [331].

#### *4.5. Arcus*

Arcus is a proposed NASA Medium Explorer mission that aims to significantly improve our spectroscopic capabilities using soft X-ray gratings. With spectral resolution *R* > 2500 between 12–50 A˚ , the Arcus proposal possesses the ability to resolve the absorption of a diverse range of metal species in the extended halos of galaxies, groups, and clusters along sight lines toward distant quasars [332]. X-ray grating spectroscopy provides a critical complementary probe to planned micro-calorimeters by having ∼10× greater resolution and probing the diffuse hot gas comprising the majority of missing metals and baryons [333,334]. Arcus is designed to achieve a 10-fold increase in sensitivity (i.e., square root of effective area times resolution) over existing grating spectrometers on *Chandra* and XMM-*Newton*.

According to cosmological simulations [335], the IGrM has the greatest potential to show a rich variety of ion species. O VIII should be the most detected species within group virial radii, while O VII should be detected in lower mass groups at *M*<sup>500</sup> - 1013.5*M*. In its main mission, Arcus should detect the *T* = 105.4–6.8 K IGrM in at least 10 group halos at a 3 mA˚ equivalent width threshold (at 5*σ*) for O VII and O VIII. Interestingly, the Fe XVII should be detectable within *<sup>R</sup>*<sup>500</sup> for groups, probing gas up to ≈107 K for at least 5 group halos. Integrating longer on the brightest X-ray quasars opens up the possibility to detect more species using a 1 or 2 mA˚ detection threshold, including Ne IX and Ne X. C V and C VI (and maybe N VII) may also be detectable in the group outskirts for deeper observations probing gas down to 105 K. Sensitive UV absorption line spectroscopy brought about by

the Cosmic Origins Spectrograph on *Hubble* discovered that the objects with the richest and most diverse set of species probing gaseous halos are star-forming, *L*∗ galaxies [336]. It is expected that groups will be the analogous richly detected, multi-species objects to be probed via X-ray absorption line spectroscopy.

#### *4.6. Lynx*

The *Lynx* mission concept [337] proposed to the US 2020 Decadal Survey is designed to carry a new generation of X-ray telescopes enabling a sub-arcsecond resolution over a <sup>22</sup> × <sup>22</sup> field of view and an effective area of 2 m2 at 1 keV. It is designed to be equipped with three complementary instruments. An active pixel array (the high-definition X-ray imager, HDXI) that would provide wide-field CCD-like spectral imaging, but with 0.3 pixels to take advantage of the exquisite spatial resolution. The *Lynx* X-ray Microcalorimeter (LXM) which would bring 3 eV spectral resolution on 1 spatial scales over a 5 field of view (0.3 eV in a ultra-high resolution sub-array). Finally, an X-ray grating spectrometer (XRG) with an effective area of 4000 cm2 and resolving power greater than 5000 to exploit the better spectral resolution of gratings for point sources in the soft energy band. The key improvements *Lynx* will bring if approved concern the ability to resolve the metal abundance structure of the gas near and outside the virial radius of groups at low redshift by combining a study of emission and absorption against background AGNs. *Lynx* will also push the realm of enrichment studies in the IGrM to the z = 2–3 range where strong trends are expected. *Lynx* is specifically targeting observations of high-redshift groups down to a mass scale of *<sup>M</sup>*<sup>500</sup> <sup>=</sup> <sup>2</sup> <sup>×</sup> 1013 *<sup>M</sup>* at z <sup>&</sup>gt; 3 (https://www.lynxobservatory.com/report, accessed on 21 June 2021. [338]).

#### **5. Concluding Remarks**

Throughout this review, we have seen how crucial the case of galaxy groups is in order to complete our understanding of the journey of metals—from stars and supernovae to the largest scales of our Universe. Groups are in fact a unique piece of the puzzle to relate chemical enrichment at (sub-) galactic scales and at cluster scales (Section 2.4), making IGrM abundance studies particularly valuable in this respect. As we have also discussed, however, such studies are still in their pathfinder steps, and enrichment in groups remains much less explored (hence, understood) than in clusters. The reasons are diverse, and include notably on the observational side: (i) the intrinsic faintness of the IGrM with respect to the ICM, making observational studies more demanding in terms of exposure time; (ii) the lack of well defined samples of groups in the X-ray band, marking again a stark contrast with respect to clusters; (iii) our lack of spectral knowledge of the Fe-L complex (ruling almost all the X-ray emission of the IGrM) and of the likely multitemperature structure of the gas (Section 2.1). As we have seen in Section 4, in the next few years, each of the above limitations will be tackled by higher quality data in terms of sizes of the sample of groups to be targeted and available high-throughput and high-resolution spectra. Those data will be coupled with an improved theoretical understanding of the spectral modeling. It is also essential to continue the efforts to improve the accuracy of the theoretical SN yields and the measurements of SN rates as a function of the cosmic time. On the simulation side, the main challenge will be to reproduce key stellar and gaseous properties on both galactic and Mpc scales, simultaneously including microscale physics and the large-scale cosmological context (Sections 3.1 and 3.2). With the ongoing exponential high-performance computing advancements, we are getting closer to a quantum leap in terms of a single high-resolution hydrodynamical cosmological simulation reaching this goal, thus providing more detailed predictions for the regime of galaxy groups. It is a reasonable bet to forecast the coming era as a golden age of maturity for the study of metal abundances in galaxy groups.

**Author Contributions:** F.G.: lead author, Sect. 1, 2.2; A.S.: Sect. 2.1, 2.3.2, 2.3.3; F.M.: Sect. 2.3.1, 2.5; V.B.: Sect. 3.2; M.G.: Sect. 3.1; K.S. and K.M.: Sect. 2.4 with contribution from F.G. F.G., A.S., F.M. and K.S contributed to Sect. 4. All authors contributed to Sect.5. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The review is based on public data and/or published papers. The results collected from literature and used to generate some of the figures in this review can be found at this link 10.5281/zenodo.5011831.

**Acknowledgments:** We thank the two anonymous referees for helpful reports which improved the quality of this review. We would like to thank Ben Oppenheimer for providing the section of the future mission Arcus and for useful discussions. We would like to thank David Buote, Silvano Molendi, Simona Ghizzardi, Fabrizio Brighenti, William Mathews for comments and suggestions. FG acknowledges financial contribution from INAF "Call per interventi aggiuntivi a sostegno della ricerca di main stream di INAF". AS is supported by the Women In Science Excel (WISE) programme of the NWO, and acknowledges the World Premier Research Center Initiative (WPI) and the Kavli IPMU for the continued hospitality. SRON Netherlands Institute for Space Research is supported financially by NWO. MG acknowledges partial support by NASA Chandra GO8-19104X/GO9-20114X and HST GO-15890.020-A grants.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Notes**


#### **References**


## *Review* **Properties of Fossil Groups of Galaxies**

**J. Alfonso L. Aguerri 1,2,† and Stefano Zarattini 3,4,\*,†**


**Abstract:** We review the formation and evolution of fossil groups and clusters from both the theoretical and the observational points of view. In the optical band, these systems are dominated by the light of the central galaxy. They were interpreted as old systems that had enough time to merge all the M\* galaxies within the central one. During the last two decades, many observational studies were performed to prove the *old and relaxed* state of fossil systems. The majority of these studies that spans a wide range of topics including halos global scaling relations, dynamical substructures, stellar populations, and galaxy luminosity functions seem to challenge this scenario. The general picture that can be obtained by reviewing all the observational works is that the fossil state could be transitional. Indeed, the formation of the large magnitude gap observed in fossil systems could be related to internal processes rather than an old formation.

**Keywords:** fossil galaxy groups; galaxy clusters; galaxy groups; X-ray and optical observations; hydrodynamical simulations

**Citation:** Aguerri, J.A.L.; Zarattini, S. Properties of Fossil Groups of Galaxies. *Universe* **2021**, *7*, 132. https://doi.org/10.3390/ universe7050132

Academic Editor: Francesco Shankar

Received: 26 March 2021 Accepted: 28 April 2021 Published: 4 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

The Lambda cold dark matter scenario (ΛCDM) predicts that structures in the Universe form following a hierarchical evolution: small objects collapsed first under their self-gravity and are then merged continuously to build larger structures. In this scenario, galaxy formed first, then merged in small groups and the process continues until the creation of massive galaxy clusters [1,2].

Ponman and Bertram [3] firstly suggested, while studying compact groups, that this building scenario could be taken to the extreme consequences. They predicted that, in some cases, all the main galaxies of a group could merge with one another, creating a giant galaxy embedded in an X-ray halo typical of a group. This prediction was supported, one year later, by the discovery of RX 11340.6 + 4018, an apparently isolated elliptical galaxy, at redshift *z* = 0.171, found in an extended X-ray halo. The estimated X-ray mass was 2.8 <sup>×</sup> 1013 <sup>M</sup>, making it a typical group-sized object [4]. These systems were named as "*fossil groups*" (FGs). They were thought to be the latest stage in the evolution of galaxy groups. For this reason, they were supposed to be old and dynamically relaxed systems [3].

The spatial density and fraction of FGs were estimated in different studies, both theoretically and observationally. The agreement on the spatial density is quite good, with estimations in the range ∼1–3 ×10−<sup>6</sup> *<sup>h</sup>*<sup>3</sup> <sup>50</sup> Mpc<sup>−</sup>3, see, e.g., in [5–7]. On the other hand, the fraction of FGs with respect to the total amount of clusters and groups is more debated. A comparison between different works can be found in Table 1 of Dariush et al. [8]: the estimated fractions varies between 1% and 40%, with a large scatter, and a mean value can be found at about ∼10–15%.

In this review, we show the main observational and theoretical works related to FGs written during the last three decades. Our aim is to show that these systems are fixed well

in the current theory of structure formation in the Universe. They are just extreme systems produced following this theory. This review is structured in the following way: in Section 2, we will describe the search for FGs in the last ∼20 years and their observational definitions. In Section 3, we will present the theoretical scenarios proposed to describe these systems. In Section 4, we will discuss the properties of the intra-cluster medium and of the galaxy populations. Then, we will describe the possible progenitors of FGs in Section 5. Finally, in Section 6, we will propose a sample of "*genuine*" FGs and draw our conclusions.

#### **2. The Search for Fossil Systems**

Since their discovery in 1994, a strong observational effort was done to find FGs. Despite their supposed frequency, more than 10 years were needed before producing reasonably large catalogues of some tens of candidates. In this sense, one of the main obstacles for the community was to agree on a practical definition. In fact, at the beginning, the search was limited to isolated galaxies surrounded by an X-ray halo, but this definition was too loose [5]. More rigorous definitions, involving photometry, spectrocopy and X-ray data, were proposed and are actually used. We will discuss them in Section 2.1. However, these rigorous definitions had important observational limitations. The result of these constraints was that fossil samples were not selected in a homogeneous way and, in Section 2.2, we will discuss the strength and weaknesses of the different approaches adopted in the literature.

#### *2.1. Operational Definitions of Fossil Groups*

The most common operational definitions of FGs are based on the magnitude gap between the brightest member galaxy of the group/cluster and other galaxy sorted by their magnitude (Δ*m*1,*j*, where *j* represents the *j*-th ranked galaxy). In particular, Jones et al. [9] suggested that a group or a cluster of galaxies should be classified as fossil if the magnitude gap between its two brightest members (Δ*m*12) is larger than two magnitudes in the *r*−band. In addition, they also imposed that the two brightest galaxies should be located within half the (projected) virial radius (defined as *r*200, the radius of a sphere whose mean density is 200 times the critical density of the Universe). Another common definition is the one presented in Dariush et al. [10]: a group/cluster of galaxies is classified as fossil if the magnitude gap between its first and fourth brightest member galaxies (Δ*m*14) is larger than 2.5 magnitudes in the *r*−band and within half the (projected) virial radius. Both definitions also require the presence of a diffuse X-ray halo, with *LX* <sup>≥</sup> 1042 *<sup>h</sup>*−<sup>2</sup> <sup>50</sup> erg s−1. This last criterium ensures that the system is located in a potential well similar in mass to groups or clusters of galaxies. An example of a typical FG and the color-magnitude diagram of its galaxy population is shown in Figure 1.

The original name and definition were thought to describe only galaxy groups. However, many studies, e.g., [11–13], found the existence of fossil clusters. This is due to the lack of an upper limit for the X-ray luminosity in both of the most common operational definitions. As a consequence, when describing the general properties of the population, *fossil groups* and *fossil clusters* are interchangeable in the literature. In addition, a more general *fossil systems* is also widely used. We invite the reader to consider these three definitions as equivalent along this review.

**Figure 1. Left panel**: SDSS image with X-ray contours of Abell 1068. **Right panel**: color-magnitude diagram of the same object. Green triangles are system members, whereas red triangles are those that are not. The redshift, Δ*m*12, and Δ*m*14 are reported in the right panel. The original image can be found in Harrison et al. [14]; in particular, it corresponds with their Figure B7.

#### *2.2. Catalogues*

We already mentioned that the prototype of FGs is RX 11340.6 + 4018, presented in Ponman et al. [4]. A few years later, Vikhlinin et al. [5] studied a sample of four *X-Ray Overluminous Elliptical Galaxies*: the authors claimed that these objects could have been part of the fossil category, but it was just a suggestion, since no operational definition was available until Jones et al. [9] proposed the use of the magnitude gap as the discriminating factor between fossils and non-fossils, proposing a sample of 5 FGs in their work.

Other studies presented small numbers of FGs candidates [11,12,15–18], amongst others, whereas the first large sample of FG candidates was presented in Santos et al. [6]: in this work, the authors selected 34 galaxy aggregations obtained from the Sloan Digital Sky Survey Data Release 5, SDSS DR5, [19] by cross matching the sample of SDSS *Luminous Red Galaxies* [20] with sources in the ROSAT all-sky *bright source catalogue* [21]. The result of the cross match was a list of elliptical galaxies surrounded by an X-ray halo. Then, the magnitude gap was computed within a fixed radius (500 kpc) and in a fixed redshift range (Δ*z* = 0.002 when spectroscopic redshift is available, Δ*z* = 0.035 when only photometric redshift is known). These 34 FG candidates were then studied in detail by the Fossil Group Origins (FOGO) project [13]. This observational project produced a set of results analyzing the properties of these systems. In the framework of this project, Zarattini et al. [22] confirmed that 15+<sup>8</sup> <sup>−</sup><sup>5</sup> of the candidates are FGs according to the Jones et al. [9] or Dariush et al. [10] definitions. The uncertainties in the number of confirmed FGs reflect those on the definition of *r*200. The large difference between the proposed candidates and the confirmed fossils can be explained with a stricter implementation of the definition criteria (e.g., differences in the search radius and membership definition). From the comparison between Santos et al. [6] and Zarattini et al. [22], it seems clear that three types of observations are needed in order to strictly define an FG: (i) X-ray data, required to estimate the mass of the system and define the virial radius, (ii) multi-object spectroscopy, in order to identify the real members of the FG, removing fore- and background objects, and (iii) an optical image, needed to measure the magnitude of each galaxy and to compute

the magnitude gap between the brightest galaxy and the other members. The combination of the strong observational effort together with the demanding observational definition is probably the main limit for the building of a large and homogeneous dataset of fossil systems. However, the number of known FGs kept growing in the last decade. Without intending to be exhaustive, La Barbera et al. [7] used SDSS-DR4 and ROSAT to build a sample of 25 FG candidates, Tavasoli et al. [23] found 109 FGs obtained from SDSS-DR7 using a friend-of-friend algorithm, Makarov and Karachentsev [24] presented a catalogue of 395 nearby groups and claimed that ∼25% of those are FGs, Harrison et al. [14] presented a sample of 17 FG candidates, and Gozaliasl et al. [25] presented a catalogue of 129 groups, of which 22 ± 6% are fossils. While the number of candidates is rising, it become more and more complicated to have dedicated multi-object spectroscopic observations to constraint membership. The main drawback of this strategy is that the purity of the sample is difficult to control and non-fossil systems can dilute the statistical relevance of the results. It is thus complicated to estimate the number of "*genuine*" FGs, namely those that strictly accomplish the operational definitions, known up to date. However, in the last section of this review, we will try to define a sample of such genuine systems.

#### **3. Theoretical Framework**

Numerical simulations of the number of satellites in galaxy groups predict the presence of a huge number of dwarf galaxies, e.g., [26]. However, these predictions are not confirmed in observations. In fact, if the number of bright galaxies is in agreement with these predictions, the number of observed dwarfs is up to two orders of magnitude lower than expected, e.g., [27]. This is the so-called *missing satellite problem*. D'Onghia and Lake [28] pointed out that FGs could scale up the missing satellite problem at the mass scales of more massive galaxies. In particular, they compared the number of satellites predicted by ΛCDM at different halo mass scales and concluded that FGs shown smaller number of galaxies such as the Milky Way and the Large Magallanic Cloud than those predicted by the structure formation theory. They claimed that the reason of this lack of bright galaxies was due to over merging processes occurred in FGs. These early findings made FG extreme objects in the structure formation of the Universe. The over merging processes in FGs could be explained in terms of differences in the orbital structure between fossil and non-fossil systems. Sommer-Larsen [29] used cosmological TreeSPH simulations to study the orbital structure of the intra-group (IG) stars for a set of clusters with masses <sup>∼</sup>1014 <sup>M</sup>. He concluded that the velocity distribution of the IG stars was significantly more radially anisotropic for fossil than for non-fossil systems. This pointed out that the initial velocity distribution of the group galaxies could play an important role in defining the fossil status of the system.

Several works have focused on the theoretical study of the mass assembly history of fossil and non-fossil systems. One of the first papers on this topic was done by D'Onghia et al. [30] where they analysed the mass assembly of systems with *Mvir* ∼ <sup>10</sup><sup>14</sup> M. They found a correlation between Δ*m*<sup>12</sup> and the formation time of the group defined as the redshift at which 50% of the total mass of the system at *z* = 0 is already in place (*z*50). In particular, they found that FGs have assembled more than half of their present mass at *z* > 1, with a subsequent growth by minor mergers alone. This early assembly gave enough time to FGs to merge their M∗ galaxies (where M∗ is the characteristic magnitude of the luminosity function, see Section 4.2.3 for details) and produce the large magnitude gaps observed at *<sup>z</sup>* <sup>=</sup> 0. The mass assembly of the low-mass group regime (*Mvir* <sup>∼</sup> 1013 <sup>−</sup>1013.5*M*) was analysed by using the Millenium Simulation by Dariush et al. [8,10]. In particular, these authors found that the selection of the systems using their magnitude gap alone does not guarantee the selection of early formed systems. They observed that the majority of the objects that have assembled more than 50% of their halo mass at *z* = 1 are not fossil systems today. A similar result was found in Deason et al. [31]: 20% of the groups selected from the Millenium Simulation with large mass gap (similar to fossil systems) turned to be young objects. Raouf et al. [32] proposed that a combination of three observational

parameters (magnitude gap, luminosity of the brightest cluster galaxy and its offset from the group luminosity centroid) considerably improve the selected rate of dynamically old systems. In Figure 2, it can be seen that the probability for a system with Δ*m*<sup>12</sup> > 2.0 and Δ*m*<sup>14</sup> > 2.5 to be old grows when the absolute magnitude of the BCG is smaller. In this case, Raouf et al. [32] defined a group as old if its halo has over 50% of its final mass at *z* = 1 and young if this fraction is less than 30%. Indeed, these plots demonstrate that Δ*m*<sup>14</sup> works better than Δ*m*12, when combined with the absolute magnitude of the central galaxies, in finding old systems. This result was recently confirmed in Zhoolideh Haghighi et al. [33], since the authors found a clear correlation between Δ*m*12, the offset of the luminosity centroid, and the dynamical age of a group/cluster. However, this criterium is less used in the literature, probably because it is newer than the Jones et al. [9] and Dariush et al. [10] ones.

**Figure 2.** Distribution of the galaxy groups in the plane of luminosity gap Δ*m*<sup>12</sup> (**left panel**) and Δ*m*<sup>14</sup> (**right panel**) within 0.5 *r*<sup>200</sup> and the *r*−band magnitude of the brightest group galaxy, in the Millennium simulations with Guo et al. (2011) semi-analytic model. Data points are colour-coded according to the ratio of the group halo mass at redshift z∼1 to its mass at *z* = 0. The plane has been sub-divided into blocks within which the probability that the halo is old or young is given. In this diagram, panels (5), (9), and (10) contain mostly old systems while the panels (3), (4), and (8) are mostly occupied by young systems. The image is taken from Raouf et al. [32]; in particular, it corresponds to their Figure 1.

In addition, the Illustris Simulation was used to analyse the properties of the FGs in the mass regime 1013 <sup>−</sup> 1013.5*M* [34]. The authors found that the magnitude gap of FGs identified at *z* = 0 were on average created about 3 Gyr ago. In addition, the fossil central galaxies became more massive than non-fossil ones. This difference was explained as due to differences in the mass acquired through mergers between *z* = 0.1–1, as can be seen in the left panel of Figure 3. Fossil BCGs also have a larger number of major mergers than non-fossil ones (right panel of Figure 3). Indeed, the last major merger of fossil BCGs was later (e.g., at lower redshift). No differences were found in the distribution of the time formation (*z*50) of fossil and non-fossil halos. The group mass assembly of fossils and non-fossils differs only in the recent group accretion history, in particular in the formation time of the 80% of the mass of the halo. However, semi-analytical models studied the dynamical evolution of galaxies in groups with different formation epochs [35]. They found that BCGs of dynamically-young groups suffered the last major galaxy merger ∼2 Gyr more recently than their counterparts in dynamically old groups and that FGs are somewhere in the middle between the other two populations. However, these authors found a lack of recent major mergers in FGs that is in agreement with the evolution of their old systems.

**Figure 3. Left panel**: average stellar mass assembly history for central galaxies within *r*200. Shaded areas are 1*σ* errors calculated from 1000 bootstrap resamplings. **Right panel**: average number of cumulative major mergers occurred at the central galaxy across z. In both panels, fossil and non-fossil systems are represented in red and blue, respectively. The image is taken from Kundert et al. [34], in particular from their Figures 6 and 7.

Raouf et al. [36] also used the Illustris Simulation to study some properties of fossil systems. They found that this simulation overproduce FGs in comparison with observations and semi-analytical predictions. They also obtained that the intra-group medium (IGM) in dynamically evolved groups is hotter, for a given halo mass, than that in still evolving ones.

Several studies found that the fossil phase of a system could be transitional. Galaxy clusters and groups pass through fossil and non-fossil phases along their evolution. von Benda-Beckmann et al. [37] found a population of groups that presented a fossil phase at high redshift which is terminated later by the accretion of new bright galaxies. The transitional phase of the fossil status is also reported by other simulations like Kundert et al. [34]. These fluctuations in the magnitude gap could be related with the large-scale environment in which the systems are located. Indeed, Diaz-Gimenez et al. found that, in the Millenium Simulation, the environment was different for fossil and non-fossil systems with similar masses. They showed an increase in the local density profile of galaxies at ∼2.5 *rvir* from the group centers. This increment was more noticeable in fossil than in non-fossil systems and was linked with the earlier formation time of fossil groups. We will discuss in Section 5 what is found in observations that can be linked to the transitional fossil phase.

The properties of the galaxy populations in fossil and non-fossil systems have also been analysed using cosmological simulations. Romeo et al. [38] reported from cosmological hydrodynamical simulations and semi-analytical models that fossil and non-fossil systems show different star forming rates at low *z*, being indistinguishable at *z* > 0.5. In contrast, Kundert et al. [34] found no differences in the stellar age, metallicity, and star formation rates of BCGs in fossil and non-fossil systems from the Illustris Simulation. Raouf et al. [36] analysed the properties of the black holes developed in the center of the BCGs for fossil and non-fossil systems. They found that the mass of the black holes hosted in BCGs is larger in dynamically evolved groups with a lower rate of mass accretion a result confirmed also in Khosroshahi et al. [39].

Kanagusuku et al. [40] found that fossil and non-fossil systems selected from the Millennium Simulation showed different galaxy populations. In particular, at early times, FGs comprised two large brightest galaxies surrounded by faint ones. At the faint end of the luminosity function, fossil systems turned to be denser at early times that non-fossil

ones. This trend reverses at a later time and became similar before *z* = 0. This was caused by an increase at a constant rate of the number of faint objects in non-fossil systems. In contrast, the number of faint galaxies reached a plateau at z∼0.6 in FGs, and then grows faster towards *z* = 0. The evolution of the galaxy luminosity function as a function of redshift for fossil and non-fossil systems was studied by Gozaliasl et al. [25]. They build up luminosity functions of galaxy aggregations based on the Millennium Simulation. They found that the bright end of the galaxy luminosity function strongly evolved for fossil systems from *z* = 0.5 to *z* = 0, with changes in M∗∼1.2 mag. This suggests that the mergers of the M∗ galaxies in fossil systems have a significant impact in the formation of the bright cluster galaxies. In contrast, the faint-end slope of the luminosity function shows no considerable redshift evolution in fossil systems, unlike in non-fossil ones where it grows by 25–42% towards low redshifts.

#### **4. Observational Properties**

In this section, we review the observational properties of FGs. In Section 4.1, we describe the properties of the intra-cluster medium; in particular, we present global scaling relations, mass and entropy profiles, cool cores, halo concentrations, and metallicities. In Section 4.2, we analyse the galaxy population and, in particular, FGs' luminosity functions, galaxy substructures, stellar populations, central galaxies, and large scale structures.

#### *4.1. Properties of the Halos*

The intra-cluster medium (ICM) is the largest baryonic component in galaxy clusters, responsible for ∼10% of the total mass of the cluster, e.g., in [41]. In fact, galaxy formation is inefficient and only ∼10% of the gas is converted in stars and galaxies [42], leaving the vast majority adrift in the intra-cluster space. This gas is trapped in the deep potential well of the cluster and heated to X-ray-emitting temperatures through shocks and adiabatic compressions [43].

Gravitational collapse predicts tight scaling relations between ICM and cluster mass, according to the so-called self-similar model [44,45]. Moreover, cosmological simulations predict that the scaled thermodynamical profiles of galaxy clusters are nearly universal, e.g., in [46]. For these reasons, the ICM is a powerful tool to study the formation and evolution of galaxy clusters: deviation from the gravitational collapse predictions can be used to investigate non-gravitational physics, such as cooling and feedback from supernovae and active galactic nuclei (AGN).

#### 4.1.1. Global Scaling Relations

In the left panel of Figure 4, we show the correlation between X-ray temperatures and luminosities for various samples of FGs and non-FGs. It can be seen that both types of objects are found in the same, tight, correlation. We won't enter into a detailed discussion of purely X-ray relations and their meaning, we refer the reader to the companion review by Lovisari et al. for a description of X-ray scaling relations in galaxy groups. The result presented in the left panel of Figure 4 can be extended to all those relations that only involve X-ray data: FGs and non-FGs are usually found in the same correlations. This seems to indicate that FGs and non-FGs are formed in a similar way.

However, discussion arose in those studies focused on the comparison between X-ray and optical properties of FGs and non-FGs. In fact, Jones et al. [9] and Khosroshahi et al. [47] found FGs to be over luminous in X-rays using samples of five and seven FGs, respectively. They claimed FGs to be a factor 5–10 brighter than regular groups or clusters in the X-ray.

On the other hand, more recent studied found no differences in the statistical properties of FGs and non-FGs samples [14,48,49]. In particular, these authors claimed that it is crucial to use homogeneous data and procedures to analyse both the FG and the control samples. According to their statements, this could be the source of the excess of X-ray luminosity (or the lack of optical luminosity) found in the previous studies.

**Figure 4. Left panel**: The X-ray temperature versus the bolometric X-ray luminosity as presented in Kundert et al. [50]. Grey triangles and squares are groups and clusters, respectively. Systems labeled with K+ are taken from Kundert et al. [50], Z14 from Zarattini et al. [22], G14 from Girardi et al. [49], M12 from Miller et al. [51], P11 from Proctor et al. [52], KPJ from Khosroshahi et al. [47], and H12 from Harrison et al. [14]. The plotted lines are the orthogonal BCES fits to the fossil sample (dashed line) and to the sample of groups and clusters (solid line) computed in the same range of parameters. **Right panel**: the total *r*−band luminosity versus the bolometric X-ray luminosity as presented in Kundert et al. [50], with the same lines of colour code as in the left panel, see the Figure 5 of [50] for details.

Nevertheless, Khosroshahi et al. [53] discussed a sample of groups, one of which defined as fossil that lies above the *LX* − *Lopt* relation of non-fossil systems, reopening the debate on fossil system scaling relations.

The (possible) final point of this debate was put by Kundert et al. [50]: as well as demonstrating that no differences are found between fossils and non-fossils in their sample of 10 groups and clusters observed with specific Suzaku follow up, they recomputed the luminosities of the FGs from Khosroshahi et al. [47] and Proctor et al. [52] in a homogeneous way. In the right panel of Figure 4, we show the relation presented in Kundert et al. [50]. The authors concluded that the discrepancies in the literature can be reconciled if X-ray and optical luminosities were computed using the same bands and radii, pointing out that many differences could be due not only to the low statistics but also the lack of homogeneous datasets.

In parallel with the discussion on the *LX* − *Lopt* relation, a debate on the mass-to-light (M/L) ratio of FGs arose. In fact, if there is a chance that FGs are under luminous in the optical bands, they should have larger M/L ratios than non-FGs [47]. Again, the studies available in the literature are somewhat contradictory. Sun et al. [11], Khosroshahi et al. [12,16] found normal values for their samples of FGs, compatible with non-fossil systems, although if marginally darker for a fixed mass. On the other hand, Vikhlinin et al. [5] found a high M/L for their sample of overluminous elliptical galaxies (OLEGs, about three times larger). The same result was found by Proctor et al. [52] in analysing a sample of 10 FG candidates. The authors suggested that FGs are simply dark clusters: they are characterised by a mass and a central galaxy that are typical of galaxy clusters, but embedded in a poor environment, so that the richness and the total optical luminosity are below the non-fossil ones. Finally, Yoshioka et al. [15] also found high M/L ratios for their sample of "isolated X-ray overluminous elliptical galaxies." However, we suggest that inconsistencies in the measured M/L ratios could be due to differences in the methodology

and quality of the data. For example, the optical luminosities of Vikhlinin et al. [5] and Khosroshahi et al. [12] are computed in the R band and within *r*<sup>200</sup> for every object in the sample, those of Proctor et al. [52] in a variable radius of 500–1000 kpc, whereas Sun et al. [11] estimated a normal M/L ratio from the gas fraction profile out to 450 kpc, and Yoshioka et al. [15] uses the B-band luminosity of the BCG as the total luminosity of the system. Thus, it seems reasonable that the disagreement between different results could be healed only with a homogeneous study of a large sample of FGs. As we already mentioned for other topics, such a study is far from being performed.

#### 4.1.2. Mass and Entropy Profiles

The study of mass profiles in clusters is an important tool to confirm the ΛCDM paradigm. In fact, this model predicts a universal mass profile that does not depend on the mass of the cluster, and it is usually assumed to have the shape of a Navarro–Frenk–White profile NFW [54].

Mass profiles were studied mainly for individual FGs, or small samples, making difficult to extrapolate general conclusions. Possibly the first mass profiles of FGs to be computed were those of NGC 6482 [16], RX J1416.4 + 2315 [12], and ESO 3060170 [11]. The first two systems shows a mass profile well described by an NFW, with a high central concentration that was interpreted as a sign of early formation. On the other hand, the mass profile of ESO 3060170 showed a flattening in the external regions not compatible with numerical simulations and also confirmed in Su et al. [55] out to the virial radius. Yoshioka et al. [15] studied the mass profiles of four FG candidates, finding no differences with normal groups/clusters. In addition, Gastaldello et al. [56] studied the mass profile of ESO 3,060,170, within a sample of 16 relaxed groups and clusters: they found a good agreement with a NFW profile, but it must be noticed that their data reached R∼200 kpc, whereas Sun et al. [11] and Su et al. [55] data reached R∼500 kpc and R∼1000 kpc, respectively. The three mass profiles are comparable within R∼200 kpc and differences with the standard NFW profiles rose in the most external regions. This clarifies again the complexity of the comparison when individual FGs are studied using data from different sources, within different radii, and treated with different techniques. Another two mass profiles for the FGs RXC J0216.7-4749 and RXC J2315.7-0222 were studied in Démoclès et al. [57]. Only the latter has a good profile, well fitted, out to *R*500, by a NFW profile plus a central stellar component.

Entropy is also of great interest because it controls ICM global properties and records the thermal history of a cluster, since it is conserved in adiabatic processes. Entropy is therefore a useful quantity for studying the effects of feedback on the cluster environment and investigating any breakdown of cluster self-similarity. Most of the studies cited for the discussion of the mass profiles were also able to compute an entropy profile. Again, since only individual systems were studied, the results are somewhat controversial and it is not trivial to generalise the conclusions to the entire FG category. In particular, Démoclès et al. [57] found that the entropy profiles out to *R*<sup>500</sup> of their two FGs show a considerable excess above the expectations from non-radiative simulations, especially for RXC J0216.7-4749. This is expected if significant non-gravitational processes affect the ICM. Su et al. [55] found and entropy profile that is in agreement with simulations out to ∼0.9 *R*<sup>200</sup> and then flattens in the outskirts, due to gas clumpiness and outward redistribution. Humphrey et al. [58] studied RXJ 1159+5531 combining Suzaku, Chandra, and XMM observations to find no evidence of the flattening in the entropy profile outside ∼R500. A similar results was also found in Su et al. [59] for the same cluster: its entropy profile is consistent with predictions from gravity-only simulations.

The urge for a systematic study of a large sample of FGs in the X-rays appears as necessary to constrain the average mass and entropy profiles of these objects. However, it seems difficult to realise, due to the small number of nearby FGs that can be deeply observed with current X-ray facilities. An improvement on this side is expected with the next all-sky survey that will be taken by eROSITA and Athena missions. The former is

expected to find ∼10<sup>5</sup> X-ray clusters and groups, and the latter will take advantage of its high-resolution for better constraint radial profiles of, for example, temperature, density, and mass.

#### 4.1.3. Cool Cores

Early observations of the gas in galaxy clusters found that it was so dense in the central regions that its cooling time was much shorter than the Hubble time, e.g., in [60]. The majority of the clusters studied in the literature show these cool cores, CC, e.g., in [61,62]. CCs are usually associated with relaxed clusters, since mergers easily erase them. For this reason, it appeared as natural to look for CCs in FGs, in order to confirm their *old and dynamically relaxed* status.

The first study on CCs for a sample of FG candidates was done by Vikhlinin et al. [5]. In their work, the authors studied four isolated elliptical galaxies selected from ROSAT X-ray data and confirmed as fossil systems with a dedicated optical follow up. It is worth noting that the authors suggested that these objects could be FGs, but, at the time, no operational definition was available, so no Δ*m*<sup>12</sup> is computed in their paper. However, at least three out of four were later confirmed as FGs in other publications, confirming the accuracy of their approach. Vikhlinin et al. [5] results indicated the presence of CCs in the central regions of these objects.

Later works were focused on deeper studies of individual FGs and found controversial results: Khosroshahi et al. [12,16] found no central drop in NGC 6482 and RX J1416.4 + 2315. On the other hand, Sun et al. [11] found a CC in ESO 3060170, as well as Démoclès et al. [57] for RXC J0216.7-4749 and RXC J2315.7-0222 and Su et al. [59] for RXJ1159 + 5531. It is interesting to note that Miraghaei et al. [63] studied three of the cited clusters (NGC 6482, RX J1416.4 + 2315, and ESO 3060170) using radio observations, finding signs of recent AGN activity only in the first two. However, the AGN power computed was not sufficient to remove CCs from these clusters.

The need for larger samples was partly satisfied only recently, when Bharadwaj et al. [64] studied a sample of 17 FGs for which Chandra archival data were available. They defined three different diagnostics to evaluate the presence of CCs, and they found that ∼80% of FGs showed clear hints of the presence of CCs (e.g., at least two diagnostics compatible with the CC).

It seems, thus, reasonable to claim that FGs are mostly cool-cored. However, the fraction of FGs with a CC is similar to that of non-FGs. For example, Hudson et al. [62] studied a large sample of 64 galaxy clusters for which high-quality X-ray data from Chandra were available, finding that ∼70% of their clusters host a CC. It thus seems that this is not a peculiar behaviour of FGs.

#### 4.1.4. Halo Concentration

One of the main parameters of the NFW model is the concentration, usually computed as *c*<sup>Δ</sup> = *r*Δ/*rs*, where *r*<sup>Δ</sup> represents the radius of a sphere of mean interior density *ρ*<sup>Δ</sup> and *rs* is the scale radius of the NFW profile. Typical values of Δ are 200 (often assumed to be equivalent to the virial radius) or 500.

Navarro et al. [54] pointed out that the concentration parameter reflects the density of the Universe when the halo formed. In particular, older halos formed in higher-density environments and tend to have larger concentrations. Several theoretical studies found that FGs assembled half of their mass at earlier epochs than non-fossil ones, see, e.g., in [30,37]. In this framework, it is expected that FGs would be located in high concentrated halos. Different numerical models are used in the literature to compute halo concentration in clusters, e.g., in [65,66]. Thus, observational results can be easily compared with theoretical predictions to test the formation scenario of FGs.

From an observational point of view, various methods can be used to compute the *c* parameter. A first approach to derive the central concentration of DM halos is to measure the gas mass profile in the X-rays out to *r*<sup>200</sup> or *r*500, fit with an NFW profile and then use the derived *rs* to compute the concentration. Using this approach, Khosroshahi et al. [16] Khosroshahi et al. [12] Khosroshahi et al. [47], and Buote [67] found concentration values higher than expected for their samples of individual FGs Other authors, like Démoclès et al. [57] and Pratt et al. [68], found normal concentrations in a total of six FGs. Again, comparing results with such small statistics and taking into account non-homogeneities in the analytic procedures makes it difficult to reach a final conclusion that can be applied to the mean FG population.

However, other approaches can be used to measure halo concentration. In particular, Vitorelli et al. [69] stacked ∼1000 systems from the CS82 survey in different magnitudegap bins, the larger of which has mean Δ*m*12∼1.7. They cross-correlate weak lensing measurements with NFW parametric mass profiles to measure masses and concentrations of their sample. They found that halos in the Δ*m*12∼1.7 bin have a higher probability to be more concentrated and, thus, probably formed earlier.

Finally, the halo concentration can be estimated using the velocity of member galaxies as tracers of the underlying mass distribution. This was done in Zarattini et al. [70], where the authors analysed a sample of ∼100 clusters and groups, dividing them into different magnitude-gap bins. For each bin, they stacked all the available galaxies to increase the statistic. They found *c*<sup>200</sup> = 2.5 ± 0.4 for the bin with the largest magnitude gap (defined as Δ*m*<sup>12</sup> > 1.5). These values are in agreement, within the uncertainties, with their results in the other three magnitude-gap bins, as well as with other similar work in the literature of non-fossil clusters, e.g., in [71,72] and references therein. However, the large uncertainties typical of this observational technique prevented the authors from reaching a strong conclusion.

#### 4.1.5. Metallicity

The hot intra-group gas contains elements that are typically synthesized in stars and SNe. For general details on this topic, we refer the reader to the companion review of Gastaldello et al. Here, we focus on the single study conducted on metal abundances in FGs, presented in Sato et al. [73]. The authors get Suzaku data out to 0.5 *r*<sup>180</sup> for NCG 1550 and were able to confirm that the abundance ratios O/Fe, Mg/Fe, Si/Fe, and S/Fe are similar to those of other poor groups observed with the same satellite. Moreover, the number ratio of type-I and type-II SNe computed in Sato et al. [73] is also similar to that obtained for non-fossil groups. As a consequence, their work can be included in those that are not finding differences between FGs and non-FGs.

#### *4.2. Galaxy Population*

The study of the galaxy population in FGs is mainly done in the optical range. In this section, we will firstly discuss the observational properties of the central galaxies. We will then move to the luminosity functions, galaxy substructures, and the large-scale structure around FGs.

#### 4.2.1. Central Galaxies: Formation Scenarios

Central galaxies in clusters are a unique class of objects. They are usually the largest and most luminous member galaxies, and they lie very close to the peak of the cluster X-ray emission, e.g., in [71,74]. Moreover, in the velocity space, they sit near the rest frame velocity of the cluster [75–77]. These characteristics imply that the BCGs are located at the minimum in the cluster potential well. Zarattini et al. [70] found that there is a dependence of the velocity segregation on the magnitude gap. This result means that BCGs in FGs are located closer to the minimum of the cluster's potential well, when compared to BCGs in non-fossil systems. This difference is not found for satellite galaxies, independent from their mass.

The formation of central galaxies in FGs is thought to be the end result of the group evolution [4,9]. The main actor, in this scenario, would be dynamical friction. However, Sommer-Larsen [29] suggested that the main difference between FGs and non-FGs has to

be found in the initial velocity distribution. In particular, he found that satellite galaxies in FGs should be located on more radial orbits than in non-FGs. This would favour low angular momentum mergers, for which dynamical friction could be more effective [78].

Méndez-Abreu et al. [79] analysed the photometric properties of central galaxies in FGs. They studied the position of the central galaxies in FGs in the fundamental plane and its projections to explain the formation of these objects (see Figure 5). Central galaxies in FGs results in having large *K*-band luminosities. The *Ks* luminosity is a good proxy of the total stellar mass since the typical M/L ∼1 for an old stellar population [80]. Thus, it seems clear that central galaxies in FGs are amongst the most massive galaxies known. The left panel of Figure 5 shows the correlations between the *Ks*−band luminosities and the central velocity dispersion, Faber–Jakson relation in [81]. Similarly, the right panel of Figure 5 shows another projection of the fundamental plane, the *Ks*−band luminosity vs. effective radius (*re*). In both relations, BCGs in FGs are found slightly outside the correlations: this bend was found for the first time in Bernardi et al. [82] for early-type galaxies, and it can be interpreted in terms of the formation scenario of the BCGs. In particular, if major dissipationless mergers between galaxies are the main mechanisms to build up the mass of the BCGs, the final size is expected to increase, but not its central velocity dispersion; however, if minor dry mergers are the predominant mechanism, they are expected to change both the size and velocity dispersion of the BCGs. Thus, the results presented in Méndez-Abreu et al. [79] seem to favour the first scenario for these massive galaxies. This is also supported by new results obtained from numerical simulations. Kundert et al. [34] investigated the origin of FGs in the Illustris simulation. With respect to the stellar mass assembly of the BCGs, they found (see their Figure 6) that the accretion is similar at high-redshifts for fossil and non-fossil systems, whereas a clear difference starts to appear at *z*∼0.3. From this point, BCGs systematically accreted more mass in FGs than in non-FGs.

**Figure 5. Left panel**: distribution of the BCGs of Méndez-Abreu et al. [79] red stars and large black points and the early-type galaxies of Pahre et al. [83] small blue points in the log *σ*<sup>0</sup> vs log *Lks* plane. The BCGs in the Pahre et al. [83] sample are marked by blue open triangles. **Right panel**: same as the left panel, but in the log *re* vs. log *LKs* plane. The solid line represents the best fit to the galaxies in the luminosity range 3 <sup>×</sup> 1010 <sup>&</sup>lt; *LKs*/*L* <sup>&</sup>lt; <sup>2</sup> <sup>×</sup> 1011. The bottom panels represent the residuals from the best fit. The original image can be found in Méndez-Abreu et al. [79] and corresponds to their Figures 9 and 10.

However, this formation scenario is in contradiction with the one proposed by Khosroshahi et al. [12]: in fact, these authors found disky isophotes in their central regions of BCGs, in contrast with most BCGs in non-fossil systems [84]. This result seems to favour a scenario in which mergers in FGs were rich in gas, thus including large M∗ spirals. A similar result was found also by Eigenthaler and Zeilinger [85], since they found many

shells around central galaxies in FGs. These shells were likely formed recently via major mergers of spiral galaxies [86].

Signs of recent mergers were indeed found by Alamo-Martínez et al. [87] while analysing the surface brightness profiles of three FGs. However, this work was mainly focused on the study of globular clusters in FGs. These objects are powerful tools to study galaxy assembly, since they are old and dense enough to survive galactic interactions. Alamo-Martínez et al. [87] results seem to point out that globular clusters in BCGs formed in a similar way in fossil and non-fossil systems. In terms of the formation scenario of the BCGs, this can be take as a confirmation that similar processes are at work in the formation of BCGs in fossil and non-fossil systems, although more statistics is needed to generalise this conclusion. A similar result, in terms of the formation scenario, is found also in Madrid [88] and Madrid and Donzelli [89], in which the authors compared the properties of ultra-compact dwarf galaxies (UCDs) in FGs and in the Coma cluster. UCDs are considered the bright-and-massive tail of the globular cluster distribution. Their results showed that UCDs are likely to be a common occurrence in all environments.

The presence of AGNs can also be used to study the formation scenarios of BCGs. In fact, AGNs need major mergers to form, since they use the gas provided by the merger as their fueling mechanism. On the other hand, if no other merger occurred, they are destined to end this fuel and inactivate. Hess et al. [90] studied the sample of 34 FG candidates from Santos et al. [6] using radio observations in order to detect the presence of AGNs in FGs. They found that 67% of these FG candidates contain a radio-loud AGN. This result seems in contrast with the old formation expected for FGs: in fact, AGN should have run out of fuel since FGs's last major merger. For this reason, Hess et al. [90] suggested that other mechanisms, such as minor mergers, cooling flows, or late time accretion should be invoked to keep the AGNs alive in FGs. However, it is worth noting that the Santos et al. [6] sample was not pure and about half of the sample was formed by non-fossil systems [22].

#### 4.2.2. Central Galaxies: Stellar Populations Properties

We already mentioned that the formation scenario proposed by Ponman et al. [4] supposed that FGs formed at high redshift, with few interactions with the large-scale structure along their lives. This would leave enough time for the M∗ galaxies to merge with the BCG, thus forming the Δ*m*<sup>12</sup> gap. On the other hand, Mulchaey and Zabludoff [91] suggested the so-called *failed group* scenario, in which the BCG is formed as a local over density and no other bright galaxy formed within the group.

However, these two scenarios should also leave clear imprints in the stellar populations of the BCGs. In fact, in the *failed group* scenario, the central galaxy formed via monolithic collapse that is expected to create large radial metallicity gradients in the distribution of the stars. On the other hand, in the *merging scenario,* the BCG suffered various major mergers that have the power to erase those gradients, since they mix up the stars and gas during the merging process, e.g., in [92].

La Barbera et al. [7] were the first in using stellar populations to investigate difference between FG's BCGs and regular elliptical galaxies. They used spectra from the SDSS DR4 for their sample of 25 BCGs in FGs and 17 field elliptical galaxies that act as the control sample. They searched for the single-stellar-population model that best fits the spectra, thus computing mean ages, metallicities, and *α*−enhancement for the two populations of BCGs. The authors showed that no significant difference is found in these parameters and concludes that BCGs in FGs did not form earlier than the other galaxies.

Harrison et al. [14] select a sample of 17 FG candidates by combining XMM observations with SDSS DR7 data. They analyse the stellar populations of the BCGs of these systems using SDSS spectra and the Starlight code [93]. Their results showed no significant differences in stellar star formation rates, age, and metallicities between FGs and their two control samples, one built by optically-selected BCGs, the other with X-ray-selected BCGs.

Eigenthaler and Zeilinger [94] studied the presence of such gradients in age and metallicity for a sample of six BGCs in FGs using longslit spectroscopy from the 4.2 m William Herschel Telescope (WHT). They found that the metallicity gradient is flatter with respect to the predictions of the monolithic collapse (∼−0.2 instead of −0.5), thus indicating the presence of mergers during the life of the BCGs. On the other hand, the age gradient is, on average, negligible.

A similar study was performed by Proctor et al. [95] for a sample of two central galaxies in FGs, using longslit spectroscopy obtained with the 8 m Gemini North telescope. The authors found different results for the two BCGs: SDSS J073422.21 + 265133.9 showed a strong metallicity gradient and a slightly positive age gradient, suggesting a relatively recent episode of stellar formation in the centre. NGC 2484, on the other hand, showed an old stellar population (∼10 Gyr) and a flat central metallicity that was interpreted as the evidence of an inside-out stellar formation, at least in the final episode of stellar formation.

Trevisan and Mamon [96] studied a large sample of 550 groups to characterise the dependence of the stellar populations of the BCGs and the second brightest galaxies with the magnitude gap. They did not find differences in the distribution of colours, starformation rates, *α*−enhancement, age, metallicities, and star-formation histories in systems with different Δ*m*12.

Corsini et al. [97] studied both the stellar populations and radial gradients for a sample of two BCGs in FGs using the 10.4 m Gran Telescopio Canarias (GTC) telescope. They confirmed the results of La Barbera et al. [7] and Eigenthaler and Zeilinger [94] out to the effective radius. They found an underlying and diffuse older stellar population, with a younger one located near the centre of the galaxies. This was interpreted as the sign of the last major merger with gas, which occurred ∼5 Gyr ago. Corsini et al. [97] also found a radial metallicity gradient in agreement with the Eigenthaler and Zeilinger [94] one.

Finally, Raouf et al. [98] divided a sample of groups from the Galaxy and the Mass Assembly (GAMA) survey into relaxed and unrelaxed, using Δ*m*<sup>12</sup> and the luminosity offset as the relaxation indicators. They found that BCGs in unrelaxed systems are bluer, more star forming, and with non-elliptical morphologies than those in relaxed systems. They conclude that the higher rate of recent mergers expected in unrelaxed groups could be responsible for these differences. A similar result was also found in Pierini et al. [99]. These authors claimed that there are few star-forming galaxies in FGs, making them more mature then coeval and similar mass groups.

Very recently, Raouf et al. [100] studied the kinematic of gas and stars in 154 central galaxies taken the Sydney-AAO Multi-object Integral field (SAMI) galaxy survey. In particular, they divided this sample into low and high luminosity gap system, with the latter that can be assimilated as FGs. They found that there is a weak statistical difference (at approx. 1−*σ* level) between the magnitude gap and the gas-star kinematics misalignment. In addition, a similar difference was observed between the magnitude gap and the regularity of the stellar rotation of the BCGs. In particular, systems with high magnitude gaps are found to be more regular rotators and with a smaller fraction of gas-star misaligned kinematics.

These studies did not find relevant differences in the stellar populations of central galaxies in fossil and non-fossil systems. The imprint of monolithic collapse is not found, all the observations point towards the creation of FGs via the *merging scenario*, in which the gap is created via major mergers of M∗ galaxies. The possibility of the existence of a fossil phase in the life of a cluster is supported also by the presence of younger stellar populations in the centre of galaxy, probably due to recent major mergers with gas. In the top panel of Figure 6, we show the relation between central velocity dispersion and central metallicity for a sample of ten FGs taken from Eigenthaler and Zeilinger [94], Proctor et al. [95], Corsini et al. [97] and compared with the sample of normal and dwarf early-type galaxies of Koleva et al. [101]. In the lower panel of the same figure, the comparison is done for the central ages of the same samples. It can be seen that in both cases FGs are found in the same correlations as normal early-type galaxies. This plot again confirms that central galaxies in FGs are amongst the most massive known in the Universe.

**Figure 6.** Central metallicity (**top panel**) and central age (**bottom panel**) as a function of the central velocity dispersion. Red diamonds are taken from Corsini et al. [97], green open circles from Eigenthaler and Zeilinger [94], green filled circles from Proctor et al. [95], open and filled squares are the early-type normal and dwarf galaxies with *σ* > 50 km s−<sup>1</sup> from Koleva et al. [101]. The original image can be found in Corsini et al. [97] (see their Figure 8).

#### 4.2.3. Luminosity Functions

The luminosity function (hereafter LF) is one of the most powerful tools to study the galaxy population of a group/cluster of galaxies. It is given by the number density of galaxies per luminosity interval and it is usually described parametrically with the Schechter function [102]. The main parameters are the characteristic magnitude (M∗) and the faint-end slope (*α*). The former describes the bright part of the LF, whereas the latter is related to the dwarf galaxy population. A debate is ongoing on the universality of the LF: in fact, photometric studies found that LFs in clusters are steeper than in the field, −2.0 < *α* < −1.8 in clusters and −1.5 < *α* < −1.3 in the field, see [103,104]. On the other hand, spectroscopic studies found no differences in the *α* parameters of the field and clusters, finding a general value of *α* ∼−1.3 [105] and references therein.

The study of LFs in FGs was mainly focused on individual FGs, due to their paucity. As a consequence, most of the first results were contradictory. Mendes de Oliveira et al. [18] found, for the FG called RX J1552.2+2013, M<sup>∗</sup> = −21.18 ± 0.57 and *α* = −0.77 ± 0.37 using spectroscopically-confirmed members, or M<sup>∗</sup> = −21.27 ± 0.62 and *α* = −0.64 ± 0.30 for photometrically-selected galaxies in the *r*−band. In the same year, Khosroshahi et al. [12] computed *M*<sup>∗</sup> = −20.40 ± 0.22 and *α* = −1.23 ± 0.28 for RX J1416.4+2315, a fossil system with a mass similar to RX J1552.2 + 2013. In addition, Trentham et al. [106] presented an LF for a single FG (NGC 1407), finding *α* = −1.35. The difference, especially in the faintend slope, is important. In fact, *α* = −1 indicates a flat LF, in which the number of dwarf galaxies is not changing with magnitude. On the other hand, in a steeper function like that of Khosroshahi et al. [12], the number of dwarf galaxies is rapidly growing and, in a flatter one like that of Mendes de Oliveira et al. [18], it is decreasing.

Zibetti et al. [107] also studied the photometric LF of a sample of five FGs. They found a faint-end slope in agreement with the one of regular clusters presented in Popesso et al. [103]. However, it is worth noting that Popesso et al. [103] found an upturn at fainter magnitudes, so

that their LF can be fitted with a double Schechter function. This behaviour is not found on the already-cited LF of FGs because none of these are deep enough. However, Lieder et al. [108] computed a very deep LF for NGC 6482 using spectroscopic data from the Subaru/Suprime-Cam, finding *α* = −1.32 ± 0.05. They did not fit a double Schechter function; however, a change in the faint-end slope is present also in their Figure 12.

Aguerri et al. [13] presented the LF of RX J105453.3 + 552102, a massive FG at *z* = 0.5. They found *M*<sup>∗</sup> = −20.86 ± 0.26 and *α* = −0.54 ± 0.18, thus confirming a flatter trend for the dwarf galaxy population. Adami et al. [109] also computed the LF for two FG, finding that their faint-end slope is relatively flat, but without giving numbers. Finally, Aguerri et al. [110] studied the spectroscopic LF of RXJ075243.6 + 455653, finding *α* = −1.08 ± 0.33.

The first systematic study of the dependence of the LF on the magnitude gap was presented in Zarattini et al. [111]. The authors selected ∼100 clusters and groups spanning a wide Δ*m*<sup>12</sup> range and dividing their analysis in four bins of Δ*m*12. Their study was based on a hybrid method for computing the LF, in which the bright part was treated as a quasi-spectroscopic LF, whereas, in the faint end, photometric data were dominant. The authors computed a classical LF and one in which the magnitudes of each systems are referred to the magnitude of the central galaxy (e.g., *Mr* − *Mr*, *BCG*, called *relative* LFs). The latter permits to compare directly the differences due to the magnitude gap, and the authors found that this technique offers the best results for highlighting the differences between their four subsamples. These *relative* LFs are shown in the left panel of Figure 7. Zarattini et al. [111] found that both M∗ and *α* changes with the magnitude gap. In particular, systems with Δ*m*<sup>12</sup> < 0.5 have the brightest M<sup>∗</sup> and the steepest *α* slope, whereas systems with Δ*m*<sup>12</sup> > 1.5 have the faintest M<sup>∗</sup> and the flattest *α*. The differences are larger than 3*σ* between the two most-extreme cases and the trend with Δ*m*<sup>12</sup> is clearly visible in the right panel, where the values of the *relative* M∗ and *α* are shown for the four subsamples.

**Figure 7. Left panel**: *relative* LFs for the four subsamples presented in Zarattini et al. [111]. Empty black squares are systems with Δ*m*<sup>12</sup> < 0.5, filled red circles are systems with 0.5 < Δ*m*<sup>12</sup> < 1.0, empty violet circles are systems with 1.0 < Δ*m*<sup>12</sup> < 1.5, and filled green circles are systems with Δ*m*<sup>12</sup> > 1.5. **Right panel**: Uncertainty contours for the Schechter fits of LFs in the left panel. Contours represent 68%, 95%, and 99% c.l. and the colour and symbol codes are the same as in left panel. The original image can be found in Zarattini et al. [111]; in particular, the left panel corresponds to their Figure 7, the right panel to Figure 8.

The discussion is usually focused on the faint end of the LF, since differences in the bright part between fossils and non-fossils can be easily explained with the same mechanisms that are responsible for the creation of the magnitude gap. Moreover, the presence of the gap itself as a selection criteria implies differences in the bright part of the LFs.

On the other hand, the debate on the differences in the faint-end slope is more complex. In fact, dwarf galaxies can not be merged into the BCG in a reasonable time, since the merging time scale is inversely proportional to the mass of the satellite. A possible explanation is that dwarf galaxies are located in radial orbits passing close to the centre of the cluster. This will result in their disruption, accounting for a part of the missing population. This explanation was also invoked as a possible reason for the high merging rate of FGs. It can also justify the formation of the magnitude gap, since Lacey and Cole [78] showed that the merging timescale for satellite on radial orbits is shorter than for tangential ones. Another possibility is that FGs could lack dwarf galaxies for differences in their accretion time. In fact, Aguerri et al. [110] found that the large-scale environment of FGS03 is very rich, so the flat LF found could be explained if the dwarf populations are still trapped in nearby groups, awaiting to be merged with the FG. In this context, FGs would be systems in early stages of their mass assembly. We will discuss in more detail the large-scale structure of FGs in Section 4.2.5.

Differences in the accretion history of dwarf galaxies were indeed found also in Kanagusuku et al. [40] while studying the bright and dwarf galaxy populations in fossil and non-fossil clusters in the Millennium simulation. They found that FGs had a denser dwarf population at an early time (*z* > 0.7); then, the trend reverses (0.5 < *z* < 0.3), and, finally, it becomes similar at *z* = 0.

To finally solve the issue of the observed lack of dwarf galaxies in FGs, deep and extended spectroscopy would be needed. We will discuss in Section 6.2 the expected impact on this topic of the next-generation spectroscopic surveys.

#### 4.2.4. Galaxy Substructures

If the *old and relaxed* model is correct, one should expect to find a smaller amount of galaxy substructures in FGs than in non-FGs. The only study on this topic was done in Zarattini et al. [112]. They analysed the sample of 34 FG candidates of the FOGO project to compute the fraction of FGs with signs of substructures using a variety of methods. In particular, the entire sample was studied with a two-dimensional approach, able to detect substructures in the projected space of the cluster. Moreover, for a subsample of candidates for which an extended spectroscopic follow up was available, they also applied a series of one- and three-dimensional tests (e.g., the Dressler–Schectman test).

Zarattini et al. [112] results depend critically on the adopted tests, but the comparison with a control sample shows that galaxy substructures are present in a similar fraction in fossil and non-fossil systems. This presence of substructures in FGs is hardly compatible with an old formation, followed by a passive evolution, with no major interactions with the surrounding large-scale structure. Indeed, the small number of genuine FGs in the sample prevent reaching a definitive conclusion.

#### 4.2.5. Large Scale Environment

Differences in the large-scale environment and in the way in which it interacts with FGs were invoked as a possible cause of the different evolution of FGs and non-FGs [4,30,113]. Observational results are scarce on this topic, since only few individual FGs were studied so far.

Adami et al. [114] studied the large-scale structure around the FG RXJ1119.7 + 2126 using spectroscoic data. They conclude that this FG is located at the centre of a low galaxy density bubble.

Pierini et al. [99] found controversial results in their analysis of two FGs. One of the two is found in an isolated environment, whereas the second one is located in a dense environment, with 27 other groups or clusters in the surroundings.

In addition, Adami et al. [109] studied the environments of other three FGs using photometric and spectroscopic data. They found that one system (1RXS J235814.4 + 150524) is in a poor environment, though its galaxy density map shows a clear signature of the surrounding cosmic web. The second FG (RX J1119.7 + 2126) is very isolated, whereas the third one (NGC 6034) is embedded is a very rich environment.

Finally, Díaz-Giménez et al. [113] analysed the large-scale structure in FGs and non-FGs from both the theoretical and observational points of view. We already mentioned their theoretical results in Section 3, here we focus on their observational tests. In fact, they used four FGs selected from Voevodkin et al. [48] and coming from the 400d cluster survey [115] and a control sample of non-FGs from the same survey. Their observational results confirmed the peak found in numerical simulations in the local density profile of galaxies around groups as a function of the normalised group-centric distance. This peak, located at about 2.5*r*/*rvir* at *z* = 0, is more prominent in FGs. However, the difference is clearer in numerical simulations than in observations, probably again due to the small sample of FGs available.

More extended studies on larger samples are thus generally needed to confirm if FGs are characterised by a special large-scale environment.

#### **5. Past and Future of Fossil Systems Evolution**

If FGs are the end product of groups/clusters evolution, a question should naturally arise: are their progenitors regular groups/clusters or do they belong to some particular class? A possible answer that we will discuss in the first part of this section is that the progenitors could be found in compact groups. In fact, in these systems, various bright galaxies are cooped up in a small area, making them ideal candidates for fast and efficient mergers.

However, von Benda-Beckmann et al. [37] suggested that the fossil status may be only a transitional phase in the life of a regular cluster. If this is the case, there is no need to find a special category of progenitors, since the acquisition of the fossil status could happen to any group/cluster in the period between the last major merger and the subsequent arrival of another bright galaxy from the cosmic web. We will discuss this topic from an observational point of view in the second part of this section.

#### *5.1. Compact and Loose Groups as Progenitors of Fossil Systems*

The discussion on the progenitors of FGs started even before the actual discovery of these systems. In fact, Ponman and Bertram [3] suggested that compact groups were the result of orbital decay in larger systems and that they should culminate in a final merger, in which all the bright galaxies would merge at the centre of the system. They also added that a new category of "fossil groups" were awaiting discovery in the ROSAT all-sky survey. A year after this claim, they announced the discovery of the first FG [4].

Since then, many studies looked for FG's progenitors, using a variety of techniques. Miles et al. [116] studied a sample of 25 clusters in the X-ray, finding that some of them are dimmed in luminosity. Their interpretation of the result was that, according to a specific toy simulation, groups with dimmed X-ray luminosity have lower velocity dispersion. This would lead to the formation of FGs, since low-velocity encounters between massive galaxies are the most efficient in terms of merging time scale. This result was also confirmed by the analysis of a compact group at *z* = 0.22 studied in Mendes de Oliveira and Carrasco [117]. In fact, these authors showed that this system has many characteristics in common with FGs and, in particular, the merging of the four brightest members would lead to the formation of a BCG of *Mr*∼−23, a typical value of central galaxies in FGs. A similar result was also found in the study of galaxy pairs [118]. In this case, the author claims that E + S pairs could be the last step in the formation of FGs, thus a sort of transition

between compact groups and FGs. In addition, Pierini et al. [99] found evidence that compact groups are favoured as progenitors over the early assembly. On the other hand, Yoshioka et al. [15] found a M/L ratio for FGs that is too high if compared with compact groups, thus claiming that these systems are not the ideal progenitors.

A novel technique to search for FG's progenitors is the use of strong gravitational lensing in galaxy groups. Johnson et al. [119] investigated the fraction of FGs in lensed and non-lensed galaxy groups, finding that the fraction of FGs is larger in lensed systems (13% versus 3%). They also identified 12 possible FG progenitors that were later investigated in detail in Johnson et al. [120] using Chandra and the Hubble Space Telescope. Their results showed that the X-ray temperatures of the candidate progenitors are higher than those of the control sample. They also find hints of differences in the LFs of FGs and non-FGs, but these differences are erased when BCGs are removed. Finally, Schirmer et al. [121] studied the strong-lensed FG J0454-0309 that is found behind a well-studied non-fossil poor cluster. Their analysis supports a scenario in which the fossil system is falling into the poor cluster and where the central galaxy of the FG will become the brightest galaxy of the new system.

Another approach was proposed by Tovmassian [122]: they compared the *K*−band absolute magnitudes of BCGs in regular clusters and FGs, finding that the latter are systematically fainter. The author concluded that FG progenitors are likely poor groups. Moreover, it is interesting to note that Tovmassian et al. [123] studied "*the properties of Hickson's compact groups and of the Loose Groups within which they are Embedded*." In this work, no link with FGs is suggested, but the result could be seen under a different light after the Tovmassian [122] study, confirming the idea that poor compact groups could be the ideal progenitors of FGs. However, this result apparently collides with what was presented in Section 4.2, where we cited various studies claiming that BCGs in FGs are amongst the most-massive galaxies in the Universe. On the other hand, Farhang et al. [124] analysed the mass assembly histories fo compact and fossil systems in the Millennium simulation and associated semi-analytical models. They found that only 30% of FGs could originate from compact groups. They conclude that most of the fossil and compact groups follow different evolutionary paths.

Finally, Buote and Barth [125] suggested that compact elliptical galaxies (CEGs) surrounded by an X-ray halo should be considered as FGs. In fact, detailed X-ray observations of two of these systems found that mass and entropy profiles and concentration are compatible with other FGs studied in the literature. In this case, the progenitors are expected to be the so-called "red-nuggets", compact galaxies found a *z*∼2 [126]. This case is indeed peculiar: the authors did not study FGs in order to find their progenitors, but better suggested that a new type of galaxy should be considered in the fossil category.

#### *5.2. Transitional Fossil Phase*

We already mentioned in Section 3 that von Benda-Beckmann et al. [37] suggested that FGs are only a transitional phase in the life of a regular group/cluster. They claimed that this phase would happen just after a major merger and before other bright galaxies are accreted to the group. An example of such a process is found in Irwin et al. [127]: the Cheshire Cat galaxy group is formed by two smaller groups, dominated by one bright galaxy each. These groups are experiencing a line-of-sight merger that will end up in approximately one Gyr with the merging of the two structures. The authors suggested that the resulting structure will be a massive fossil group, dominated by a large *Mr* = −24 galaxy.

A similar case is the one presented in Aguerri et al. [110]: RX J075243.6 + 455653 was found to actually accomplish the fossil definition of Δ*m*<sup>12</sup> > 2 within half the virial radius; however, another galaxy almost as bright as the BCG is found just outside that radius. Depending on its orbit, RX J075243.6 + 455653 became fossils in the very last part of its life, or, in the opposite case, it will become non-fossils in the near future.

The existence of a fossil phase may thus explain some of the controversial results presented along this review. It is possible that the observational definition based on the magnitude gap alone is not sufficient to clearly separate the population of real FGs to that of non-FGs dominated by a massive central galaxy. This would confirm the results of Raouf et al. [32], since the authors suggested that other observational quantities (like the luminosity of the BCG and its separation from the luminosity centroid of the group) should be used to create a sample dominated by purely old FGs. We thus suggest to start using this new definition in the search for FGs as a way for creating a sample of old systems. However, using these additional observational constraints could dramatically reduce the number of identified systems. In Section 6.1, we will give a list of the most-secure FGs up to date: only one out of 18 FGs for which the absolute magnitude of the BCG is available will survive the application of the Raouf et al. [32] criterium (Δ*m*<sup>12</sup> > 2.0 and *Mr*,*BCG* > −22.5).

#### **6. Discussion and Conclusions**

In this section, we propose a sample of genuine FGs that can be the starting point for new follow ups of these objects. Then, we discuss what we presented along the review and draw our general conclusions.

#### *6.1. Sample of Genuine Fossil Groups*

In Table 1, we present a list of confirmed FGs in the literature. The goal is to offer to the reader a sample as pure as possible for future follow ups. The list is probably not complete, but we did our best to select FGs applying a rigorous criterium on the Δ*m*<sup>12</sup> parameter. In particular, we consider as fossils those systems with Δ*m*<sup>12</sup> ≥ 2.0 within half the (projected) virial radius. Moreover, we exclude FGs for which membership was done using a fixed cut in Δ*z*, except when no ambiguous galaxy was found within half the (projected) virial radius. The magnitude gap between the first and fourth brightest galaxies (Δ*m*14) is also given, when available, but it was not used for the selection, since it was computed only in the most recent studies. The absolute *r*−band magnitude of the BCG is included, when available, to simplify the application of the Raouf et al. [32] criterium. Moreover, we also list the mass of the system, when available. However, we note that the mass is computed in a very inhomogeneous way (different methods and radii), and our goal is to offer an at-a-glance reference to the reader. Finally, the redshift is given for all FGs listed in the table.

**Table 1.** A non-exhaustive list of confirmed FGs for which at least Δ*m*<sup>12</sup> ≥ 2 (and eventually Δ*m*<sup>14</sup> ≥ 2.5) is computed within half the virial radius in the literature.



**Table 1.** *Cont.*

Notes. Column (1): System name, as presented in the cited publication. Column (2): Magnitude gap between the two brightest member galaxies. Column (3): Magnitude gap between the first and fourth brightest member galaxies. Column (4): *r*−band absolute magnitude of the BCG. (5): redshift. (6): Mass. Column (7) Reference paper. It is worth noting that we only cite minimal references for each FG and the same object can be also found in other publications. Moreover, we only cite systems for which Δ*m*<sup>12</sup> is strictly larger than 2, in order to propose a sample of genuine fossil systems. \* This system is disqualified as a fossil in Mendes de Oliveira et al. [130] using *i*− and *g*−bands. \*\* This system is disqualified as a fossil in Zibetti et al. [107]. † Computed in the *<sup>i</sup>*−band.

> We note that, if contradictory information is available, we always choose to apply the Jones et al. [9] criteria in the most severe way. For example, in Proctor et al. [52], the sample of Miller et al. [51] was studied in more detail, computing *r*<sup>200</sup> in two different ways: one obtained from weak lensing analysis and the other from X-ray data. The latter is found to be ∼50% larger than the former. As a consequence, the number of FGs found using the smallest radius is 10, a number that reduces to 3 if the largest radius is used. In order to provide the cleanest sample of genuine FGs, we include in Table 1 only the three obtained with the largest *r*200, citing only Proctor et al. [52], even if most of the candidates were also present in Miller et al. [51]. This choice is done in order to direct the reader to the most up-to-date and/or relevant information.

> It is worth noting that some famous FGs are excluded from the list. As an example, we discuss the prototype of this category, NGC 1132 [91], for which we were not able to find Δ*m*12. There are indeed information on the fainter galaxies, e.g., in [131], but not a clear computation of the magnitude gap. However, Kim et al. [131] claimed that the second brightest galaxy is NGC 1126, a spiral galaxy located at 8.4 arcminutes or 230 kpc in projection. The virial radius of this group is estimated to be *r*200∼800 kpc; thus, this galaxy should be inside 0.5 *r*200. The difference in the velocity space is Δ*v* = 438 km s−1, as obtained using the Nasa Extragalactic Database (NED), so the two galaxies can be part of the same group, although a precise dynamical study should be done to confirm the membership. In Kim et al. [131], NGC 1126 is described as "seven times fainter in B". We check in the SDSS DR16 the magnitudes of both NGC 1132 and NGC 1126: the former has *mr* = 12.20, the latter *mr* = 14.01, leading to a Δ*m*<sup>12</sup> = 1.81, rejecting it as a genuine FG. However, as we already mentioned, an accurate study of the membership of NGC 1126 to the group of NGC 1132 should be done and errors in SDSS magnitudes can not be excluded (NGC 1126 is flagged with "unreliable photometry", as many other bright galaxies, mainly due to an over estimation of the sky around bright objects). In conclusion, with this example, we aim at demonstrating that also the definition of the most commonlyaccepted FGs may be not rigorous, or may need deeper studies to include them in a sample of genuine FGs.

#### *6.2. Conclusions and Future Prospects*

Along this review, we analysed the most-studied topics on FGs. The aim of these studies was to test the so-called *merging scenario*, which predicts that fossil systems formed earlier than non-fossils, having enough time to merge all the bright galaxies with the BCG and remaining somewhat isolated from the cosmic web (e.g., they did not receive other bright galaxies from the merging with other groups/clusters). However, the general framework that can be obtained from this review is that FGs probably formed and evolved in a similar way as non-FGs. In particular, we show that early differences reported in global properties such as the scaling relations and M/L ratios of the halos of fossil systems can be reconciled when homogeneous datasets are used. Probably, an analogous result would be obtained for the differences observed in the mass and the entropy profiles in some individual systems. A more homogeneus and large sample is required to be analysed in this case. Moreover, no differences are found in the fraction of galaxy substructures identified in FGs and non-FGs. This again indicates that the halos of FGs are not significantly older than those from non-FGs.

The central galaxies in fossil groups show similar stellar ages and metallicities than BCGs in the center of non-fossil systems. In addition, the location of these galaxies in the fundamental plane and its projections indicate a formation process driven by dissipationless mergers in a similar way to other bright early type galaxies.

The similarities found in the formation of fossil and non-fossil systems seem to indicate that the large magnitude gap could just be a transient phase in the evolution of groups and clusters, as reported by different numerical simulations. This magnitude gap would be more connected with recent major mergers rather than with an old formation.

If this is the case, one should find an explanation for those differences that can not be reconciled with inhomogeneities in the data. We already mentioned that Sommer-Larsen [29] proposed that more radial orbits for galaxies in fossils could be responsible for the formation of the gap. This idea is supported also by Lacey and Cole [78]: the merger timescale with the central halo is shorter for M∗ galaxies on radial orbits than for galaxies on tangential orbits (see their Equation (4.2)). From an observational point of view, hints of this difference are found in Zarattini et al. [132]. The authors studied the orbital structure of a sample of ∼100 groups and clusters, dividing them in four bins of Δ*m*12. Their larger magnitude gap bin (Δ*m*<sup>12</sup> > 1.5) shows the presence of radial orbits in the external regions (0.8–1 *r*200) that is not found in the other three bins, all with Δ*m*<sup>12</sup> < 1.5. However, the results should be confirmed with a larger sample of genuine FGs, as we already mentioned along this review for a significant part of the discussed topics.

The other main topic that remains open is the difference found in the faint-end slope of FGs LFs. This is difficult to explain within the current models of formation and evolution of clusters. In fact, most of the studies point towards a sort of *global* value for the faint-end slope in clusters and groups. It is worth noting, however, that the majority of the studies of LFs in FGs used photometric data and that, in the literature, significant differences were found even in regular clusters when only photometric data were used. Thus, the next step in this discussion awaits the use of large spectroscopic datasets that will become available with the next generation of astronomical instruments (e.g., WEAVE, 4MOST, DESI). However, we can tentatively say that the presence of radial orbits could give an answer also to the problem of the faint-end slope of the LF: in fact, if massive galaxies on radial orbits have a shorter timescale to be merged within the central galaxy, dwarf galaxies could be more easily disrupted on such orbits, if they pass near the BCG [133]. Another possible explanation for the differences in the galaxy populations between FGs and non-FGs could be found in the surrounding environment, since hints of different largescale structures are found in some individual studies. In particular, we can not exclude that FGs are still in the process of accreting dwarf galaxies, but the general picture remains to be clarified.

The creation of a large and strict sample of genuine FGs and a homogeneous follow up will be the key to the characterisation of FGs in the near future. For this reason, we gave in Section 6.1 a table with the most-secure FGs to date. The computation of the Δ*m*<sup>12</sup> is not a real issue with surveys like SDSS, DES, or Pan-STARRS1, already available for 3/4 of the sky. The arrival of new facilities will be useful for the confirmation of the FGs candidates found with these photometric surveys. New X-ray data will be available with the new all-sky surveys like eROSITA (we refer the reader to the companion review of Ekert et al. for a detailed description on the impact of eROSITA and other X-ray surveys on the study of galaxy groups). In addition, the spectroscopic follow up will be possible with extended spectroscopic surveys like WEAVE, 4MOST, and DESI or with precise photometric redshifts surveys like J-PAS. The firm identification of at least 50/100 FGs will be the main scientific goals in this field for the next decade. This will be easily achieved in the near future, since eROSITA is expected to find ∼105 groups/clusters. For comparison, the REFLEX cluster catalogue has ∼1500 groups/clusters. Most of these new clusters will have dedicated spectroscopic follow ups with the next generation multi-object spectrographs.

**Author Contributions:** Both authors contributed equally to the paper. Both authors have read and agreed to the published version of the manuscript

**Funding:** S.Z. is funded by Padua University grant ARPE-DFA-2020. J.A.L.A. was founded by the project AYA2017-83204-P.

**Data Availability Statement:** The data used in this review were found in other published articles.

**Acknowledgments:** The authors thanks MNRAS, A&A, and the AAS, together with the authors of the corresponding publications, for granting permission for using images published in their journals.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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