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Review

Hot Stars, Young Stellar Populations and Dust with Swift/UVOT

by
Michael H. Siegel
1,* and
Caryl Gronwall
1,2
1
Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA
2
Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
*
Author to whom correspondence should be addressed.
Universe 2024, 10(8), 330; https://doi.org/10.3390/universe10080330
Submission received: 3 June 2024 / Revised: 25 July 2024 / Accepted: 29 July 2024 / Published: 16 August 2024

Abstract

:
In this review, we highlight the contributions made by the Swift/UVOT instrument to the understanding of the ultraviolet (UV) attenuation and extinction properties of interstellar dust and provide insight into hot stars and young stellar populations. The study of these two fields is interconnected: UV-bright objects can only be understood if the effects of foreground dust are accounted for, but foreground dust can only be accounted for by studying the properties of UV-bright objects. Decades worth of work have established that the effects of dust on background starlight vary in the ultraviolet, with proposed extinction laws having a wide variety of slopes and a strong “bump” spectroscopic feature at 2175 Å. We show that UVOT is uniquely suited to probe variations in the UV extinction law, specifically because of the u v m 2 filter that is centered on the bump and the telescope’s ability to resolve nearby stellar populations. When used in combination with optical and infrared imaging, UVOT can provide strong constraints on variations in the extinction law, both from galaxy to galaxy and within individual galaxies, as well as the properties of young stellar populations. Surveys of UVOT have included the Milky Way, the galaxies of the Local Group, the Local Volume Legacy Survey (LVLS) and two deep fields. All of these are being utilized to provide the most detailed information yet about the UV dust attenuation law and the connection of its variation to underlying physical processes as well as the UV properties of hot stars and young stellar populations.

1. Introduction

A unique aspect of interstellar dust is that, outside of the infrared, it can not be observed directly. The presence and properties of dust have been primarily measured by its effect on background light since the discovery of interstellar reddening by Trumpler [1]. However, any source of background light must be well understood if the foreground dust is to be characterized. We are thus presented with a dilemma: we can not understand the properties of dust without understanding the properties of background objects, and we can not understand the background objects without understanding the effects of the obscuring foreground dust (for a recent review, see Salim & Narayanan [2]).
Generally, the effects of dust are characterized by an extinction law—a mathematical formulation that should account for the wavelength-dependent effects of dust and can be scaled up or down by the amount of dust along the line of sight. However, there is no agreed-upon universal extinction law whose shape can depend on the composition, density, size and shape of the dust grains along the line of sight. The extinction law has been characterized to have a continuously increasing slope from the IR to the UV, with some modifications in the IR (see, e.g., Rieke & Lebofsky [3]) and the presence of a bump at 2175 Å in the UV. However, there have long been indications that the extinction law varies between galaxies or even within a galaxy itself [4,5]. Formulations vary dramatically in mathematical form, the slope of the extinction curve in the UV and the strength of the bump at 2175 Å [6,7,8,9].
Figure 1 shows some of the most commonly used laws, derived from a variety of sources and using a variety of methods. A select sample include:
  • The Milky Way law of Cardelli et al. [7], which has a strong UV slope dependent upon a single parameter and a prominent bump at 2175 Å
  • The starburst attenuation law of Calzetti et al. [6], which has a shallow UV slope and no bump.
  • The “LMC” law of Pei [9], derived from LMC stars, which is similar to the Milky Way law, but with a smaller bump.
  • The “SMC” law of Pei [9] or Gordon et al. [8], which shows no bump but a steeper far-UV slope.
As can be seen, these laws result in dramatically different effects on the background light, by up to a magnitude or more in the NUV and up to three magnitudes in the FUV. These can vastly impact the derived parameters of any underlying source.
Complicating this picture is that UV emission primarily comes from three sources—active galactic nuclei, young stellar populations and stars in highly energetic states or unusual phases of stellar evolution. For the Local Group, it is exclusively the last two. Many of these luminous UV sources are poorly understood and their UV properties are poorly constrained [9]. This is primarily due to a lack of observational data, particularly data with the high spatial and spectral resolution needed to characterize UV emission.
This problem is particularly acute as we extend our reach outside of the Local Group and into the early universe. While these young distant objects are studied in the infrared, the rest frame emission is in the ultraviolet, created by young massive stars and young stellar populations. If our understanding of either the emission source or the foreground reddening is erroneous, our understanding of the early universe will be similarly compromised. As with many aspects of astrophysics, our understanding of the most distant and ancient objects depends upon an understanding of the nearest and youngest.
Historically, the intertwined problems of extinction and spectral energy distribution have been approached separately. Young stellar populations and hot stars have been studied through objects that have minimal foreground extinction. UV extinction curves have been explored spectroscopically, using the “pair-method” of comparing two similar stars of different extinction [8]. However, the last decade has shown that panchromatic multi-filter photometry can provide good constraints on both young stellar populations and the foreground extinction or attenuation [4,10,11]. This approach has an advantage over purely spectroscopic approaches in that an entire galaxy or stellar population can be studied at once, allowing, effectively, the simultaneous measurement of both the extinction and the underlying spectral energy distributions (SEDs) using thousands of data points.
The rapid advancement of spectral synthesis models—both for individual stars and for composite stellar populations—has been a key part of this endeavor. In particular, spectral energy distribution fitting models such as MCSED [12] and spectral synthesis models including FSPS the PEGASE models [13,14] and various families of isochrones (see., e.g., Marigo et al. [15]) have proven particularly amenable to working with UV data generally and UVOT data in particular.
UVOT is uniquely suited to this field of study. Its wide-field imaging capabilities ( 17 × 17 ), moderate resolution (2.3”) and intermediate-band NUV filters fill a critical niche in the study of nearby galaxies, stellar populations and dust attenuation. It has three NUV filters: u v w 1 (central wavelength λ c = 2600 Å), u v m 2 ( λ c = 2246 Å) and u v w 2 ( λ c = 1928 Å) that span the 2175 Å bump, providing three data points in this critical NUV range. While the u v w 1 and u v w 2 filters have known red leaks, the importance of these leaks have been well-characterized [16,17] and the below studies all include the effect of these red leaks in their modeling, allowing direct comparison between observational data and models without ad-hoc corrections.
In this contribution, we review the role that Swift/UVOT has played in this field since its launch in 2004. It has provided unique insight into stars within the Milky Way (Section 2), stars and unresolved stellar populations within the Local Group (Section 3) and the extragalactic realm (Section 4). The emerging picture is that stellar populations are well-characterized by existing models and that the UV properties of the dust vary from galaxy to galaxy and within individual galaxies. The nature of the dust extinction and attenuation along with the underlying cause of that variation remains an outstanding question that we continue to address with Swift/UVOT both as an end in itself and a pathfinder to the next generation of UV/optical telescopes.

2. Hot Stars and Extinction in the Milky Way

In order to characterize the extinction properties of dust within the Milky Way, which is the primary curtain of extinction in front of both Galactic and extragalactic objects, it is critical that we have strong constraints on the SEDs of the background stars illuminating the dust. These SEDs come from theoretical models of stellar atmospheres and can be tested either individually, for stars with UV spectra, or en mass, for stars in stellar populations. The latter approach is particularly useful as a background stellar population provides dozens to thousands of data points of identical age, metallicity and distance with which to constrain the effects of the foreground dust. This approach echoes the original discovery of interstellar extinction, which used star clusters to discern the very existence of dust.
One of Swift’s first forays into this was the study of the WeBo1 binary system. This unresolved system consists of a red giant and a hot white dwarf. The latter provides abundant UV emission while the former provides abundant IR emission. The combined spectrum is a combination of two stellar SEDs, modulated by the foreground dust.
The result of the UVOT investigation [18], which combined optical and UV data, excluded an SMC-like extinction law and favored a Milky-Way-like extinction law. However, even the Milky-Way law was inadequate, with the photometry hinting at an even larger 2175 Å bump than provided by the Milky Way law (see Figure 2). This result partially motivated our future technique of abandoning “out of the box” extinction laws in favor of flexible laws that allow the slope of the extinction law ( R V ) and the strength of the bump to be varied independently.
Swift has continued to use white dwarfs and other hot objects as templates for exploring the dust law, most recently with Abell 57 [19]. This is a capability that utilizes both Swift’s unique capabilities and synergizes with ground- and space-based facilities, with GALEX, in particular, providing critical FUV data for objects that can range in temperature up to 100,000 K and therefore emit the bulk of their energy in the UV spectral range.
Swift’s most thorough exploration of local stellar populations has been its survey of nearby open clusters [20]. Open clusters are ideal targets for study by Swift because their typical size is comparable to the UVOT FOV. They are also what are called simple stellar populations: stars of nearly uniform abundance, age, distance and reddening, which removes many of the free parameters that cloud the study of field stars.
The UVOT survey provided precise three-color photometry of 103 clusters spanning a wide range of properties. The initial study focused on clusters with minimal extinction to test the efficacy of theoretical isochrones. The age range was approximately 0.1–1 Gyr given the brightness constraints on UVOT’s observing capabilities. This study also utilized UVOT’s synergy with the GAIA mission [21,22] to provide critical proper-motion-based membership information [23] that allowed the narrow cluster sequences to be picked out against the heavy Galactic background. This study outlined methods needed to use standard point-source photometry from DAOPHOT [24] and account for the unique challenges presented by UVOT [20].
Figure 3 shows a typical color-magnitude diagram (CMD) compared to the Padova theoretical isochrones [15]. These data not only show excellent agreement between the theoretical isochrones and the observed photometry but also demonstrate the power of UVOT data to constrain the foreground reddening. Note that in this representation, the reddening vectors are non-linear, changing with temperature due to the extreme changes in UV flux as well as the red leaks in the u v w 1 and u v w 2 filters. However, at the MSTO, the reddening in the two diagrams goes in opposite directions, with the isochrones becoming progressive redder in the u v m 2 u v w 1 plane with increased extinction but somewhat bluer in the u w v 2 u v w 1 plane, again likely an effect of the red leaks. This quirk in the photometry is, however, beneficial, as it allows the overall E ( B V ) value to be constrained very precisely with minimal assumptions. Siegel et al. [20] hinted that some clusters may be better fit with a different extinction law (a Milky Way law was assumed) but were unable to draw definitive conclusions due to the sample being selected for low reddening. A survey extension including more heavily extincted clusters or even differentially extincted clusters could provide stronger constraints on dust law variation in the Galaxy now that the utility of the underlying isochrones is confirmed and the properties of the underlying stellar populations can be derived from less-extincted OIR (optical-infrared) bands.
In addition to these efforts, Swift is engaged in long-term surveys of the Milky Way that will provide a legacy needed for future investigators. A decade ago, Swift completed a survey of the inner regions of the Galactic midplane [25]. This survey has now been extended to the entire Galactic midplane, providing a legacy NUV survey that GALEX was unable to do because of brightness limitations. In addition, Swift has recently started a survey of the Orion star-forming complex to match prior work using GALEX [26]. This will provide detailed information on some of the youngest dust complexes in the nearby universe, potentially showing variations in the extinction law on small scales and allowing that to be connected to ongoing star-formation processes and/or dust properties.
A final endeavor is the ongoing Swift/UVOT survey of Galactic globular clusters. Swift has surveyed 101 of these objects. The point source and integrated light photometry can feed a variety of studies including surveys of the UV properties of RR Lyrae stars, constraints of older UV isochrones and studies of unusual stars above the horizontal branch (HB), all of which are beyond the abilities of either GALEX or HST.
The most unique niche may be the class of objects called Above the Horizontal Branch (AHB) stars. After a low- or intermediate-mass star reaches the top of the AGB, it moves blueward across the HR diagram, with luminosity proportional to its mass. For higher-mass objects, this evolution proceeds very quickly, so that the mass lost on the AGB is still in the vicinity of the star when it reaches temperatures of T > 30 , 000 K. The star then ionizes the material and becomes a planetary nebula. Conversely, if stellar mass is low, the evolutionary timescale is slow enough to allow all the surrounding material to disperse. These naked Post-Asymptotic Giant Branch (PAGB) stars are significant sources of UV radiation and are likely partially responsible for the UV upturn seen in late-type galaxies [27]. Theoretical expectations are that the inverse dependence of AHB lifetime upon core mass and the dependence of luminosity upon mass place upper and lower limits upon the luminosity function. In short, PAGB stars should have a very narrow range of luminosity, making them potential standard candles.
Other stars in this class include extreme horizontal branch stars (EHB) and Asymptotic Giant Branch manque (AGB-M) stars, which represent unusual short-lived paths of stellar evolution. While these stars can be studied with HST, the narrow field of its cameras means that complete surveys are impossible. GALEX can study these objects but has only imaged a few dozen clusters and has poorer spatial resolution than UVOT. In short, UVOT is the only instrument that combines the wide field needed to find these rare stars and the moderate spatial resolution to distinguish them from the field.
A recent u B V I survey of 97 Galactic globular clusters [28] identified five non-variable, intermediate temperature (A- and F-type) yellow PAGB stars (yPAGB) all at essentially the same absolute V magnitude. Using these data, [28] concluded that the yPAGB stars of the Galactic globular cluster system have a mean bolometric magnitude of M bol = 3.38 with a dispersion of only 0.09 mag. They would thus be an excellent standard candle: bright, non-variable and easily distinguished based on UV color–magnitude or color–color diagrams.
Ciardullo et al. [29] identified intermediate temperature (spectral type F and A) AHB stars and therefore likely missed blue PAGB candidates (bPAGB). Moreover, even if such stars were identified, their bolometric magnitudes could not be determined due to the limited wavelength coverage. These bluer stars are best studied in the NUV.
Figure 4 shows the optical and near-UV color–magnitude diagrams of the globular cluster M 79 from Siegel et al. [17]. As a predominantly old population with a blue horizontal branch, the cluster contains a significant number of UV-bright evolved stars—BHB, EHB, AGB-M and PAGB stars. However, they are still only partially understood, with recent efforts being among the first to unveil large populations of UV-bright stars. The connection between these UV bright stars and properties such as cluster age, abundance, and foreground extinction remains highly uncertain and will be a point of focus for Swift/UVOT going forward, with potential far-reaching impact for studying young stellar populations and extinction.

3. Stellar Populations in the Local Group

The galaxies of the Local Group are outstanding areas to study star formation, the properties of hot stars, and the effect of interstellar dust on UV light. These galaxies are close enough to be resolved into individual stars, yet far enough away that a global picture of the galaxy’s evolutionary history can be derived and cover a broad range of age, metallicity and UV extinction. Indeed, the paradigm for studying UV extinction was set by studies of the Local Group, which indicated that the extinction laws of the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud differed in substantial ways (see Figure 1). Local Group galaxies remain the most powerful laboratories with which to study these issues through panchromatic imaging bolstered by spectroscopic surveys.
As with studies of nearby stars within the Milky Way, the fundamental problem is that, in order to measure what foreground dust is doing to the light of luminous objects, the SED of the luminous object itself must be well-constrained. As noted above, the “pair method”, which was pioneered in the Magellanic Clouds, can account for this with individual stars compared on a spectroscopic basis. However, it is limited in scope to stars, rather than stellar populations, and only those that are bright enough for spectroscopy and can be compared to similar stars.
UVOT has been at the forefront of a new method of analysis: spectral synthesis. In this method, the bulk properties of stellar populations are compared to predictions of theoretical models. This can be performed on a star-by-star basis using multi-color photometry of individual stellar populations. Or it can be performed on a bulk basis using the unresolved integrated light of the galaxy, essentially “dumbing down” UVOT’s data into large pixels of combined light. Whatever comparison is being used, the overall philosophy remains the same: to solve for the SED of the source and the effect of reddening simultaneously, an effort that can only succeed if the number of photometric data points exceeds the number of free parameters.
UVOT is uniquely well-suited to using this method to explore the Local Group. Its UV sensitivity, moderate resolution and wide field fill an important gap between GALEX (wide field, poor resolution) and HST (small field, exceptional resolution). In surveying these galaxies, UVOT data complements the rich legacy of OIR data from previous surveys such as 2MASS, Spitzer, SMASH, etc., providing the “missing piece” needed to obtain full SEDs both on a global and star-by-star basis. It provides sufficient UV data points to break degeneracies and solve for star formation history and extinction at the same time.
The SUMaC (Swift Ultraviolet Survey of the Magellanic Clouds) program is the first multi-filter UV survey of the Large and Small Magellanic Clouds [30]. Designed to address a number of scientific issues, its primary focus was on measuring the star formation history and dust extinction properties of the clouds. The survey comprised 50 and 171 fields of the SMC and LMC, respectively, taken between 2010 September and 2013 November in UVOT’s three NUV filters. Full-color mosaic images were released in 2013 (Figure 5).
For both galaxies, point-source photometry was generated with DAOPHOT [24] using the modifications and calibration procedures detailed in Siegel et al. [17]. Star-forming regions in the SMC were photometered using Source Extractor [31], as detailed in Hagen et al. [30], with pixel-by-pixel measures of photometric brightness generated from the summed counts in masked bins, as also detailed in Hagen et al. [30]. We have thus been able to study the properties of both the resolved stellar populations and the unresolved background light of fainter stellar populations. The Swift UVOT data were then combined with optical data from Massey [32] and IR data from 2MASS [33] and SAGE [34].
Attenuation laws and star formation histories were fit using a Markov-Chain Maximum likelihood Monte Carlo method to find the best fits to photometry ranging from the NIR to the FUV (the FIR was excluded because the models, at that time, did not include emission by the dust. Figure 6 shows a comparison of the panchromatic photometry to a variety of synthetic model spectra for one star-forming region in the SMC. Of particular note is the extraordinary power of the UV bands to constrain the overall attenuation ( A V , upper left), the slope of the extinction law ( R V , upper right) and bump strength (lower left). The various attenuation laws look identical in the OIR passbands. Only in the NUV do we see the kind of strong variation that allows reasonable constraint of these parameters.
Figure 7 shows the pixel-by-pixel maps of the physical parameters of the SMC, overlaid with the u v m 2 image. In contrast to previous studies, we show that the bump is present, albeit weakly so, over the entirety of the SMC with a gradient across the face of the galaxy. We also show that the extinction law is steeper than that of the Milky Way, although that too shows variation across the face of the galaxy.
The figure demonstrates why mapping the extinction law across the entire galaxy using spectral synthesis is such a powerful method for studying this issue. Using the pair method only produces tiny pencil beams through the galaxy (and indeed, we recover the prior extinction law at the specific points probed by previous studies). With spectral synthesis from panchromatic photometry, the larger picture becomes clear. Variations are revealed and, potentially, can be connected with underlying physical parameters. This approach is a quantum leap in our understanding of the extinction law.
One of the most popular theories for the origin of the 2175 Å bump is the presence of polycyclic aromatic hydrocarbons (PAHs). PAHs are easily detected in the IR and therefore combining the UV extinction maps with wide-field IR images is an excellent test of this hypothesis. Figure 8 shows the SAGE-SMC image overlaid against the map of the 2175 Å bump strength. We find little to no correlation between the appearance of PAHs and the strength of the bump other than a dearth of areas with high bump strength and high PAH emission. This suggests that other physical processes are at play.
Our exploration of the SMC’s star-formation history is less thorough, given that older populations tend to be faint in the UV. However, the data yield strong constraints on the last few hundred Myr, showing an SFH roughly consistent with previous investigations (Figure 9). In particular, we confirm bursts of star formations that may correlate with perigalactic passages of the clouds. However, as can be seen, our measures diverge from previous work at ∼1 Gyr, where the population begins to vanish in the UV, providing poorer constraint with a bias exceeding the formal errors of the Markov-Chain Maximum Likelihood fits.
Figure 10 shows the point-source photometry for two fields in the SMC, one within the SMC bar, which is a source of ongoing star formation, and one in the SMC periphery. The CMDs clearly show a longer “blue plume” of young stars in the central regions, one that is absent in the older less-active periphery of the galaxy.
The right panels show simulated CMDs using the software of Harris & Zaritsky [35] modified to use UVOT isochrones and luminosity functions. The CMDs depict a star-formation history similar to that derived from the integrated light, with the central regions showing very recent star formation (∼20 Myr) compared to the outlying regions. The simulation software has been tweaked to vary reddening instead of metallicity over the face of the SMC, which has allowed both more consistent SFH measures and the measurement of the reddening law.
The analysis of the LMC has proven to be a greater challenge, due to the larger data volume, the high crowding and the very recent burst of star-formation in the bar. However, very preliminary analysis indicates a similar ability to resolve the SFH and reddening law [37].
In addition to these studies, the SUMaC survey, by providing UV point source photometry of hundreds of thousands of stars in the Magellanic Clouds, allows for the identification and study of stars in very rare phases of stellar evolution. In addition to the aforementioned PAGB stars, a recent study identified intermediate mass ( 2 M s u n < M < 8 M s u n ) helium stars that have been stripped of their hydrogen envelopes in binary interactions, filling in a critical gap in stellar evolution studies [38].
Extending our reach even further, Swift/UVOT has surveyed the Local Group spiral galaxies M 31 and M 33. In these cases, the galaxies are too far away for point-source photometry. In addition, old and intermediate-age populations are too faint for good constraint of the extended star-formation history. However, photometry of the star-forming regions and pixel-by-pixel analysis of the surface brightness features remains quite viable for the exploration of the extinction law and the properties of the youngest stellar populations.
Our study of these two galaxies is built on the methods pioneered with the Magellanic Clouds. UVOT data were combined with UV data from GALEX, optical data from Massey et al. [39] and SDSS, and IR data from 2MASS and the Spitzer Local Volume Legacy Survey [40]. As with the Magellanic Clouds, the photometric data points were fit using a Markov-Chain Maximum likelihood Monte Carlo method.
Figure 11 shows the resultant star formation history and reddening maps from Hagen [41]. As can be seen, the lower resolution tends to blur M33’s younger stellar populations into the older disk. However, the extinction law is well-constrained, showing significant variation across the face of the galaxy. Analyzing the extinction law in each 250 × 250 pc pixel (Figure 12 shows a variety of extinction laws, ranging from nearly flat to very steep with a large blue bump).
Hagen [41] compared the 8 μ PAH maps of M33 to the UV bump strength and, unlike the SMC, found a weak negative correlation between the two (coefficient of 0.24), which suggests against some other factor producing the blue bump. Intriguingly, the blue bump shows a much stronger correlation with the spatial location of M33’s spiral arms. This suggests that some factor other than PAH abundance may be primarily responsible for the strength of the blue bump.
An almost identical result is seen in the analysis of M31 (Figure 13). Again, we see correlations between the slope of the UV curve and the strength of the blue bump. Again, we see that the steeper bumpier curves are found near the spiral arms. And again, ref. [41] found there is little to no correlation between the presence of the bump and PAH emission, suggesting that some other unknown factor is driving the strength of the bump.
However, with all three cases of Local Group objects, we need to keep in mind several caveats. First, the pixel resolution of both Swift and the 8 μ maps is low, likely lower than the PAH features themselves. This may blur out the correlation (which is very noisy), confounding our efforts to confirm or refute a connection between the two. Second, our fits are still heavily model-dependent and utilize only a few NUV/FUV filters. This may leave some ambiguity in the fits if the UV extinction law is more complex than we have used or if the data points represent multiple overlapping extinction laws. It is possible that the resolution of the UV extinction law is within Swift’s reach but exceeds its grasp; that we are able to hint at the possible solution but the ultimate answer lies beyond even UVOT’s remarkable capabilities.
A high-resolution, multi-filter NUV/FUV imaging mission is desperately needed to confirm these tentative results, with a specific focus on the nearby local group objects for which star-formation histories can be directly confirmed via deep HST imaging. Although such missions have been proposed, none have been selected thus far, which leaves a decisive resolution to this issue tantalizingly unresolved.

4. Extragalactic

As shown in Figure 1, the three NUV filters on UVOT provide strong constraints on the slope of the dust attenuation curve, 2200 Å bump strength and SFH in local galaxies. However, this sensitivity extends well beyond the Local Group into the realm of the unresolved stellar population of extragalactic objects. While HST can provide UV observations of resolved stellar populations in nearby galaxies through surveys such as the Legacy ExtraGalactic UV Survey (LEGUS; [42]) and Galaxy UV Legacy Project (GULP; HST Proposal # 16316; PI Sabbi), the limited field of view of HST limits extragalactic observations to small numbers of galaxies with distance limits in order to fit the entire galaxy within the HST FOV or imaging only part of the galaxy. The wide field of view of UVOT enables us to observe large samples of nearby galaxies in order to study their dust attenuation and unresolved stellar populations.
Over the course of the mission, Swift/UVOT has extended its survey range into the extragalactic realm with surveys of the SINGS galaxies [43], the Local Volume Legacy Survey (LVLS; [40]) and the Chandra Deep-Field South [44] and the GOODS north field. Figure 14 shows images of galaxies from the SINGS/KINGFISH survey imaged in the near-ultraviolet with UVOT. These programs, intended to complement both OIR surveys and the GALEX surveys, provide a unique window into the star formation history and dust extinction in the local universe and extend the bridge of detailed photometric study toward the most distant objects Swift/UVOT can image within its redshift range (out to z 1.9 for the NUV filters; z 5 for the optical filters).
As a pathfinder to this field of study, our first endeavor was an investigation of the nearby galaxies M 81 and Holmberg IX [4] (Figure 15). This interacting pair consists of a large face-on spiral galaxy and a young dwarf companion galaxy. The study was the first in our endeavors to use panchromatic photometry to study stellar populations and extinction. OIR data were provided by the SDSS, and the photometry was measured using both Source Extractor and pixel-by-pixel mapping of the two galaxies. A grid of models was generated from the PEGASE models [14] convolved with a variety of extinction curves, a precursor to the more sophisticated analysis that would be used for future endeavors.
The combination of OIR and NUV/FUV imaging with state-of-the-art spectral models produced outstanding results (Figure 16). The SFH model confirmed the recent interaction of the two galaxies 200 Myr ago. We also showed that M 81 has a “Milky Way-like” attenuation law with a prominent blue bump. Interestingly, the outer regions of M 81 and the bulk of Holmberg IX show a hint of more “SMC-like” attenuation curves. This study not only provided the first insight into variations in the dust law of M 81, it showed that the UVOT, in combination with other OIR data, is a unique and powerful tool for exploring the properties of nearby galaxies.
The Hoversten et al. [4] study was somewhat limited in scope as it restricted the dust models to the four basic models listed in Section 1. It also used basic χ 2 algorithms to derive the best fit from a few dozen models. However, it was upon this framework that the studies of the SMC, LMC, M31 and M33 were built using more flexible extinction models and Markov-chain maximum likelihood analysis, as described in Section 3.
Expanding upon all of the previous work described above, Belles et al. [45] have recently combined NUV photometry from UVOT observations with archival multiwavelength photometry ranging from the far-UV to the infrared of 78 SINGS/KINGFISH galaxies [46]. This was the first study to add UVOT data to a rich legacy archive of OIR data of the nearby universe, a combination that not only fed our own study but will enable future studies by the astronomical community.
An example spectral energy distribution (SED) is shown in Figure 17. Belles et al. [45] used the SED fitting code MCSED ([12]) to derive SED fits to the SINGS/KINGFISH sample of a nearby galaxy and derive various galaxy physical parameters, including star formation rate (SFR), galaxy stellar mass, and dust attenuation. The average attenuation curves for the SINGS/KINGFISH sample are shown in Figure 18. Belles et al. [45] found that the average UV dust attenuation curve for SINGS/KINGFISH galaxies is significantly steeper than the canonical [6] starburst galaxy attenuation law that is typically assumed for rest-frame ultraviolet observations of high redshift galaxies. This work is currently being extended to a larger sample of 258 galaxies from the LVLS [43] so that we can explore the effect of a galaxy’s physical properties on the dust attenuation curve to better inform observations of galaxies at high redshift.
Interestingly, the SED fits in Belles et al. [45] change depending on whether UVOT data are included. Including UVOT data results in smaller blue bumps than fits based on GALEX alone. This highlights why UVOT data are so critical to these studies. Because it has filters that narrowly bracket the 2175 Å bump, UVOT provides tighter constraints than the broader filters of GALEX. This prohibits the models from trying to “hide” problematic fits by assuming a larger blue bump. We are continuing to explore this issue to determine the nature of this discrepancy and what it reveals about the extinction law, the modeling, or both.
Even with five data points through the NUV/FUV from GALEX and UVOT, however, the analysis of the attenuation law and SFH retains a degree of uncertainty that denies a complete understanding of the underlying physical processes behind those relations. Even more than with the Local Group galaxies, the comparatively poor resolution of UVOT may blur any correlations that would allow us to connect variations in the attenuation law to the underlying properties of the emitting regions. We now have a global picture of the attenuation law and its variations, but we are denied the explanation for those relations. This again emphasizes the critical need for a future mission to provide high-resolution wide-field multi-filter UV survey data of nearby galaxies.
The ultimate extension of Swift’s reach is into the realm of unresolved galaxies in deep fields. To this end, Swift has carried out twin surveys of the Chandra Deep Field South (CDF-S) and the Great Observatories Origins Deep Survey (GOODS) North fields [45,47,48] in the NUV. These two fields, which have been the target of deep observations by multiple observatories, were imaged by Swift to depths of u 24 , allowing unprecedented panchromatic exploration of the UV galaxy number counts and luminosity function to moderate redshift.
We used the deep NUV imaging of both CDF-S and GOODS-N to explore the UV galaxy number counts and the evolution of the NUV galaxy luminosity function out to z 1 . Figure 19 shows the summed u v m 2 image of our deep observations of GOODS-N from Belles et al. [49]. We show the u v m 2 galaxy number counts in GOODS-N from Belles et al. [49] and CDF-S from Hoversten et al. [48] in Figure 20 along with galaxy number counts from the literature, including the GALEX NUV all-sky number counts from Xu et al. [50] and the HST FUV number counts from Teplitz et al. [51]. We find there is good agreement at the ∼10% level. The number counts from our Swift observations have larger errors than the Xu et al. [50] values due to the different survey sizes (∼260 square arcminutes versus many square degrees in Xu et al. [50]), but our measurements go a magnitude deeper. We note the number counts in the CDF-S from Hoversten et al. [48] go slightly deeper than those in GOODS-N from Belles et al. [49] due to greater exposure time (80 ks here vs. ∼130 ks).
Galaxy number counts are the most straightforward measurement of the overall galaxy population in the absence of redshift information. However, GOODS-N and CDF-S have robust multiwavelength photometry available (e.g., [52]) allowing for the measurements of photometric redshifts for galaxies in these fields. We combine UVOT near-UV photometry and photometric redshifts to measure the UV luminosity function. The luminosity function (LF) is the density of galaxies per luminosity interval as a function of luminosity. The UV luminosity function can be used to trace the evolution of the star formation rate density (SFRD) as the UV luminosity is a direct probe of recent star formation [53].
Figure 21 shows the UV galaxy luminosity function from our Swift/UVOT observations of GOODS-N in four different redshift bins [45] ranging from z 0.2 to z 1.2 There is clear luminosity evolution as a function of cosmic time. We use the integration of the Schechter function fits to the UV luminosity functions at various redshifts to determine the integrated total UV luminosity density, as shown in Figure 22. UV luminosity density can be translated into star formation rate density (SFRD) but this conversion is subject to uncertainties in our understanding of dust attenuation, so we focus on the evolution of UV luminosity density as a function of redshift. Figure 22 compares our UV luminosity density measurements in CDF-S and GOODS-N from Hagen et al. [47] and Belles et al. [49]. We find good agreement with other results in the literature using photometry from GALEX and XMM-OM over the redshift range of z = 0 1 . Future work on our UVOT deep field observations will concentrate on SED fitting of individual galaxies combining our NUV observations with archival optical and infrared photometry to better understand the dust attenuation properties of star-forming galaxies at these cosmic epochs. Improved understanding of dust attenuation will allow for improved measurements for star formation rates and constraints on the evolution of SFRD, which are crucial for our understanding of galaxy evolution.

5. Conclusions

In this review, we have highlighted the contributions Swift has made to understanding the dust extinction curve in the ultraviolet as well as the properties of young luminous stellar populations. The Swift/UVOT instrument has very specific advantages that makes it ideal for this field of study. It has a wide field-of-view, which enables the kind of surveys that have fed this endeavor. It has moderate resolution, which allows individual stars and star-forming regions to be picked out. It has three filters that bracket the 2175 Å bump, enabling strong constraint on this feature. It synergizes well with GALEX, Gaia and ground-based OIR surveys, allowing precise delineation of nearby stellar populations and panchromatic studies of objects from the nearby to the deep universe.
We can not overemphasize the scientific return that the panchromatic study of UV-bright objects unlocks. For this particular branch of science, it allows us to ‘nail down’ aspects of dust extinction and attenuation in passbands that are well-understood. This liberates the UV passbands to explore the detailed properties of stars and stellar populations that are dominated by their UV flux as well as study the shape of the attenuation curve in the ultraviolet, scaled to measures in the OIR. Panchromatic studies give the energy of a system nowhere to escape, and they give models of SEDs and dust attenuation nowhere to hide problematic fits. By surrounding these problems from all sides, we gain new insights into UV emission and attenuation.
In addition, the very nature of the Swift mission lends itself to these types of investigations. Swift primarily studies high-energy transients. However, its schedule must be filled out with other targets—target of opportunity, guest investigator programs, team programs and calibration targets. This allows the mission to slowly but surely survey large areas of the sky and assemble large catalogs of objects. After nearly 20 years of operations, this has resulted in a rich archive that enables many of these questions to be addressed in a thorough and systematic fashion. The studies detailed in this review only scratch the surface of what these data are capable of.
In the future, we look to see Swift complete its survey of the Galactic midplane, complete studies of the Orion star-forming complex and gather even more data on distant unresolved galaxies. The advent of JWST opens even more possibilities for studying the SEDs of distant objects. As the Swift mission enters its third decade of work, its capabilities only continue to expand.

Author Contributions

M.H.S. and C.G. contributed to all phases of the UVOT resaerch programs. M.H.S. and C.G. contributed to writing and editing of this contribution. All authors have read and agreed to the published version of the manuscript.

Funding

We acknowledge support from NASA Astrophysics Data Analysis grants NNX12AE28G, NNX14AJ62G, NNX16AF35G, 80NSSC19K0577 and sponsorship at PSU by NASA contract NAS5-00136.

Data Availability Statement

All Swift/UVOT data are available through the HEASARC and MAST archives. Photometry of the open clusters is also available through the MAST archive. Mosaics of the Local Group galaxies are available upon request and will be made available, together with photometric catalogs, in the MAST archive.

Acknowledgments

We acknowledge the efforts of our studies of stars and galaxies with UVOT in particular Alex Belles, Lea Hagen and Erik Hoversten who enabled us to pursue the science in this review. We thank the anonymous reviewers for their useful comments.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. A comparison of several literature dust laws against the filter function of Swift/UVOT and GALEX (which have been scaled for easier comparison). Note the particular sensitivity of the u v m 2 filter to the presence or absence of the 2175 Å dust bump.
Figure 1. A comparison of several literature dust laws against the filter function of Swift/UVOT and GALEX (which have been scaled for easier comparison). Note the particular sensitivity of the u v m 2 filter to the presence or absence of the 2175 Å dust bump.
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Figure 2. A comparison of photometry to theoretical spectra for the WeBo 1 binary system. The dotted red and blue lines are predicted spectra for the bright K-giant and pre-white dwarf, respectively. The solid red and blue lines are the predicted spectra after applying a Milky-Way-like extinction law with an enhanced blue bump at 2175 Å. The solid black line is the combined spectra while the black dots are the photometric data points. Note, in particular, the three leftmost points representing the NUV filters and how they bracket the blue bump, a combination that is unique to UVOT. From Siegel et al. [18].
Figure 2. A comparison of photometry to theoretical spectra for the WeBo 1 binary system. The dotted red and blue lines are predicted spectra for the bright K-giant and pre-white dwarf, respectively. The solid red and blue lines are the predicted spectra after applying a Milky-Way-like extinction law with an enhanced blue bump at 2175 Å. The solid black line is the combined spectra while the black dots are the photometric data points. Note, in particular, the three leftmost points representing the NUV filters and how they bracket the blue bump, a combination that is unique to UVOT. From Siegel et al. [18].
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Figure 3. A comparison of different isochrone fits to the photometry of the open cluster NGC 2360. The three lines are all set at a metallicity of −0.1 and a distance modulus of 10.05. However, they are set at different reddening values, with age adjusted to better match the MSTO. From Siegel et al. [20].
Figure 3. A comparison of different isochrone fits to the photometry of the open cluster NGC 2360. The three lines are all set at a metallicity of −0.1 and a distance modulus of 10.05. However, they are set at different reddening values, with age adjusted to better match the MSTO. From Siegel et al. [20].
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Figure 4. M 79 optical and NUV color–magnitude diagrams. On the left panel, the PAGB star is identified with a square while four AGB-M objects, as identified from Swift/UVOT data, are shown as triangles. On the right panel, the UV-bright stars are labeled. M 79’s dominant RGB and MS sequences are too faint in the UV to be detected by Swift, while the blue horizontal branch (BHB), EHB and AGB-M stars stand out. (From Siegel et al. [17]).
Figure 4. M 79 optical and NUV color–magnitude diagrams. On the left panel, the PAGB star is identified with a square while four AGB-M objects, as identified from Swift/UVOT data, are shown as triangles. On the right panel, the UV-bright stars are labeled. M 79’s dominant RGB and MS sequences are too faint in the UV to be detected by Swift, while the blue horizontal branch (BHB), EHB and AGB-M stars stand out. (From Siegel et al. [17]).
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Figure 5. False color UVOT images of the SMC (left) and LMC (right) with u v w 2 (blue), u v m 2 (green), and u v w 1 (red). The SMC image is about 2.°3 (2.4 kpc) across, and the LMC image is 4.°4 (3.9 kpc) across. North is to the top and east is to the left.
Figure 5. False color UVOT images of the SMC (left) and LMC (right) with u v w 2 (blue), u v m 2 (green), and u v w 1 (red). The SMC image is about 2.°3 (2.4 kpc) across, and the LMC image is 4.°4 (3.9 kpc) across. North is to the top and east is to the left.
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Figure 6. The photometry (black circles) of star-forming region 165 within the SMC, compared with the best-fitting spectrum (blue), which corresponds to A V = 0.24 mag, R V = 2.95, a bump strength of 1.35, and an age of 6.4 Myr. (Top left): varying A V from 0 to 0.6 mag. Changes in A V have the largest effect at shorter wavelengths, with very little change in the IR. (Top right): varying R V from 1.5 to 5.5. (Bottom left): varying the bump strength from 0 to 2. (Bottom right): varying the age from 4 to 8 Myr. From Hagen et al. [30].
Figure 6. The photometry (black circles) of star-forming region 165 within the SMC, compared with the best-fitting spectrum (blue), which corresponds to A V = 0.24 mag, R V = 2.95, a bump strength of 1.35, and an age of 6.4 Myr. (Top left): varying A V from 0 to 0.6 mag. Changes in A V have the largest effect at shorter wavelengths, with very little change in the IR. (Top right): varying R V from 1.5 to 5.5. (Bottom left): varying the bump strength from 0 to 2. (Bottom right): varying the age from 4 to 8 Myr. From Hagen et al. [30].
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Figure 7. Pixel-by-pixel maps of reddening within the SMC. The panels show the overall reddening, the slope of the reddening law and the bump strength. The screen of foreground Milky Way extinction has already been corrected for. From Hagen et al. [30].
Figure 7. Pixel-by-pixel maps of reddening within the SMC. The panels show the overall reddening, the slope of the reddening law and the bump strength. The screen of foreground Milky Way extinction has already been corrected for. From Hagen et al. [30].
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Figure 8. A comparison of the SMC bump strength to the 8 micron emission from PAHs within the SMC. The screen of foreground Milky Way extinction has already been corrected for. From Hagen et al. [30].
Figure 8. A comparison of the SMC bump strength to the 8 micron emission from PAHs within the SMC. The screen of foreground Milky Way extinction has already been corrected for. From Hagen et al. [30].
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Figure 9. Recent star formation history of the SMC, as derived from the large pixels. Blue and red points are the star formation histories (SFHs) from Harris & Zaritsky [35] and Rubele et al. [36], respectively. From Hagen et al. [30].
Figure 9. Recent star formation history of the SMC, as derived from the large pixels. Blue and red points are the star formation histories (SFHs) from Harris & Zaritsky [35] and Rubele et al. [36], respectively. From Hagen et al. [30].
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Figure 10. The (left) panels show observed CMD for a field in the central bar of the SMC and the outlying halo of the SMC. The (right) panel shows simulated CMDs based on theoretical isochrones and luminosity functions. Lines show isochrones of ages 20 Myr (blue), 200 Myr (green) and 500 Myr (red) for comparison.
Figure 10. The (left) panels show observed CMD for a field in the central bar of the SMC and the outlying halo of the SMC. The (right) panel shows simulated CMDs based on theoretical isochrones and luminosity functions. Lines show isochrones of ages 20 Myr (blue), 200 Myr (green) and 500 Myr (red) for comparison.
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Figure 11. Maps of physical parameters of large pixels in M 33. Overlaid is a greyscale u v m 2 image for reference. White areas in the A V , age, stellar mass, and τ maps were not modeled due to either low signal-to-noise or bright foreground stars. From Hagen [41].
Figure 11. Maps of physical parameters of large pixels in M 33. Overlaid is a greyscale u v m 2 image for reference. White areas in the A V , age, stellar mass, and τ maps were not modeled due to either low signal-to-noise or bright foreground stars. From Hagen [41].
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Figure 12. Dust extinction curves for the pixels in M33. The green dashed lines mark, for each wavelength, the median extinction curve value and the uncertainty of the median, which includes the uncertainties in R V and the 2175 Å bump strength for each curve. From Hagen [41].
Figure 12. Dust extinction curves for the pixels in M33. The green dashed lines mark, for each wavelength, the median extinction curve value and the uncertainty of the median, which includes the uncertainties in R V and the 2175 Å bump strength for each curve. From Hagen [41].
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Figure 13. Maps of physical parameters of large pixels in M 31. Overlaid is a greyscale u v m 2 image for reference. White areas in the A V , age, stellar mass, and τ maps were not modeled due to either low signal-to-noise or bright foreground stars. From Hagen [41].
Figure 13. Maps of physical parameters of large pixels in M 31. Overlaid is a greyscale u v m 2 image for reference. White areas in the A V , age, stellar mass, and τ maps were not modeled due to either low signal-to-noise or bright foreground stars. From Hagen [41].
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Figure 14. False color images of select SINGS/KINGFISH galaxies using Swift UVOT ( u v w 2 , u v m 2 , and u v w 1 filters). From left to right, NGC 1566, NGC 3031 (M81), NGC 4594 (M104), NGC 5194 (M51), and NGC 6946.
Figure 14. False color images of select SINGS/KINGFISH galaxies using Swift UVOT ( u v w 2 , u v m 2 , and u v w 1 filters). From left to right, NGC 1566, NGC 3031 (M81), NGC 4594 (M104), NGC 5194 (M51), and NGC 6946.
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Figure 15. False color images of M 81 and Holmberg IX in the NUV from UVOT (left) and in the optical from SDSS (right). From Hoversten et al. [4].
Figure 15. False color images of M 81 and Holmberg IX in the NUV from UVOT (left) and in the optical from SDSS (right). From Hoversten et al. [4].
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Figure 16. Maps of overall extinction, extinction model, age and star-formation history in M81. From Hoversten et al. [4]. Right panels show the uncertainties in the parameters.
Figure 16. Maps of overall extinction, extinction model, age and star-formation history in M81. From Hoversten et al. [4]. Right panels show the uncertainties in the parameters.
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Figure 17. An example SED of NGC 628 (M74) showing the flux observed in each bandpass. The inset in the upper left shows the additional UV coverage provided by Swift/UVOT in red. The error bars on the fluxes are shown but are negligible in most cases. These data are then used as the inputs for our SED fitting. From Belles et al. [45].
Figure 17. An example SED of NGC 628 (M74) showing the flux observed in each bandpass. The inset in the upper left shows the additional UV coverage provided by Swift/UVOT in red. The error bars on the fluxes are shown but are negligible in most cases. These data are then used as the inputs for our SED fitting. From Belles et al. [45].
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Figure 18. Average attenuation curves for the SINGS/KINGFISH sample. Left: Mean attenuation law of the entire sample, calculated by averaging over the entire sample at each wavelength for each different SFH tested. Right: Mean attenuation law from the piecewise SFH fits compared to the starburst law, excluding galaxies consistent with no dust. The 16th and 84th percentiles are shown for the piecewise SFH result, and the Calzetti et al. [6] error in R V is displayed. We see that the derived attenuation law for each SFH is steeper than the Calzetti et al. [6] law. From Belles et al. [45].
Figure 18. Average attenuation curves for the SINGS/KINGFISH sample. Left: Mean attenuation law of the entire sample, calculated by averaging over the entire sample at each wavelength for each different SFH tested. Right: Mean attenuation law from the piecewise SFH fits compared to the starburst law, excluding galaxies consistent with no dust. The 16th and 84th percentiles are shown for the piecewise SFH result, and the Calzetti et al. [6] error in R V is displayed. We see that the derived attenuation law for each SFH is steeper than the Calzetti et al. [6] law. From Belles et al. [45].
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Figure 19. GOODS-N as observed using the Swift UVOT u v m 2 filter. The UVM2 image is shown due to its low background compared to the other filters. The green circle marks the region where we detected the sources presented here. Sources outside this region were excluded due to the lower effective exposure time at the edge of the mosaicked field. From Belles et al. [49].
Figure 19. GOODS-N as observed using the Swift UVOT u v m 2 filter. The UVM2 image is shown due to its low background compared to the other filters. The green circle marks the region where we detected the sources presented here. Sources outside this region were excluded due to the lower effective exposure time at the edge of the mosaicked field. From Belles et al. [49].
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Figure 20. The u v m 2 number counts (green) compared to GALEX NUV counts from Xu et al. [50] (black), u v m 2 number counts of CDF-S from Hoversten et al. [48] (blue), and HST FUV number counts from Teplitz et al. [51] (red). We see good agreement and differences can be attributed to survey area and exposure times. The corrections for Milky Way extinction are minimal (∼0.1 mag) as is the color difference between u v m 2 and GALEX NUV. The correction to compare u v m 2 and the HST values depends on the assumed spectrum of the observed source. From Belles et al. [49].
Figure 20. The u v m 2 number counts (green) compared to GALEX NUV counts from Xu et al. [50] (black), u v m 2 number counts of CDF-S from Hoversten et al. [48] (blue), and HST FUV number counts from Teplitz et al. [51] (red). We see good agreement and differences can be attributed to survey area and exposure times. The corrections for Milky Way extinction are minimal (∼0.1 mag) as is the color difference between u v m 2 and GALEX NUV. The correction to compare u v m 2 and the HST values depends on the assumed spectrum of the observed source. From Belles et al. [49].
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Figure 21. The UV LF in four different redshift bins was determined using UVOT observations of GOODS-N. The black dots are from the V m a x method with errors from bootstrap resampling. The faintest bins are only comprised of a handful of galaxies due to incompleteness. As a result, the bootstrap error estimates are likely an underestimate of the true error. The solid red line is the MLE best-fit Schechter function with the shaded region showing the 1 σ uncertainty from M * and ϕ * . In each redshift bin, α is fixed using the values from Arnouts et al. [54]. We see a clear evolution in M * . From Belles et al. [49].
Figure 21. The UV LF in four different redshift bins was determined using UVOT observations of GOODS-N. The black dots are from the V m a x method with errors from bootstrap resampling. The faintest bins are only comprised of a handful of galaxies due to incompleteness. As a result, the bootstrap error estimates are likely an underestimate of the true error. The solid red line is the MLE best-fit Schechter function with the shaded region showing the 1 σ uncertainty from M * and ϕ * . In each redshift bin, α is fixed using the values from Arnouts et al. [54]. We see a clear evolution in M * . From Belles et al. [49].
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Figure 22. Our observed luminosity density (black stars) as a function of redshift compared to Wyder et al. [55] (blue), Schiminovich et al. [56] (yellow), Hagen et al. [47] (purple), Sharma et al. [57] (green), and Sun et al. [58] (red). We see good agreement across all redshift bins. We focus on observed UV luminosity density as the chosen dust attenuation correction and SFR calibrations differ. From Belles et al. [49].
Figure 22. Our observed luminosity density (black stars) as a function of redshift compared to Wyder et al. [55] (blue), Schiminovich et al. [56] (yellow), Hagen et al. [47] (purple), Sharma et al. [57] (green), and Sun et al. [58] (red). We see good agreement across all redshift bins. We focus on observed UV luminosity density as the chosen dust attenuation correction and SFR calibrations differ. From Belles et al. [49].
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Siegel, M.H.; Gronwall, C. Hot Stars, Young Stellar Populations and Dust with Swift/UVOT. Universe 2024, 10, 330. https://doi.org/10.3390/universe10080330

AMA Style

Siegel MH, Gronwall C. Hot Stars, Young Stellar Populations and Dust with Swift/UVOT. Universe. 2024; 10(8):330. https://doi.org/10.3390/universe10080330

Chicago/Turabian Style

Siegel, Michael H., and Caryl Gronwall. 2024. "Hot Stars, Young Stellar Populations and Dust with Swift/UVOT" Universe 10, no. 8: 330. https://doi.org/10.3390/universe10080330

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