**1. Introduction**

Jets, in the form of collimated outflows of plasma possibly endowed with magnetic fields, are ubiquitous in astrophysics. They typically extend over orders of magnitude in distance from their birthplace (from parsec scales in protostars to >kpc scales in galaxies hosting supermassive black holes), in redshift (with jet signatures being detected in association with the most distant galaxies known so far up to *z* ∼ 9) and in luminosity, reaching the largest values in gamma-ray bursts (GRBs).

GRBs are luminous, extra-galactic transients powered by compact objects (black holes– BH, neutron stars–NS) produced by the core-collapse of a massive star or by the merger of a compact object binary (most likely NS-NS or NS-BH). In the most widely accepted scenario, the 'central engine' (that is, the system consisting of the compact object and possibly a surrounding accretion disk) launches a bipolar relativistic collimated outflow. Bulk energy dissipation in such an outflow produces a bright, highly variable, non-thermal 'prompt' emission in the X-ray/*γ*-ray band. The outflow deceleration by the external circum-burst medium produces the long-lasting multi-wavelength 'afterglow' emission extending from the *γ*-rays through the optical to the radio band.

The presence of *relativisic* outflows in GRBs is supported by some theoretical arguments and a few compelling observational pieces of evidence. The very fast prompt emission light curve variability requires the source to be very compact, but the observation of non-thermal prompt emission spectra extending above MeV photon energies indicates that the source is optically thin to pair production by photon–photon annihilation. This apparent contradiction can hardly be reconciled without invoking highly relativistic expansion, which eases the constraints by both decreasing the comoving photon energy by a Γ factor (the bulk expansion Lorentz factor) and increasing the source size limit imposed by variability by a Γ 2 factor (e.g., [1–5]). Even more directly, the apparent size increase of ∼0.3 pc in

**Citation:** Salafia, O.S.; Ghirlanda, G. The Structure of Gamma Ray Burst Jets. *Galaxies* **2022**, *10*, 93. https:// doi.org/10.3390/galaxies10050093

Academic Editors: Elena Moretti, Francesco Longo and Yosuke Mizuno

Received: 21 June 2022 Accepted: 23 August 2022 Published: 30 August 2022

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∼50 rest-frame days as measured for the first time in the nearby GRB 030329 [6] suggested an apparently superluminal expansion speed, indicating relativistic bulk motion [7]. *Collimation* of GRB outflows is required to reduce the otherwise huge *γ*-ray isotropic equivalent. This nomenclature refers to the energy and/or luminosity of a GRB computed assuming isotropic emission. Because of relativistic 'beaming' (i.e., aberration) of radiation, the vast majority of the observable photon flux comes from emitting regions moving within a tiny 1/Γ angle around the line of sight, making an isotropic outflow (and hence isotropic emission) essentially indistinguishable from one that expands radially within a *θ*<sup>j</sup> & 1/Γ collimation angle [8]. Energy reaching *<sup>E</sup>γ*,iso <sup>∼</sup> <sup>10</sup>54−<sup>55</sup> erg (e.g., GRB 990123 [9] and GRB 130427A [10]), which would require the mind-boggling conversion of 1–5 *M* rest mass energy into *γ*-rays with 100% efficiency without invoking collimation. If the outflow is collimated within an angle *θ*<sup>j</sup> , such an energy budget is reduced by a 'beaming' factor *f*<sup>b</sup> = (1 − cos *θ*j) ∼ *θ* 2 j /2 ≈ 0.004(*θ*j/5 ◦ ) 2 . The collimation angle *θ*<sup>j</sup> is typically estimated from a steepening of the afterglow light curve around a few days after the initial gamma-ray burst, interpreted as the signature of the presence of a jet [8,11–15], see also Section 4.2. Such a feature, often referred to as a 'jet break', arises as the relativistic beaming angle 1/Γ (which increases during the afterglow phase due to the deceleration of the blastwave, i.e., the expanding shock produced as the jet expands within the external medium) becomes comparable to *θ*<sup>j</sup> [8], allowing the observer to 'see' the jet borders. Typical collimation angles estimated from the observation of jet breaks range Opening angles as small as *θ*<sup>j</sup> < 1 ◦ have been reported in some studies, e.g., [16,17]. We caution that, while opening angles as small as these are not impossible in principle, these estimates are based on assumptions on the interstellar medium density and prompt emission efficiency, and they rely on the interpretation of an observed steepening in the afterglow light curve as a jet break. For the latter interpretation to hold, the steepening must be achromatic, i.e., it must show up independently of the observing band, but it is often impossible to verify it due to the absence of multi-wavelength observations at the relevant time. For these reasons, such estimates must be taken with a grain of salt. from *θ*<sup>j</sup> ∼ 4 ◦ in 'long' GRBs [18] to *θ*<sup>j</sup> ∼ 16◦ in 'short' GRBs [19].

For simplicity, the jets of GRBs have been long modeled as a conical outflow with a constant energy per unit solid angle d*E*/dΩ(*θ*) and bulk Lorentz factor Γ(*θ*) within its aperture *θ* ≤ *θ*<sup>j</sup> (here, *θ* is the angle from the jet symmetry axis). This basic model is typically referred to as the 'uniform', 'homogeneous' or 'top-hat' jet structure model. If the jet is observed within *θ*<sup>j</sup> , the steepening in the afterglow light curve is used to infer the jet opening angle *θ*<sup>j</sup> from where the true burst energy can be derived *E<sup>γ</sup>* ∼ *Eγ*,iso*θ* 2 j /2. It was found by [18,20,21] that *E<sup>γ</sup>* is narrowly distributed around 10<sup>51</sup> erg, suggesting a standard energy reservoir in GRBs. Within a 'top-hat' jet model, this implies that *Eγ*,iso scales as *θ* −2 . On the other hand, some authors [22–24] soon realized that the same observations could be explained assuming GRB jets possess a universal *structure* d*E*/dΩ ∝ *θ* −2 (see Section 2.1 for a precise definition).

The evolving interest in the structure of GRB jets can be seen in Figure 1, where we have collected from the NASA ADS all the papers mentioning "gamma-ray burst" and "structured jet" or "jet structure" in their abstracts. The red line is the cumulative distribution of the grey histogram and shows two clear "steps": an initial growing interest in structured jets corresponding to the 2000–2006 period and a recent "explosion" of interest prompted by the discovery and interpretation of the gamma-ray burst GRB 170817A associated to the first binary neutron merger gravitational wave event [25–27].

**Figure 1.** Timeline of scientific papers about GRB structured jets. The red solid line shows the cumulative number (shown on the left-hand axis) of refereed papers that contain "gamma-ray burst" and "structured jet" or "jet structure" in their abstract, according to the NASA ADS [28]. The grey histogram (number shown on the right-hand axis) shows the corresponding number of papers published per year. The dates of the two seminal papers [23,24] and of the GW170817 discovery [25–27] are annotated. We note that alternative nomenclatures with respect to the 'structured jet'/'jet structure' used here exist, hence the actual number of papers on the subject could be higher.

The initial interest in structured jets in the early 2000s was in part driven by attempts at explaining the diversity of GRB energetics within a unifying scenario where all jets share a universal structure. Two analytical functions were explored initially to describe the jet structure: a power law jet with d*E*/dΩ ∝ *θ* −2 , as suggested by the *E<sup>γ</sup>* clustering described above and supported by early analytical studies [29] and numerical simulations [30] of the jet emerging from its progenitor star envelope (see Section 2.2); a Gaussian jet with d*E*/dΩ ∝ exp(−(*θ*/*θ*c) <sup>2</sup>/2) [22,24,31,32], where most of the jet energy is contained within two times the 'core' opening angle *θ*c, which is a more realistic representation of a nearly sharp-edged jet. Less continuous structures, such as one composed of two nested uniform jets (a narrow, fast and energetic jet surrounded by a wider, slower and weaker layer. Notably, a two-component jet structure has also been proposed to interpret jets in radio galaxies [33]) were considered, motivated by the possibility to explain the optical afterglow bumps observed in a few GRBs [20,34].

In the same period, many attempts were made at identifying, in the observational data then available, distinctive features of a structured jet. Modeling of the afterglow light curve of GRB030329 [35] suggested a structured jet as a viable interpretation of the low-frequency data, although alternative interpretations were not excluded. The sharpness of the light curve change across the jet break time, which in the structured jet scenario provides a measure of the viewing angle *θ*<sup>v</sup> [24], depends on the jet structure and on the viewing angle, with sharper breaks corresponding to larger *θ*<sup>v</sup> [36]. However, the jet lateral expansion also affects the shape of the light curve around the jet break time [37]. Attempts at testing the universal jet structure model [38–40] were mainly limited by the few events with measured redshifts and jet breaks [41]. Linear polarization measurements of the afterglow emission were also considered as diagnostics for the jet structure [42,43], despite the polarization depends also on the configuration of the magnetic field in the emission region [36,44,45]. Considerably different rates of GRB afterglows without a corresponding prompt emission detection (so-called orphan afterglows) are predicted in the case of a structured jet with respect to the conical uniform scenario [46–53].

Owing to the difficulties in identifying distinctive signatures in the available data of the structured jet scenario (see [54]), the community started to lose interest in it during the 2006–2017 period. The discovery of GRB 170817A [26,55,56] associated with the GW170817 gravitational wave source [25] suddenly changed everything (see also Section 5): after more than six months of monitoring of the puzzling non-thermal afterglow of GRB 170817A, a structured jet appeared as the only scenario able to provide a self-consistent interpretation of the shallow evolution of the afterglow light curves [57–65] and of the proper motion [66] and small size [67] of the very long baseline interferometry (VLBI) images of the source (see [68] for a review of the multi-messenger aspects of GW170817, and [69] for a more general review of electromagnetic counterparts of compact binary mergers).

Why is the structure important? The structure determines the properties of the emission for different observers, therefore determining in part the distribution of observable properties and the detectability of these sources. The jet structure carries information about the processes that shape it (the jet-launching mechanism and the interaction between the jet and the ambient medium surrounding the central engine) and is therefore an indirect probe of otherwise unobservable phenomena. Several works developing the concept of the jet structure, its origin, and how it determines the observed properties of GRBs appeared in the literature in the last five years. The presence of a jet with some structure appears unavoidable, considering the phases following the formation of the central engine and, therefore, a growing part of the community is starting to systematically consider GRB observations under this more realistic assumption when interpreting both their prompt and afterglow emission components. However, often the available observations are insufficient to allow for distinguishing between a structured jet from a less realistic assumption of a uniform jet. Most likely, the combination of several observables and the further development of numerical simulations will lead to constraining the structure of GRB jets in the near future.

The scope of this review is that of introducing the general definition of jet structure (Section 2.1) and present a very intuitive description of how the jet acquires its angular structure (Section 2.2). A very simplified overview of the mechanisms responsible for the jet launch (Section 2.3) and for its propagation up to where it can freely expand (Section 2.4) is provided. The possible signatures of the presence of a structured jet on the observed properties of the prompt GRB emission are presented in Section 3. The afterglow emission from a structured jet considering different possible structures and its dependence on the key jet structure parameters is summarized in Section 4. Finally, in Section 5, we briefly review the observations of the non-thermal electromagnetic counterparts of GW170817 and their interpretation in the structured jet scenario.
