1. Introduction
Gravitational waves (GWs) are perturbations of the spacetime propagating as waves at the speed of light. Although their interaction with matter is weak, extreme astrophysical processes are able to release through GWs such a huge amount of energy to be detectable by us. A class of such extreme astrophysical events is the merger of two compact objects – namely objects with a huge mass compressed in a very small volume – orbiting one around the other, where the emission of GWs removes angular momentum from the system shrinking the orbital separation between the two objects and leading to their ultimate coalescence. Examples of compact objects are neutron stars (NSs) and black holes (BHs), for which a mass of the order of a solar mass is compressed within a radius of 
${\sim }10$ km or less. It was indeed the merger of a system formed by two BHs, the first GW event ever detected, which was observed on 14 September 2015 by the LIGO and Virgo Scientific Collaborations (LVC) using the LIGO laser interferometers (Abbott et al. Reference Abbott, Abbott, Abbott, Abernathy, Acernese, Ackley, Adams, Adams, Addesso and Adhikari2016c). The discovery was followed in subsequent years by other detections of BH–BH mergers (Abbott et al. Reference Abbott, Abbott, Abbott, Abernathy, Acernese, Ackley, Adams, Adams, Addesso and Adhikari2016a,Reference Abbott, Abbott, Abbott, Abernathy, Acernese, Ackley, Adams, Adams, Addesso and Adhikarib, Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2017a,Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adyab,Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adyac, Reference Abbott, Abbott, Abbott, Abraham, Acernese, Ackley, Adams, Adhikari, Adya and Affeldt2018). On 17 August 2017 a different signal, originated by the coalescence of two NSs was observed by the LIGO and Virgo interferometer network (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2017d). This detection was particularly interesting because, while for a BH–BH merger the emission of photons is not generally expected, the coalescence of an NS–NS system should be accompanied by a copious amount of electromagnetic (EM) radiation. Indeed, a few seconds after the merger, the satellites FERMI and INTEGRAL detected a flare of 
$\gamma$-rays in a direction of the sky compatible with the arrival direction of the GWs (Goldstein et al. Reference Goldstein, Veres, Burns, Briggs, Hamburg, Kocevski, Wilson-Hodge, Preece, Poolakkil and Roberts2017; Savchenko et al. Reference Savchenko, Ferrigno, Kuulkers, Bazzano, Bozzo, Brandt, Chenevez, Courvoisier, Diehl and Domingo2017). A few hours later, ground-based telescopes identified the host galaxy of the GW source, NGC4993, by detecting the optical and near-infrared (NIR) counterpart (e.g. Chornock et al. Reference Chornock, Berger, Kasen, Cowperthwaite, Nicholl, Villar, Alexander, Blanchard, Eftekhari and Fong2017; Coulter et al. Reference Coulter, Foley, Kilpatrick, Drout, Piro, Shappee, Siebert, Simon, Ulloa and Kasen2017; Drout et al. Reference Drout, Piro, Shappee, Kilpatrick, Simon, Contreras, Coulter, Foley, Siebert and Morrell2017; Pian et al. Reference Pian, D'Avanzo, Benetti, Branchesi, Brocato, Campana, Cappellaro, Covino, D'Elia and Fynbo2017; Shappee et al. Reference Shappee, Simon, Drout, Piro, Morrell, Prieto, Kasen, Holoien, Kollmeier and Kelson2017). A few days later the source was observed also in the X-ray and radio bands, and the observations continued for years after the GW event (Haggard et al. Reference Haggard, Nynka, Ruan, Kalogera, Cenko, Evans and Kennea2017; Troja et al. Reference Troja, Piro, van Eerten, Wollaeger, Im, Fox, Butler, Cenko, Sakamoto and Fryer2017; Alexander et al. Reference Alexander, Margutti, Blanchard, Fong, Berger, Hajela, Eftekhari, Chornock, Cowperthwaite and Giannios2018; D'Avanzo et al. Reference D'Avanzo, Campana, Salafia, Ghirlanda, Ghisellini, Melandri, Bernardini, Branchesi, Chassande-Mottin and Covino2018; Mooley et al. Reference Mooley, Deller, Gottlieb, Nakar, Hallinan, Bourke, Frail, Horesh, Corsi and Hotokezaka2018; Ghirlanda et al. Reference Ghirlanda, Salafia, Paragi, Giroletti, Yang, Marcote, Blanchard, Agudo, An and Bernardini2019; Hajela et al. Reference Hajela, Margutti, Kathirgamaraju, Giannios, Laskar, Alexander, Coppejans, Fong and Berger2020; Troja et al. Reference Troja, van Eerten, Zhang, Ryan, Piro, Ricci, O'Connor, Wieringa, Cenko and Sakamoto2020). This NS–NS merger, known as GW170817, which was observed through gravitational and multiwavelength EM radiation (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2017e), marked the dawn of the new field of multimessenger astronomy with GWs.
The impact of the first GW-EM multimessenger detection has been wide. It contributed to answering many fundamental questions within the field of high-energy astrophysics and fundamental physics, such as the origin of a class of very energetic 
$\gamma$-ray emissions coming from distant galaxies known as short 
$\gamma$-ray bursts, and the existence of optical sources powered by the radioactive decay of heavy elements, known as kilonovae (or macronovae). The NS–NS mergers show themselves to be able to form collimated and very energetic outflows of matter, and to be important (likely dominant) formation sites of the heaviest elements in the universe such as gold, platinum, the lanthanides and the actinides. Moreover, this event furnished constraints, independent from those already extant, to the unknown equation of state of NS (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2018) and the Hubble constant (Fishbach et al. Reference Fishbach, Gray, Magaña Hernandez, Qi, Sur, Acernese, Aiello, Allocca, Aloy and Amato2019), extending the range of influence of multimessenger astronomy to the fields of quantum chromodynamics and cosmology. It is evident thus that the scientific potential of multimessenger astronomy is huge and covers many branches of physics.
Gravitational wave astrophysics and the physics governing the electromagnetic emission from GW sources are still in their early phase, and there is still an enormous theoretical effort required to be ready to interpret the multimessenger observations expected in the upcoming years. In this context, the physics of plasma plays a key role. The majority of the problems, which are not fully understood yet, require a deep knowledge of the dynamics of the plasmas in extreme regimes. Examples include the amplification of magnetic field during an NS–NS merger, the acceleration of particles responsible for the observed radiation and the role of magnetic reconnection in high-energy astrophysical processes. On the other hand, the universe constitutes a unique laboratory in which to get a better insight on the physics of plasma. It allows us to observe and study regimes of temperature, density and magnetic field that cannot be reached in laboratory experiments. In the near future, we expect great possibilities to explore these regimes due to the recently developed GW detectors and their next generation operating in synergy with innovative multiwavelength observatories, such as the Cherenkov Telescope Array (CTA) (Actis et al. Reference Actis, Agnetta, Aharonian, Akhperjanian, Aleksić, Aliu, Allan, Allekotte, Antico and Antonelli2011; Acharya et al. Reference Acharya, Actis, Aghajani, Agnetta, Aguilar, Aharonian, Ajello, Akhperjanian, Alcubierre and Aleksić2013), the proposed THESEUS mission (Amati et al. Reference Amati, O'Brien, Götz, Bozzo, Tenzer, Frontera, Ghirlanda, Labanti, Osborne and Stratta2018; Stratta et al. Reference Stratta, Ciolfi, Amati, Bozzo, Ghirlanda, Maiorano, Nicastro, Rossi, Vinciguerra and Frontera2018), the Vera C. Rubin Observatory (Ivezić et al. Reference Ivezić, Kahn, Tyson, Abel, Acosta, Allsman, Alonso, AlSayyad, Anderson and Andrew2019), the European Extremely Large Telescope (ELT) (Gilmozzi & Spyromilio Reference Gilmozzi and Spyromilio2007), the Square Kilometre Array (SKA) (Carilli & Rawlings Reference Carilli and Rawlings2004) and more. This will boost considerably our understanding of the high-energy universe.
Here, we review the main EM counterparts of compact binary mergers – in particular NS–NS and NS–BH mergers – describing in a synthetic form the leading theoretical models and the most important open problems in the field. Our aim is not to give the reader a complete dissertation of the topic, but to provide a basic insight on the astrophysical processes involved in the coalescence of a compact binary system. For more detailed information, we will refer the interested reader to other reviews devoted to the specific topics summarized here (e.g. Piran Reference Piran2004; Shibata & Taniguchi Reference Shibata and Taniguchi2011; Bartos, Brady & Márka Reference Bartos, Brady and Márka2013; Berger Reference Berger2014; Kumar & Zhang Reference Kumar and Zhang2015; Rosswog Reference Rosswog2015; Baiotti & Rezzolla Reference Baiotti and Rezzolla2017; Metzger Reference Metzger2017; Ciolfi Reference Ciolfi2018; Nakar Reference Nakar2019; Ciolfi Reference Ciolfi2020b).
This review is organized as follows. In § 2 we clarify some basic definitions useful for the reader. In § 3 we describe the dynamics of a compact binary merger. In § 4 we describe the process occurring after the merger, the EM emission they are responsible for and the open problems in the field. Finally, in § 5 we present our final remarks.
2. Basic definitions and constants
In this section we summarize some basic terms that are commonly used in astrophysics but which the plasma physics community may not be familiar with.
• ‘Transient’. A transient is an astrophysical phenomenon with a short temporal duration compared with human time scales, namely it can last from seconds (or less) to years. For example, a supernova, which can be observable for months, is a transient, while a non-variable star, whose lifetime lies in the range
$10^6\text {--}10^{10}$ years, is not.• ‘Metallicity’. An abundance of elements heavier than Helium (hence with atomic number greater than 2). In astrophysics generally we refer to these elements as metals.
• ‘Compact object’. An astrophysical object with high mass compressed in a small volume. In particular, here compact object will refer only to NSs and (stellar-mass) BHs. An NS has a mass equal to 1–2 times the mass of the Sun within a radius of
$10\text {--}13\ \textrm {km}$. Black holes treated in this review have a mass between a few times and 100 times the mass of the Sun. Their Schwarzschild radius increases linearly with the BH mass. For a BH of one solar mass, the Schwarzschild radius is ${\sim }3\ \textrm {km}$.• ‘Lightcurve’. The lightcurve of a transient is the temporal evolution of the luminosity (or flux) of the source in a given frequency range. We refer to bolometric lightcuvre when the frequency range coincides with the whole EM spectrum.
Throughout the review the masses will be commonly expressed in terms of solar masses, where a solar mass corresponds to 
$1.989 \times 10^{33}\ \textrm {g}$ and is indicated by the symbol 
$\textrm {M}_\odot$. Distances of astrophysical sources are expressed in multiples of parsec (pc), where 
$1\ \textrm {pc} = 3.09 \times 10^{18}\ \textrm {cm}$.
3. Coalescence dynamics
The merger of an NS–NS or an NS–BH binary system is a complex event that requires full general relativistic magnetohydrodynamical (MHD) simulations to be properly studied. In fact, different initial orbital parameters and/or NS equation of state (EOS) can lead to a substantially different merger dynamics and in the case of an NS–NS merger even to different types of remnant objects. All the possible merger channels are summarized in figure 1. While an NS–BH merger can only result in the formation of a more massive BH, with an accretion disk if the NS is disrupted outside the BH's innermost stable circular orbit or without a disk in the opposite case, an NS–NS merger can result in the formation of a BH, a stable NS or, in most cases, a metastable NS collapsing to a BH after some time (e.g. Shibata, Taniguchi & Uryū Reference Shibata, Taniguchi and Uryū2005; Shibata & Taniguchi Reference Shibata and Taniguchi2006; Baiotti, Giacomazzo & Rezzolla Reference Baiotti, Giacomazzo and Rezzolla2008; Rezzolla et al. Reference Rezzolla, Baiotti, Giacomazzo, Link and Font2010; Hotokezaka et al. Reference Hotokezaka, Kyutoku, Okawa, Shibata and Kiuchi2011; Bauswein, Baumgarte & Janka Reference Bauswein, Baumgarte and Janka2013; Giacomazzo & Perna Reference Giacomazzo and Perna2013; Ciolfi et al. Reference Ciolfi, Kastaun, Giacomazzo, Endrizzi, Siegel and Perna2017; Bernuzzi Reference Bernuzzi2020). This last case can be divided in two subregimes: if the NS can be supported against collapse by uniform rotation the star is called supramassive neutron star (SMNS) and it remains stable as long as the rotation is not quenched. It is not clear for how long the collapse can be delayed and still result in a BH surrounded by a massive accretion disk (Margalit, Metzger & Beloborodov Reference Margalit, Metzger and Beloborodov2015; Ciolfi et al. Reference Ciolfi, Kastaun, Kalinani and Giacomazzo2019). If the star is instead so massive that can only be supported in the presence of differential rotation, it will collapse as soon as the NS core has acquired uniform rotation, which happens on time scales of 
$O(100\ \textrm {ms})$. This object is named hypermassive neutron star (HMNS), and it likely leads to the formation of an accretion disk.
Different scenarios for an NS–NS and an NS–BH merger and the merger remnant. The EM radiation is expected when an accretion disk and unbound mass are left outside the merger remnant.
It is worth noting that during an NS–NS merger general relativistic MHD simulations show the development of the Kelvin–Helmholtz (KH) instability in the shear layer separating the two NS cores when they first come into contact. The generation of vortices amplifies the toroidal component of the magnetic field, even by one order of magnitude or more in the first few milliseconds (e.g. Kiuchi et al. Reference Kiuchi, Cerdá-Durán, Kyutoku, Sekiguchi and Shibata2015). Later on, further amplification is provided by magnetic field line winding and the magnetorotational instability (MRI) (Balbus & Hawley Reference Balbus and Hawley1991; Duez et al. Reference Duez, Liu, Shapiro, Shibata and Stephens2006; Siegel et al. Reference Siegel, Ciolfi, Harte and Rezzolla2013). Combined together, these processes are expected to increase the magnetic field strengths from premerger levels of the order of 
$B\sim 10^{12}\ \textrm {G}$ up to 
$B\sim 10^{15}\text {--}10^{16}\, \mathrm {G}$ (e.g. Price & Rosswog Reference Price and Rosswog2006; Giacomazzo et al. Reference Giacomazzo, Zrake, Duffell, MacFadyen and Perna2015). An NS with such a high magnetic field is usually called magnetar.Footnote 1 In this context, an important issue is represented by the finite spatial resolution of the simulations, which is currently not sufficient to fully capture small-scale amplification mechanisms like the KH instability (Kiuchi et al. Reference Kiuchi, Cerdá-Durán, Kyutoku, Sekiguchi and Shibata2015). To overcome this limitation, effective subgrid amplification methods have been proposed (e.g. Giacomazzo et al. Reference Giacomazzo, Zrake, Duffell, MacFadyen and Perna2015; Carrasco, Viganò & Palenzuela Reference Carrasco, Viganò and Palenzuela2020; Viganò et al. Reference Viganò, Aguilera-Miret, Carrasco, Miñano and Palenzuela2020).
A further important aspect to explore in compact binary mergers (CBMs) is the ejection of mass during the merger and post-merger phases. Part of the NS matter can expelled and become unbound (Davies et al. Reference Davies, Benz, Piran and Thielemann1994; Rosswog et al. Reference Rosswog, Liebendörfer, Thielemann, Davies, Benz and Piran1999). Tidal forces right before merger can cause partial disruption of the (two) NS(s), with material launched at mildly relativistic velocities on the orbital plane of the system (especially for binary systems characterized by objects of unequal mass). Moreover, once the accretion disk is formed, neutrino irradiation, nuclear recombination and magnetohydrodynamic viscosity can drive mass outflows from the disk (see § 4.3 for more details and references). In the specific case of NS–NS mergers, further ejection of matter in all directions (including polar regions) is produced by the shocks launched in the contact interface between the two stars when they touch. Moreover, the (meta)stable massive NS resulting from the merger can launch an additional baryon-loaded wind up to its collapse to a BH, if any (e.g. Ciolfi & Kalinani Reference Ciolfi and Kalinani2020). More details on these different ejecta components are given in §§ 4.3 and 4.4.
We conclude this section by briefly providing a qualitative description of the GW signal expected from a CBM. This signal can be divided into three phases: the inspiral, where the two objects are still distant and can be treated as point-like masses; the merger, where the objects come into contact and matter and finite size effects play an important role; and the ringdown, the final phase in which the newly formed compact object relaxes in a stationary configuration emitting an exponentially damped oscillating signal. The GW waveform of the inspiral part is a signal oscillating at a frequency of 
$f_{\textrm {GW}} = 2f_{\textrm {K}}$, where 
$f_{\textrm {K}}$ is the Keplerian orbital frequency of the system which increases in time as the stars get closer. Its amplitude in turn follows the increase of frequency as 
$f_{\textrm {GW}}^{2/3}$. The resulting waveform is called chirp.Footnote 2
Contrary to the inspiral signal, detailed simulations in general relativity are required to calculate the merger and post-merger GW signals, which strongly depend on the (still unknown) EOS describing NS matter at supranuclear densities. For NS-NS mergers, the post-merger signal (until collapse to a BH, if any) is typically dominated by a single frequency, related to the fundamental oscillation mode of the remnant. On longer time scales, if a long-lived SMNS or a stable NS is formed, it is expected to assume an ellipsoidal shape. This object will then further emit GWs at both 
$2f_{\textrm {rot}}$ and 
$f_{\textrm {rot}}$ frequencies, where 
$f_{\textrm {rot}}$ is the spin frequency. Since the object keeps spinning down and the amplitude of the signal is proportional to 
$f^2_{\textrm {rot}}$, the resulting waveform will be a sort of inverse chirp. The amplitude is also directly proportional to the remnant deformations with respect to axisymmetry around the spin axis, encoded by a quadrupolar ellipticity. Significant deformations can be expected, e.g. if the object has a strong internal magnetic field (e.g. Cutler Reference Cutler2002; Dall'Osso, Shore & Stella Reference Dall'Osso, Shore and Stella2009; Ciolfi & Rezzolla Reference Ciolfi and Rezzolla2013; Dall'Osso, Stella & Palomba Reference Dall'Osso, Stella and Palomba2018; Lander & Jones Reference Lander and Jones2020).
4. Electromagnetic emission
In general, when at least one NS is involved in the merger, emission of photons is expected along with GWs. In figure 2 we illustrate the different EM emission components represented with a different colour. The only cases where the EM emission may be suppressed are when a BH is promptly formed and leaves no accretion disk nor ejected material in NS binary mergers, and when the NS is swallowed by the BH without being disrupted in NS–BH mergers.
Artistic representation of the scenario following an NS–NS/NS–BH merger, when an accreting BH is formed. The red component denotes the tidal ejecta, the blue component the hydrodynamic and wind ejecta, the purple component the jet and the yellow component the matter of the ejecta heated by the jet (cocoon). The different components are not represented in scale.
It is also possible that EM emission takes place even before the merger. This kind of emission, known as precursor emission, would occur irrespective of the final fate of the merger, namely it would be present even if a BH with no accretion disk results from the coalescence. Precursor emission will be discussed in § 4.1.
The remnant object resulting from the merger, either a differentially rotating massive NS or a BH surrounded by an accretion disk, is expected to launch a jet of relativistic matterFootnote 3 (purple component in figure 2) by physical processes which are, at present, not completely understood. The mechanisms to launch a jet are discussed later in § 4.2.1.
Once formed, the jet drills through a dense circumburst medium, constituted by the material previously expelled by the merger (blue component in figure 2). During the jet crossing, the material in front of the jet's head is heated and moved aside, forming a hot structure called cocoon (yellow component in figure 2). The cocoon, in turn, exerts a transverse pressure which confines and further collimates the jet (Bromberg et al. Reference Bromberg, Nakar, Piran and Sari2011; Lazzati & Perna Reference Lazzati and Perna2019; Salafia et al. Reference Salafia, Barbieri, Ascenzi and Toffano2019). If sufficiently energetic, the jet successfully emerges from the surrounding material (whose radius at this time is of the order 
${\sim }10^{10}\ \textrm {cm}$), otherwise the jet can be choked. In the successful case, the jet travels until it becomes transparent at a radius of the order 
${\sim }10^{12}\ \textrm {cm}$ from the central engine (Piran Reference Piran1999; Daigne & Mochkovitch Reference Daigne and Mochkovitch2002). At a distance range of 
$10^{13}\text {--}10^{16}\ \textrm {cm}$ the jet dissipates part of its kinetic energy powering an energetic gamma-ray radiation known as the GRB prompt emission. Alternatively, this emission can occur at the photosphere if the energy is dissipated below it. The internal dissipation mechanism is still poorly understood. Later on, the jet decelerates shocking the interstellar medium (in light blue in figure 2), powering a fading synchrotron emission from X-ray to radio called GRB afterglow. The GRB prompt and afterglow emission will be discussed in more detail in § 4.2. It is worth noticing that further EM radiation can originate from the cocoon when it breaks out from the circumburst medium and when it cools down by thermal emission. This kind of counterpart will not be discussed in the present review and we refer the interested reader to Nakar (Reference Nakar2019).
The other component of the matter left outside after the CBM and unbound from the central remnant (blue and red components in figure 2) is rich of free neutrons and neutron-rich nuclei and represents an ideal site for the r-process nucleosynthesis of heavy elements (Lattimer & Schramm Reference Lattimer and Schramm1974; Symbalisty & Schramm Reference Symbalisty and Schramm1982), whose radioactive decay heats up the material itself. This results in a thermal emission from the ejecta that generates a transient known as KN which will be discussed in more detail in § 4.3. It is also worth noting that the shock onto the interstellar medium of these mildly relativistic and subrelativistic outflows could in principle power a synchrotron emission expected to be observable in radio frequencies (Nakar & Piran Reference Nakar and Piran2011).
If the merger remnant is a very long-lived SMNS or a stable NS, the conditions required to form a magnetosphere can be met, leading to a magnetic dipole spindown radiation phase. Such emission would then energize the surrounding material (i.e. the previously emitted baryon-rich ejecta) powering an additional SDPT.
The EM counterparts of CBM briefly described here will be discussed in more detail in the following, with a special focus on the open problems in the field.
4.1. Precursor emission
The precursor emission is an EM signal preceding in time the peak of GW radiation, namely it is supposed to be emitted during the inspiral phase of the binary.
The general idea is that the signal is generated by the interaction between NS's magnetospheres (in case of an NS–NS system) or the orbital motion of a non-/weakly magnetized object through the magnetosphere of the companion. The latter framework, known as unipolar inductor has been studied analytically both for NS–NS (Vietri Reference Vietri1996; Hansen & Lyutikov Reference Hansen and Lyutikov2001; Lai Reference Lai2012; Piro Reference Piro2012; Sridhar et al. Reference Sridhar, Zrake, Metzger, Sironi and Giannios2020) and NS–BH systems (McWilliams & Levin Reference McWilliams and Levin2011). In this framework the motion of the non-magnetized object through the companion magnetic field generates, due to Faraday's law, an electromotive force on the non-magnetized object. In this way a direct current circuit is established between the two stars, where the field lines behave like wires and the non-magnetized object as a battery. The accelerated charges may dissipate on the stellar surface or in the space between the two stars. In the latter case they may emit radio waves in a pulsar-like fashion or trigger a pair cascade resulting in a wind emitting in the X-rays (Hansen & Lyutikov Reference Hansen and Lyutikov2001; Piro Reference Piro2012). Furthermore, shocks arising within the wind may generate an observable coherent radio emission through a synchrotron maser process (Sridhar et al. Reference Sridhar, Zrake, Metzger, Sironi and Giannios2020).
The problem has been studied also with general relativistic resistive MHD (Palenzuela et al. Reference Palenzuela, Lehner, Ponce, Liebling, Anderson, Neilsen and Motl2013), special relativistic (Sridhar et al. Reference Sridhar, Zrake, Metzger, Sironi and Giannios2020), force-free (Most & Philippov Reference Most and Philippov2020) and particles-in-cell (Crinquand, Cerutti & Dubus Reference Crinquand, Cerutti and Dubus2019) simulations. These works allow us to appreciate the important role of magnetic reconnection in accelerating particles, which can further contribute to the emission.
Since this kind of emission takes place during the inspiral phase, its occurrence is insensitive of the merger product, namely it can be generated even in those cases in which no matter is left outside the newly formed BH. In these cases precursors represent the only possible EM counterpart. Although there is not a compelling observation for the above-described precursor yet, surveys able to detect them can provide candidate counterparts to be used for a coincident search of GWs.
4.2. $\gamma$-ray bursts
Gamma-ray bursts are highly energetic transient astrophysical sources of extragalactic origin, which have non-thermal spectra peaking at 
$10$ keV–
$10$ MeV. The 
$\gamma$-ray flaring activity of GRBs, which is called prompt emission, lasts typically less than a hundred of seconds and its lightcurve manifests a plethora of different morphologies and a time variability (time scale in which the fluxes vary by more than a factor of two) that can be of the order of few milliseconds (Walker, Schaefer & Fenimore Reference Walker, Schaefer and Fenimore2000). Examples of typical prompt emission lightcurves are shown in figure 3, where the GRB data are taken by Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma Ray Observatory (CGRO) and the lightcurves are expressed in terms of counts per seconds. The prompt emission is followed by the fainter afterglow across the whole EM spectrum which decay in time. An example of a typical afterglow lightcurve in different spectral ranges is shown in figure 4.
Examples of GRB prompt emission lightcurves (
$E>20\ \textrm {~keV}$) from the online BATSE catalogue (https://gammaray.nsstc.nasa.gov/batse/grb/lightcurve/).
Example of a GRB afterglow in different spectral ranges. The data reported are for GRB 130427A afterglow (Panaitescu, Vestrand & Woźniak Reference Panaitescu, Vestrand and Woźniak2013). (Figure courtesy of Alin Panaitescu.)
The duration of the prompt emission shows a bimodal distribution (Kouveliotou et al. Reference Kouveliotou, Meegan, Fishman, Bhat, Briggs, Koshut, Paciesas and Pendleton1993), with two peaks at 
$0.3\ \textrm {s}$ and 
$30\ \textrm {s}$, which unveils the presence of two distinct GRB populations, also characterized by a different hardness of the spectrum: the population of short duration events with a harder spectrum, called short GRBs (SGRBs), and the population of long duration events with a softer spectrum, called long GRBs (LGRBs). The duration commonly used to separate short GRBs from long ones is 
$2\ \textrm {s}$ in the BATSE energy range (
$20\text {--}600\ \textrm {~keV}$).
From the 
$\gamma$-ray fluence and the distance of the source it is possible to calculate the isotropic equivalent energy of the burst, which can reach 
$E_{\gamma , \textrm {ISO}} \sim 10^{54}\ \mathrm {erg}$ (Briggs et al. Reference Briggs, Band, Kippen, Preece, Kouveliotou, van Paradijs, Share, Murphy, Matz and Connors1999; Abdo et al. Reference Abdo, Ackermann, Arimoto, Asano, Atwood, Axelsson, Baldini, Ballet, Band and Barbiellini2009) for the most energetic GRBs. However, there is very strong evidence that the emission is not isotropic but beamed (Rhoads Reference Rhoads1997, Reference Rhoads1999; Frail et al. Reference Frail, Kulkarni, Sari, Djorgovski, Bloom, Galama, Reichart, Berger, Harrison and Price2001). This reduces the value of the real energy by a factor equal to the solid angle of collimation 
$\theta ^2/2$, limiting it in the range 
$10^{49}\text {--}10^{51}\ \mathrm {erg}$ (Frail et al. Reference Frail, Kulkarni, Sari, Djorgovski, Bloom, Galama, Reichart, Berger, Harrison and Price2001; Panaitescu & Kumar Reference Panaitescu and Kumar2001; Bloom, Frail & Kulkarni Reference Bloom, Frail and Kulkarni2003).
The variability time scales 
$\delta t$ can give us further insight on the origin of this emission. It constrains the emitting region to a characteristic size of 
$l \sim c \delta t$. This size, together with the high luminosity and the fact that the emission lies in the 
$\gamma$-ray frequency range, leads to a source that should be so compact to be opaque to 
$\gamma -\gamma$ pair-production, which is in tension with the non-thermal nature of the observed spectra. This problem, known as the compactness problem (Ruderman Reference Ruderman1975; Goodman Reference Goodman1986; Paczynski Reference Paczynski1986; Piran Reference Piran1995), is solved by requiring that the source is moving relativistically towards the observer with a Lorentz factor 
$\varGamma \ge 100$. This results in an increase of the true size of the source by a factor 
$\varGamma ^2$, and in a blue-shift of the energy, which increases in the observer frame by a factor 
$\varGamma$ (for a more detailed discussion of the compactness problem see Piran (Reference Piran2004)).
All the above considerations indicate that GRBs are generated by a collimated source moving relativistically towards the observer, the relativistic jet. The jet must be launched by some physical processes occurring within a short-livingFootnote 4 object, which is usually referred to as a central engine, originated from a progenitor system.
The SGRBs and LGRBs have different progenitors. This was revealed by studies of the GRB energetics and redshift distribution (Nakar Reference Nakar2007), properties of their afterglow (Panaitescu, Kumar & Narayan Reference Panaitescu, Kumar and Narayan2001; Kann et al. Reference Kann, Klose, Zhang, Covino, Butler, Malesani, Nakar, Wilson, Antonelli and Chincarini2011), their host galaxies (Berger Reference Berger2009; Fong et al. Reference Fong, Berger, Chornock, Margutti, Levan, Tanvir, Tunnicliffe, Czekala, Fox and Perley2013) and the recent observations of GWs.
A fraction of LGRBs optical afterglows show a late-time (in few weeks) bump due to an emergent associated type Ic supernova.Footnote 5 Thus, the LGRB afterglow observations empirically associate the sources of LGRBs with the death of massive stars (masses 
$M>20M_{\odot }$) (Woosley & Bloom (Reference Woosley and Bloom2006) and references therein). The same conclusion comes from the study of their host galaxies which are typically irregular and star-forming galaxies (Fruchter et al. Reference Fruchter, Levan, Strolger, Vreeswijk, Thorsett, Bersier, Burud, Castro Cerón, Castro-Tirado and Conselice2006). The LGRBs are preferentially located in the brightest spots of their host galaxies, i.e. highly star-forming regions where the massive stars are born. The supernovae signatures in LGRBs observations and the preferential location in actively star-forming regions, are strong evidence that massive stars are the progenitors of LGRBs.
On the other hand, most of the host galaxies of SGRBs show a relatively low star-formation rate (Fong, Berger & Fox Reference Fong, Berger and Fox2010). When SGRBs are in star-forming galaxies, they are located in regions with lower star-formation rate and associate with an older star population with respect to LGRBs. This indicates that progenitors of SGRBs are older than those of LGRBs, since the region where they had formed is not active anymore or/and they had enough time to move away from their birth place. Astrophysical events satisfying all the required characteristics to be progenitors of SGRBs are the mergers of NS–NS or NS–BH binaries (Blinnikov et al. Reference Blinnikov, Novikov, Perevodchikova and Polnarev1984; Paczynski Reference Paczynski1986; Eichler et al. Reference Eichler, Livio, Piran and Schramm1989). The first strong observational evidence to identify their progenitors came from the coincident detection of the first GW signal from the merger of NS–NS, GW170817, by the advanced LIGO and Virgo interferometers and the SGRB named GRB 170817A by the 
$\gamma$-ray detectors FERMI-GBM and INTEGRAL (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2017e; Goldstein et al. Reference Goldstein, Veres, Burns, Briggs, Hamburg, Kocevski, Wilson-Hodge, Preece, Poolakkil and Roberts2017; Savchenko et al. Reference Savchenko, Ferrigno, Kuulkers, Bazzano, Bozzo, Brandt, Chenevez, Courvoisier, Diehl and Domingo2017). Together with the multiwavelength observations spanning more than two years, which demonstrated the presence of a relativistic jet, this proved that the merger of two NS (in this specific case of total mass of 
$2.74_{-0.01}^{+0.04}\ \textrm {M}_{\odot }$) can give rise to SGRBs.
Both core-collapse of a massive star and CBM involving NS are able to generate GRBs by forming either a temporary accretion disk around the remnant BH or a massive (meta)stable NS. These remnant systems are potentially able to power a relativistic jet via different mechanisms, and thus they are considered the most plausible GRB central engines. The internal dissipation of the jet energy at 
$R_{\gamma } \sim 10^{13} \ \textrm {cm}\text {--}10^{16}\ \textrm {cm}$ produces the observed short-duration (
$10^{-3}\text {--}10^{3}\ \textrm {s}$) prompt emission seen in the keV–MeV energy range (Meszaros, Rees & Papathanassiou Reference Meszaros, Rees and Papathanassiou1994; Rees & Meszaros Reference Rees and Meszaros1994; Daigne & Mochkovitch Reference Daigne and Mochkovitch1998; Piran Reference Piran1999) or, alternatively, the jet energy can be dissipated below the photosphere (
$R \sim 10^{12}\ \textrm {cm}$) and released at the photosphere (e.g. Rees & Mészáros Reference Rees and Mészáros2005; Pe'er Reference Pe'er2008; Beloborodov Reference Beloborodov2010; Lazzati et al. Reference Lazzati, Morsony, Margutti and Begelman2013; Bhattacharya & Kumar Reference Bhattacharya and Kumar2020).
The deceleration of the jet in the surrounding medium gives rise to the long-lived afterglow observed in the X-ray, optical and radio bands (Paczynski & Rhoads Reference Paczynski and Rhoads1993; Mészáros & Rees Reference Mészáros and Rees1997a; Sari, Piran & Narayan Reference Sari, Piran and Narayan1998). The characteristic physical size of the afterglow emitting region is 
$R_{\textrm {aft}} \sim 10^{16}\text {--}10^{17} \ \textrm {cm}$. The sketch of the basic model of the GRB phenomenon is shown in figure 5.
Pictorial representation of the basic model of the GRB: the core-collapse of a massive star or the coalescence of an NS–NS (or NS–BH) leads to the formation of an accreting BH, which launches an ultrarelativistic outflow in a form of a jet. Internal dissipation of the jet's kinetic energy through shocks produces the prompt emission in the keV–MeV range. The forward shock of the jet with ambient medium forms the afterglow radiation observed in the X-ray, optical and radio bands.
Since SGRBs originate from CBMs, they are the main objective of the present review. Nevertheless, various aspects discussed in the following apply also to the case of LGRBs.
4.2.1. Central engine of short GRBs
One of the fundamental unresolved questions in the GRB physics lies in the identification of the powerhouse of the relativistic jet (see, e.g. Ciolfi (Reference Ciolfi2018) for a more extensive review). The proposed scenarios as the central engine of GRBs need to satisfy some minimal physical requirements.
One of them is the ability to power a jet with bulk Lorentz factors of order 
$\varGamma \ge 100$. This implies that the formed jet should contain a small number of baryons, otherwise their large inertia will prevent the fast motion (Shemi & Piran Reference Shemi and Piran1990). Moreover, highly variable light curves of the prompt emission suggest a discontinuous release of energy. As mentioned before, the main candidate that satisfies the above requirements is the hyperaccretion of a stellar mass BH, accreting at a rate 
$\dot {M} = 1\ \textrm {M}_\odot \ \textrm {s}^{-1}$ (Woosley Reference Woosley1993). This rate is very high and exceeds by several orders of magnitude the Eddington limit, above which the feedback of radiation released by the accretion is strong enough to sweep off the infalling material hampering in this way the accretion. This limit in GRBs can be overcome because the disks are thought to be in a peculiar accretion regime, named neutrino-dominated accretion flow, where due to the high density and pressure,photons are trapped inside the matter and the neutrino emission dominates the disk cooling (see Liu, Gu & Zhang (Reference Liu, Gu and Zhang2017), for a recent review). Alternatively, a magnetar in fast rotation (periods of milliseconds) can power the relativistic jet via its rotational energy (Usov Reference Usov1992).
The duration of the prompt emission is a further constraint on the nature of the central engine. While the prompt emission lasts for less than two seconds, we can observe late-time X-ray plateaus and/or flares (at 
$10^{3}\text {--}10^{4}$ s) (Nousek et al. Reference Nousek, Kouveliotou, Grupe, Page, Granot, Ramirez-Ruiz, Patel, Burrows, Mangano and Barthelmy2006; O'Brien et al. Reference O'Brien, Willingale, Osborne, Goad, Page, Vaughan, Rol, Beardmore, Godet and Hurkett2006; Zhang et al. Reference Zhang, Fan, Dyks, Kobayashi, Mészáros, Burrows, Nousek and Gehrels2006; Chincarini et al. Reference Chincarini, Moretti, Romano, Falcone, Morris, Racusin, Campana, Covino, Guidorzi and Tagliaferri2007; Falcone et al. Reference Falcone, Morris, Racusin, Chincarini, Moretti, Romano, Burrows, Pagani, Stroh and Grupe2007). If we interpret these as a continuation of the energy output from the central engine (Rees & Mészáros Reference Rees and Mészáros1998), then the central engine needs to be very long-lived and/or reactivated at such late times (e.g. Dai & Lu Reference Dai and Lu1998; Zhang & Mészáros Reference Zhang and Mészáros2001; Yu, Cheng & Cao Reference Yu, Cheng and Cao2010).
In the case of an accreting BH central engine, the latter can power the jet by different mechanisms. The most discussed are the neutrino–antineutrino annihilation process (Goodman, Dar & Nussinov Reference Goodman, Dar and Nussinov1987; Eichler et al. Reference Eichler, Livio, Piran and Schramm1989; Zalamea & Beloborodov Reference Zalamea and Beloborodov2011) and the Blandford–Znajek (BZ) mechanism (Blandford & Znajek Reference Blandford and Znajek1977). The first mechanism is based on the fact that in the hottest inner part of the accretion disk, neutrino cooling is expected to become very efficient. When this happens, the annihilation of neutrino and antineutrino pairs above the disk should lead to the formation of an expanding fireball (electron–positron plasma mixed with photons). An estimate of the expected luminosity of the jet in this scenario comes from the power of neutrino–antineutrino annihilation and it is 
${\sim }10^{52}$ erg s
$^{-1}$ for a 
$3\ \textrm {M}_\odot$ black hole with an accretion rate 
$\dot {M} \sim 1\ \textrm {M}_{\odot }\ \textrm {s}^{-1}$ (Zalamea & Beloborodov Reference Zalamea and Beloborodov2011). It is worth noticing that, in contrast, photon–photon pair production is not an available mechanism because of the above-mentioned regime of GRB's disks, in which photons are trapped and only neutrinos and antineutrinos are able to escape. The second mechanism, currently favoured, consists of extracting the rotational energy of a Kerr BH through a strong magnetic field threading it, which is sustained by electric currents within the accretion disk.
The energy is transported away in the form of a Poynting flux flowing mainly along the BH's rotational axis. For such a Poynting flux to exist a non-zero toroidal component of the magnetic field is required along the axis.Footnote 6 The toroidal magnetic field is generated by a poloidal current, streaming along the poloidal field lines that behave as wires. The electric currents must be sustained by an electromotive force. This is provided by a purely general relativistic effect, namely the frame-dragging around a rotating mass. The frame-dragging applied to the poloidal magnetic field lines results in the appearance of an electric field providing the required electromotive force. It is possible to prove that inside the BH's ergosphere – a region outside the event horizon where the frame-dragging is so intense that even photons are dragged to corotate with the BH – in order to attain the screening of this electric field, the required above mentioned poloidal current cannot vanish (Komissarov Reference Komissarov2004).
A rapidly rotating NS remnant, with a period of the order of few milliseconds and dipolar magnetic field strengths of the order 
${\sim }10^{15}$ G represents a viable alternative to the accreting BH as a machine for the production of a relativistic jet. This central engine is often called a millisecond magnetar. Note that this type of engine can only apply to the case of NS–NS mergers. In such a scenario, the NS remnant, characterized by strong differential rotation, gradually builds up a strong helical magnetic field structure along the spin axis and the corresponding magnetic pressure gradients accelerate a collimated outflow in such direction (Ciolfi Reference Ciolfi2020a). This magnetorotational mechanism will remain active only so long as the differential rotation in the core of the NS remnant persists, which is typically limited to subsecond time scales.
Recent simulations showed that the neutrino–antineutrino annihilation mechanism is likely not powerful enough to explain SGRB energetics (Just et al. (Reference Just, Obergaulinger, Janka, Bauswein and Schwarz2016) and Perego, Yasin & Arcones (Reference Perego, Yasin and Arcones2017b), but see Salafia & Giacomazzo (Reference Salafia and Giacomazzo2020)), pointing in favour of the alternative magnetically driven jet formation. A number of numerical relativity simulations of NS–NS and NS–BH mergers including magnetic fields as a key ingredient studied the potential to form a SGRB jet in the accreting BH scenario (e.g. Rezzolla et al. Reference Rezzolla, Giacomazzo, Baiotti, Granot, Kouveliotou and Aloy2011; Kiuchi et al. Reference Kiuchi, Kyutoku, Sekiguchi, Shibata and Wada2014; Paschalidis, Ruiz & Shapiro Reference Paschalidis, Ruiz and Shapiro2015; Kawamura et al. Reference Kawamura, Giacomazzo, Kastaun, Ciolfi, Endrizzi, Baiotti and Perna2016; Ruiz et al. Reference Ruiz, Lang, Paschalidis and Shapiro2016) and in the magnetar scenario (only for NS–NS mergers; e.g. Ciolfi et al. (Reference Ciolfi, Kastaun, Giacomazzo, Endrizzi, Siegel and Perna2017), Ciolfi et al. (Reference Ciolfi, Kastaun, Kalinani and Giacomazzo2019) and Ciolfi (Reference Ciolfi2020a)). While a final answer is still missing, the most recent results support the BH scenario, either by showing that an incipient jet could form in this case (Paschalidis et al. Reference Paschalidis, Ruiz and Shapiro2015; Ruiz et al. Reference Ruiz, Lang, Paschalidis and Shapiro2016) or by showing that the collimated outflow from a magnetar would most likely be insufficient to explain the energy and Lorentz factors of SGRBs (Ciolfi Reference Ciolfi2020a).Footnote 7
4.2.2. Jet acceleration
Once the jet is formed, it must accelerate to ultrarelativistic velocity. How it happens is strongly connected to the nature of the jet. There exist two limiting cases: a hot internal-energy-dominated jet and a cold magnetic-energy-dominated jet.
The first case is the most explored scenario and is known as hot fireball model (Cavallo & Rees Reference Cavallo and Rees1978; Goodman Reference Goodman1986; Paczynski Reference Paczynski1986). The general idea beyond this framework is that the internal energy of the jet is converted into bulk kinetic energy, such that the temperature of the fireball decreases while the jet accelerates. If we use the typical observed prompt emission luminosity 
$L \sim 10^{52}$ erg s
$^{-1}$ and the variability time scale of 
$10^{-2}$ s, we can estimate the initial temperature of the ejecta as 
$T \sim ( L/4 {\rm \pi} (c \delta t)^2 \sigma _{B} )^{1/4} \sim 2 \times 10^{10}$ K. At this high temperature photons are coupled with electron–positron pairs and baryons. Jets with a small enough number of baryons will undergo an adiabatic expansion while photons cool. Therefore, the initial energy of photons, electrons and positrons is transferred to protons. The acceleration of the jet continues until photons decouple from baryons (Shemi & Piran Reference Shemi and Piran1990; Piran Reference Piran1999).
The photosphere can be defined as a surface at which the optical depth to the Thomson scattering (
$\tau$) is equal to 1. The optical depth is 
$\tau \sim n_{p}\sigma _{T} R/2 \varGamma$, where 
$R$ is the radius of the ejecta and 
$n_{p}$ is the proton density in the outflow. The comoving proton density estimate comes by the proton flux in the jet 
$\dot {M}$ as 
$n_{p}' = \dot {M}/(4 {\rm \pi} R m_{p} c \varGamma )$. Defining the ratio between the radiation luminosity 
$L$ and the baryonic load 
$\dot {M}$ as 
$\eta = L/\dot {M}c^{2}$ we can get the photosphere radius 
$R_{\textrm {ph}} = R(\tau =1)$ as 
$R=L \sigma _{T}/8 {\rm \pi} m_{p} c^{3} \eta \varGamma ^{2}$. Its typical value is 
$R_{\textrm {ph}} \sim 6 \times 10^{12}$ cm (if we use 
$L \sim 10^{52}$ erg s
$^{-1}$, 
$\eta \sim 100$ and 
$\varGamma \sim 100$) (Piran Reference Piran1999; Daigne & Mochkovitch Reference Daigne and Mochkovitch2002). The parameter 
$\eta$ is the test parameter for identification of the jet composition. If thermal emission from the fireball is observed in the prompt emission spectra, its temperature constrains 
$\eta$ and we have knowledge of the initial form of the jet's energy. Unfortunately, we do not have significant observational claims on the thermal components in GRBs spectra to answer to this question.
The alternative is a cold jet, dominated by the Poynting flux (as, for example, in the BZ mechanism). These kinds of jets can be accelerated by converting the magnetic energy in kinetic energy of the bulk flow. This can occur, for example, due to the adiabatic expansion of the outflow, where, in the axisymmetric and stationary limit, the conservation of mass and energy flux leads to the identification of the following conserved quantity:
\begin{equation} \varGamma(1+\sigma) = \textrm{const.}, \end{equation}
where 
$\sigma$ is the plasma magnetization, defined as the ratio of Poynting flux and matter energy flux. This means that the magnetic energy stored in the jet is able, in principle, to accelerate the jet up to the maximum Lorentz factor of 
$\varGamma _{\max } = 1 + \sigma _0 \sim \sigma _0$, where 
$\sigma _0 \gg 1$ is the magnetization at the base of the jet. The acceleration is due to magnetic pressure gradients associated with the build-up of toroidal magnetic field via the winding of field lines caused by the fast and differentially rotating central engine. However, in order to reach 
$\varGamma _{\max }$, the head of the jet must be in causal contact with its base and this condition is reached as long as the flow is subsonic with respect to the speed of a fast-magnetosonic wave. Since this speed is approximately equal to the (relativistic) Alfvén velocity, whose corresponding Lorentz factor is 
$\varGamma _A = \sqrt {1+\sigma }$, the condition 
$\varGamma = \varGamma _A$ sets a limit to the Lorentz factor of 
$\varGamma _{\textrm {MS}} = (1+\sigma _0)^{1/3}\sim \sigma ^{1/3}$, reached at the distance 
$R_{\textrm {MS}}$ from the central engine, which is known as magnetosonic point (Goldreich & Julian Reference Goldreich and Julian1970). This value can be increased by a factor of 
$\theta ^{-2/3}_j$, when the outflow is collimated within an angle 
$\theta _j$ due to the confinement exerted by the circumburst medium (the envelope of the progenitor star for LGRBs, the merger ejecta for SGRBs) (Tchekhovskoy, McKinney & Narayan Reference Tchekhovskoy, McKinney and Narayan2009).
Above the magnetosonic point, the jet can be accelerated either due to adiabatic acceleration, when a non-stationary outflow in place of a time-independent jet is considered (Granot, Komissarov & Spitkovsky Reference Granot, Komissarov and Spitkovsky2011), or by the dissipation of magnetic field due to magnetic reconnection, which converts magnetic energy into thermal energy and, in turn, into bulk kinetic energy, as in the hot fireball case (Drenkhahn Reference Drenkhahn2002; Drenkhahn & Spruit Reference Drenkhahn and Spruit2002). It is worth noting that dissipation processes able to convert a Poynting flux dominated jet into a hot fireball can occur also where the interaction between the jet and the circumburst medium leads to the jet collimation, due to magnetic reconnection driven by unstable internal kink modes as appears in three-dimensional MHD simulations (Bromberg & Tchekhovskoy Reference Bromberg and Tchekhovskoy2016).
For a more detailed description of the jet acceleration mechanisms we refer the reader to Kumar & Zhang (Reference Kumar and Zhang2015) and Zhang (Reference Zhang2018).
4.2.3. Jet dissipation mechanisms
The observed prompt emission is originated by the dissipation of the jet's energy. The short variability of prompt emission lightcurves suggests that the dissipation occurs within the jet (internal dissipation) because the lightcurve produced by the forward shock of the jet into the surrounding ambient medium (external dissipation) is expected to be smoothed over a time scale which is longer than the total duration of the burst (see Fenimore, Madras & Nayakshin Reference Fenimore, Madras and Nayakshin1996; Sari & Piran Reference Sari and Piran1997; Piran Reference Piran1999, Reference Piran2004).
The internal shocks model is widely used as a dissipation mechanism in baryon dominated jets (Rees & Meszaros Reference Rees and Meszaros1994). In that model the central engine produces outflows with random Lorentz factors. The faster part of the outflow catches the slower one. The shocks propagate in both shells converting the bulk kinetic energy of the flow into the kinetic energy of the particle accelerating them, and also leading to a local magnetic field amplification (Heavens & Drury (Reference Heavens and Drury1988) and Sironi & Spitkovsky (Reference Sironi and Spitkovsky2011); for a review on the acceleration of particle in shocks we refer the interested reader to Sironi, Keshet & Lemoine (Reference Sironi, Keshet and Lemoine2015a)). Relativistic electrons in magnetic field are expected to radiate their energy through synchrotron and inverse Compton processes.
The main advantage of the internal shocks model is the possibility of having a short variability time scale. For simplicity, let us consider that the central engine produces two shells (with bulk Lorentz factors 
$\varGamma _1$ and 
$\varGamma _2$) with time difference 
$\delta T$. If the first shell is slower 
$\varGamma _1 < \varGamma _2$ then they collide at time 
$t_{\textrm {coll}}$ defined by 
$v_1 t_{\textrm {coll}} = v_2 (t_{\textrm {coll}}-\delta T)$ (where 
$v_1$ and 
$v_2$ are the shells’ velocities). The radius at which shells collide is 
$R_{\textrm {coll}} = t_{\textrm {coll}} v_1 \sim 2 c \varGamma _{1} \delta T \kappa$ where 
$\kappa = \varGamma _2/\varGamma _1$. The observed variability tracks then the intrinsic central engine variability. However, the efficiency of internal shocks dissipation, which depend on the velocity difference between the two shells, is very low (approximately 
$20\,\%$ or lower) (Kobayashi, Piran & Sari Reference Kobayashi, Piran and Sari1997; Daigne & Mochkovitch Reference Daigne and Mochkovitch2002) and it represents one of the main issues of this model (but see Beniamini, Nava & Piran (Reference Beniamini, Nava and Piran2016)). Moreover, it was realized that the magnetization of the jet should be relatively low, i.e. 
$\sigma \sim 0.01\text {--}0.1$, otherwise the shocks will be suppressed (Sironi, Petropoulou & Giannios Reference Sironi, Petropoulou and Giannios2015b).
Alternatively, the prompt emission can be released at the photosphere, from subphotospheric dissipation (e.g. Rees & Mészáros Reference Rees and Mészáros2005; Pe'er Reference Pe'er2008; Beloborodov Reference Beloborodov2010; Lazzati et al. Reference Lazzati, Morsony, Margutti and Begelman2013; Bhattacharya & Kumar Reference Bhattacharya and Kumar2020). The subphotospheric dissipation can proceed through different mechanisms. One example is radiation dominated shocks, where the dissipation is controlled by photon scattering (e.g. Beloborodov (Reference Beloborodov2017); see also Levinson & Nakar (Reference Levinson and Nakar2020) for a recent review about the topic). Another mechanism involves the turbulence within the jet, which transfer the kinetic energy of the flow to plasma particles, if the turbulence cascade reaches the microscopic scales, or directly to the radiation, in case turbulence cascade is damped at larger scales by bulk Compton scattering (Zrake, Beloborodov & Lundman Reference Zrake, Beloborodov and Lundman2019). Furthermore, if free neutrons are present, nuclear collision can constitute another important dissipation channel (Beloborodov Reference Beloborodov2017).
In the case of a Poynting flux dominated jet the basic dissipation mechanism, as already mentioned in the previous section, is the magnetic reconnection. During the reconnection the magnetic energy is dissipated to accelerate the charges, which then radiate through different emission processes (e.g. synchrotron emission). Particle acceleration can proceed also through a Fermi mechanism. This occurs when the particle scatters through the magnetic islands produced due to tearing instabilities in reconnection events, and moving close to the Alfvén speed (for acceleration of particles in reconnection layers see Spruit, Daigne & Drenkhahn (Reference Spruit, Daigne and Drenkhahn2001), Drenkhahn & Spruit (Reference Drenkhahn and Spruit2002), Sironi & Spitkovsky (Reference Sironi and Spitkovsky2014), Sironi et al. (Reference Sironi, Petropoulou and Giannios2015b) and Petropoulou et al. (Reference Petropoulou, Sironi, Spitkovsky and Giannios2019)). Moreover, tearing instability is also fundamental for enhancing the rate of reconnection events (for reviews on tearing instability see,e.g. Loureiro et al. (Reference Loureiro, Samtaney, Schekochihin and Uzdensky2012) and Comisso et al. (Reference Comisso, Lingam, Huang and Bhattacharjee2016)).
In GRBs magnetic reconnection can be triggered by internal shocks, as proposed by Zhang & Yan (Reference Zhang and Yan2011) in their Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) model. In the ICMART model the shock between shells endowed by ordered magnetic field (generated by the winding of magnetic field line in proximity of the central engine) cause a tangling of the field line, which favours magnetic reconnection on a length scale much smaller than the transverse size of the jet. Moreover, during the reconnection process, the plasma is accelerated and this further distorts the field lines, triggering further reconnection processes in a cascade fashion. The charges accelerated toward the observer radiate through a synchrotron process, and this should generate the 
$\gamma$-ray radiation constituting the GRB prompt emission. The distance from the central engine at which the dissipation occurs in the Zhang & Yan (Reference Zhang and Yan2011) model is rather large, of the order of 
${\sim }10^{16}\ \textrm {cm}$, however, the millisecond observed variability can be attained considering that not the entire jet, but small regions of it, switch on independently.Footnote 8 Contrary to the internal shock model described at the beginning of this section, the ICMART model has a very high radiative efficiency.
4.2.4. Afterglow
As mentioned before, the deceleration of the jet in the surrounding medium gives rise to a long-lived emission, called afterglow, observed in radio frequencies, optical, X-ray, GeV and very recently also at TeV energies (Abdalla et al. Reference Abdalla, Adam, Aharonian, Ait Benkhali, Angüner, Arakawa, Arcaro, Armand, Ashkar and Backes2019; MAGIC Collaboration et al. Reference Acciari, Ansoldi, Antonelli, Arbet Engels, Baack, Babić, Banerjee, Barres de Almeida, Barrio and Becerra González2019). The characteristic radius, measured from the central engine, at which the deceleration, and thus the afterglow, occurs is 
$R_{\textrm {aft}} \sim 10^{16}\text {--}10^{17} \ \textrm {cm}$.
The afterglow theory was developed before the first afterglow had been observed. It predicted an emission with a temporal power-law fading 
$t^{-\alpha }$ in a wide range of frequencies after the deceleration time (defined as the time at which the jet Lorentz factor halves). Here 
$\alpha$ depends on the power-law index 
$p$ of the distribution of the emitting charges (see discussion below) and 
$\alpha \sim 1$ for expected values of 
$p$ (Paczynski & Rhoads Reference Paczynski and Rhoads1993; Mészáros & Rees Reference Mészáros and Rees1997b; Sari et al. Reference Sari, Piran and Narayan1998). This prediction has been confirmed by the first afterglow observations (mainly in the optical band).Footnote 9 However, later observations with the Neil Gehrels Swift Observatory, (hereafter Swift), show that the X-ray lightcurve departures from the simple power-law behaviour , in a substantial fraction of events. The X-ray lightcurves show features like flares and a long-lasting plateau phase, whose origin is, at present, not clearly understood. This open question will be addressed in more detail in § 4.2.5.2.
The afterglow photons arises from the dissipation of the outflow kinetic energy. The supersonic flow of plasma interacts with the ambient developing a forward shock, where particles are accelerated by the Fermi acceleration mechanism (Fermi Reference Fermi1949) and magnetic field is amplified, likely due to the Weibel instability (Weibel Reference Weibel1959). In such a process, charged particles repeatedly cross the shock front gaining an energy proportional to the velocity of the shock front and forming a population of accelerated particles with a power-law distribution of Lorentz factor 
$N_{\gamma } \propto \gamma ^{-p}$, where the index 
$p$ is the power-law index of the distribution, expected to assume a value 
$p\sim 2.5$. These charges then radiate via a synchrotron process, generating the observed emission (Sari et al. Reference Sari, Piran and Narayan1998).
Along with the forward shock crossing the ambient medium, a reverse shock, propagating backward through the afterglow is expected to form if the jet, at this distance, is not strongly magnetized (i.e. 
$\sigma \ll 1$) ( Meszaros & Rees (Reference Meszaros and Rees1993) and Sari & Piran (Reference Sari and Piran1999); see also Kumar & Zhang (Reference Kumar and Zhang2015) for a review).
As long as the outflow is in relativistic motion, the radiation, emitted isotropically in the rest frame, is beamed within an angle 
$\theta _{\textrm {beam}} \sim \varGamma ^{-1}$ in the observer frame. While the jet decelerates and 
$\varGamma$ drops, the beaming angle increases and a wider portion of the emitting surface becomes visible to the observer. When 
$\theta _{\textrm {beam}} \ge \theta _j$ the entire emission surface becomes visible to the observer, which means that there are no more debeamed photons that can be revealed by a further increase in 
$\theta _{\textrm {beam}}$ and the flux start to drop faster, as 
${\sim }t^{-2}$, in the whole EM spectrum (Rhoads Reference Rhoads1999). This achromatic feature, known as jet break, has been one of the strongest pieces of evidence pointing towards the collimated nature of GRB outflows, and, when observed, the time at which it occurs allows us to measure the jet collimation angle 
$\theta _j$ (Sari, Piran & Halpern Reference Sari, Piran and Halpern1999). This information, in turn, is fundamental in measuring the true energetic of the 
$\gamma$-ray prompt emission (Frail et al. Reference Frail, Kulkarni, Sari, Djorgovski, Bloom, Galama, Reichart, Berger, Harrison and Price2001).
4.2.5. Open problems
In this section we address two of the principal open problems of GRBs: the physics behind the prompt emission spectra and the origin of the afterglow X-ray lightcurve.
4.2.5.1. Prompt emission: the mystery of the GRB spectra.
The prompt emission spectrum indicates that the radiative processes are non-thermal. In particular, most of the observed GRB spectra are modelled as two power laws smoothly connected at the peak energy in the flux spectrum (in units of erg cm
$^{2}~\textrm {s}^{-1}$) (Band et al. Reference Band, Matteson, Ford, Schaefer, Palmer, Teegarden, Cline, Briggs, Paciesas and Pendleton1993; Preece et al. Reference Preece, Briggs, Mallozzi, Pendleton, Paciesas and Band1998; Frontera et al. Reference Frontera, Amati, Costa, Muller, Pian, Piro, Soffitta, Tavani, Castro-Tirado and Dal Fiume2000; Ghirlanda, Celotti & Ghisellini Reference Ghirlanda, Celotti and Ghisellini2002). The power-law tail above the peak energy 
$\propto E^{-0.5}$, well resolved for the brightest GRBs, is prolonged in the energy range from hundreds of keV to sub-GeV range. It clearly supports the idea that the GRB spectrum most probably originates from a power-law distributed population of charged particles (i.e. 
$dN/d\gamma \propto \gamma ^{-p}$, where 
$\gamma$ is their random Lorentz factor), e.g. electrons accelerated in shocks (Rees & Meszaros Reference Rees and Meszaros1994; Piran Reference Piran1999).
The most straightforward process that could efficiently release the energy of charged electrons into the radiation is the synchrotron mechanism, which works both in the magnetic reconnection and internal shock dissipation scenarios. Therefore, the leptonic synchrotron radiation model used to interpret the prompt emission fits the general paradigm of the internal dissipation of the jet. Its main advantage is to explain the non-thermal nature of the observed GRB spectra by invoking a single and efficient radiative process.
In a simple scenario, a population of accelerated electrons are injected in a single shot into the emitting region with a given averaged magnetic field 
$B$. This idealization is representative of the internal shocks scenario, where the collision between two shells produce shocks which propagate into each of the shells resulting in the charged particles acceleration and in the amplification of the pre-existing magnetic field. While the physical system seem to be oversimplified, the synchrotron model has a solid prediction of the spectral index of the prompt emission below its peak energy, independent from the exact shape of the accelerated particles. The reason resides in the spectrum of the single particle, which is characterized by a power-law segment, growing as 
$\propto E^{4/3}$, followed at higher energy by an exponential cutoff. When a power-law distribution of the emitters is considered, the low energy spectrum is dominated by the contribution of the particles with the lowest 
$\gamma$ resembling a single particle spectrum with the typical 
$E^{4/3}$ behaviour. Above the peak instead, the spectrum is given by the envelope of the peaks of the single particle spectra with different 
$\gamma$, such that the shape of the spectrum is a power law with a slope dependent on 
$p$. The lowest 
$\gamma$ of the particle distribution do not coincide in general with the lowest 
$\gamma$ of the initial distribution, which we call 
$\gamma _m$, because the charges lose energy by synchrotron emission at a rate 
$\propto \gamma ^2$. After a certain time the emitters will populate states with 
$\gamma _c < \gamma < \gamma _m$ with a distribution like 
$dN/d\gamma \propto \gamma ^2$, where 
$\gamma _c$ is a minimum Lorentz factor determined by the cooling, and the states above 
$\gamma _{m}$ with 
$dN/d\gamma \propto \gamma ^{-p}$. The spectrum generated by such a distribution is a power law 
$\propto E^{4/3}$ below 
$E_c$ (characteristic synchrotron energy for a particle with 
$\gamma = \gamma _c$), a power law 
$\propto E^{1/2}$ between 
$E_c$ and 
$E_m$ (same for 
$E_c$ for 
$\gamma = \gamma _m$) and a power law 
$\propto E^{1 -p/2}$ above 
$E_m$ (Rybicki & Lightman Reference Rybicki and Lightman1986; Sari et al. Reference Sari, Piran and Narayan1998; Ghisellini Reference Ghisellini2013).
The main assumption here was that the electrons’ cooling time via synchrotron losses 
$t_{c}$ is much shorter than the dynamical time scale of the emitting region 
$t_{R}$ (i.e. 
$t_{c}\gg t_{R}$), or alternatively, the integration time of the observed spectrum. This assumption is a requirement for an efficient radiation of the energy deposited in the electron population. It was shown, that the above-mentioned scenario, known as fast cooling regime is the expected regime in the internal shocks model (Ghisellini, Celotti & Lazzati Reference Ghisellini, Celotti and Lazzati2000). In this regime, the break at 
$E_m$ occurs in the hard X-rays, while the break at 
$E_c$ occurs at very low frequencies (e.g. radio). Thus, from X-ray to 
$\gamma$-ray the spectrum is expected to be a broken power-law with a single break at 
$E_m$.
The crisis of this scenario rises from the comparison of the low-energy photon indices with the expectation from the fast cooling regime of the synchrotron radiation. While the fast cooling regime predicts a spectrum of 
$\propto E^{1/2}$ below the peak energy, the typical observed spectra return 
$\propto E$ (Tavani Reference Tavani1996; Cohen et al. Reference Cohen, Katz, Piran, Sari, Preece and Band1997; Crider et al. Reference Crider, Liang, Smith, Preece, Briggs, Pendleton, Paciesas, Band and Matteson1997; Preece et al. Reference Preece, Briggs, Mallozzi, Pendleton, Paciesas and Band1998). Steeper spectra are also observed. Even more, there is some number of GRB spectra that are steeper than the steepest possible low-energy tail predicted in the synchrotron radiation model, namely 
$\propto E^{4/3}$ (see, e.g. Acuner, Ryde & Yu Reference Acuner, Ryde and Yu2019; Yu, Dereli-Bégué & Ryde Reference Yu, Dereli-Bégué and Ryde2019).
This problem has been widely discussed in the literature. The proposed solutions can be classified into two types: models which invoke emission mechanisms different than synchrotron radiation, and models which propose modifications to the basic synchrotron scenario. Among the first class of models, we recall scenarios invoking reprocessed emission, i.e. via Comptonization below the GRB fireball reaches its transparency, mixed thermal plus non-thermal processes and inverse Compton reprocessing of softer photon field (e.g. Liang et al. Reference Liang, Kusunose, Smith and Crider1997; Blinnikov, Kozyreva & Panchenko Reference Blinnikov, Kozyreva and Panchenko1999; Rees & Mészáros Reference Rees and Mészáros2005; Giannios Reference Giannios2006; Pe'er Reference Pe'er2008; Beloborodov Reference Beloborodov2010; Chhotray & Lazzati Reference Chhotray and Lazzati2015; Vurm & Beloborodov Reference Vurm and Beloborodov2016; Bhattacharya & Kumar Reference Bhattacharya and Kumar2020). For the second class of models (studies that consider synchrotron radiation above the photosphere), effects producing a hardening of the low-energy spectral index have been invoked, such as (1) effect of an energy dependent inverse Compton radiation (Klein–Nishina regime) (Derishev, Kocharovsky & Kocharovsky Reference Derishev, Kocharovsky and Kocharovsky2001), or self-absorption effect (Lloyd & Petrosian Reference Lloyd and Petrosian2000), (2) effects of the magnetic field profile within the emitting region (Uhm & Zhang Reference Uhm and Zhang2014), (3) the non-uniform small-scale magnetic fields (Medvedev Reference Medvedev2000), (4) adiabatic cooling of electrons (Geng et al. Reference Geng, Huang, Wu, Zhang and Zong2018; Panaitescu Reference Panaitescu2019), (5) reacceleration and slow or balanced heating of the cooling electrons (Kumar & McMahon Reference Kumar and McMahon2008; Asano & Terasawa Reference Asano and Terasawa2009; Beniamini, Barniol Duran & Giannios Reference Beniamini, Barniol Duran and Giannios2018; Xu, Yang & Zhang Reference Xu, Yang and Zhang2018) (6) supercritical regime of hadronic cascades, i.e. a rapid energy conversion from protons to pions and muons triggered by the 
$\gamma$-ray photons (Petropoulou et al. Reference Petropoulou, Dimitrakoudis, Mastichiadis and Giannios2014).
All these proposals suggest a specific configuration of the physical environments in which the observed emission is produced. Therefore, a clear identification of the radiative processes shaping the observed prompt emission spectra would be able to establish the physics of the relativistic jets responsible for GRBs, i.e. the jet composition and its dissipation processes. In spite of all theoretical efforts, there is still no consensus on the origin of the prompt emission.
In recent years, there were some additional observational and theoretical efforts aimed at resolving the dominant radiative processes responsible for the production of the GRB spectra. Among them, one intriguing discovery (Oganesyan et al. Reference Oganesyan, Nava, Ghirlanda and Celotti2017) was made in the broadband studies of the prompt emission spectra. It turned out that the prompt emission spectra extended down to soft X-rays require the presence of an additional power-law segment. Once this break is included, the spectral indices become consistent with the predicted synchrotron emission spectrum in the fast cooling regime. Namely, the spectrum below the break energy (few keV) is consistent with the synchrotron spectrum from a single electron 
$\propto E^{4/3}$, while above they are in agreement with the fast cooling segment 
$\propto E^{1/2}$. These findings were later confirmed with a different instrumentation and with the break energy at larger energies (
$\sim$100 keV) (Ravasio et al. Reference Ravasio, Ghirlanda, Nava and Ghisellini2019). The synchrotron radiation model in a marginally fast cooling regime (Kumar & McMahon Reference Kumar and McMahon2008; Daigne, Bošnjak & Dubus Reference Daigne, Bošnjak and Dubus2011; Beniamini & Piran Reference Beniamini and Piran2013), i.e. when electrons cool down very little (
$\gamma _{c} \sim \gamma _{m}$) in a single observed time-window, was confirmed by the direct application of the synchrotron model to the GRB data and by the early optical data, being consistent with 
$\propto E^{4/3}$ (Oganesyan et al. Reference Oganesyan, Nava, Ghirlanda, Melandri and Celotti2019). This scenario, suggested by the data, is quite challenging the single-shot acceleration model (where electrons are accelerated in a single episode) since it requires that electrons involved to produce the observed radiation, are somehow kept from efficient and fast cooling. Additionally, the parameter space of GRB emitting side is non-trivial. It requires that the radiation is produced in weak magnetic fields (
$B$ of few 
$G$), at relatively large radii (
$R>10^{16}$ cm) which contradicts the observed variability time scale of 
$t_{ang}\simeq R_{\gamma }/2c\varGamma ^{2} \sim 0.1$ s for a reasonable range of bulk Lorentz factors 
$\varGamma \sim 100\text {--}300$. Several modifications to the standard model, i.e. to the single-shot acceleration of electrons emitting from a surface of a jet with an angular size of 
$\theta > >1/\varGamma$, could in principle provide this regime of radiation. Some models invoke continuous acceleration of electrons, and/or emission from large radii, invoking mini-jets to explain the short time variability (Narayan & Kumar Reference Narayan and Kumar2009). However, mini-jets are likely to produce Comptonization,Footnote 10 which is not observed in the spectra. Another possibility is that there is a continuous heating/reacceleration of the electrons. If the acceleration time scale becomes comparable with the electrons’ cooling time, then the synchrotron cooling frequency can be kept close to the peak energy, since particles are not allowed to cool down. This scenario was proposed in different dissipation models as a way to explain the observed spectral breaks in the X-rays (Beniamini et al. Reference Beniamini, Barniol Duran and Giannios2018; Gill, Granot & Beniamini Reference Gill, Granot and Beniamini2020). The reacceleration of particles would require the presence of small-scale turbulence and/or the close by magnetic reconnection islands.
Recently Ghisellini et al. (Reference Ghisellini, Ghirlanda, Oganesyan, Ascenzi, Nava, Celotti, Salafia, Ravasio and Ronchi2020) pointed out that is quite challenging to find a self-consistent and ‘comfortable’ parameter space for models invoking electrons as the synchrotron emitters and proposed a model in which the synchrotron emission it is due to protons. In this proton-synchrotron scenario, the observed marginally fast-cooling spectrum can be explained even at low emitting region size (e.g. 
$R \sim 10^{13}\ \textrm {cm}$) and this can in principle solve the tension with the short time variability requirement.
At present the puzzle of the prompt emission still remains unsolved. We do not have a complete understanding of the initial composition of the relativistic jets of GRBs, and the dissipative mechanisms operating in them. It is quite intriguing to try to unveil a clear picture of how the GRB jets are formed, accelerate and dissipate prior to their interaction with the interstellar medium. Therefore, GRBs open an interdisciplinary laboratory, where the emerged magnetohydrodynamics, blast wave physics and plasma physics could find a platform to face the astrophysical observables.
4.2.5.2. Afterglow: the mystery of X-ray emission.
Before the launch of the Swift satellite in 2004, GRB afterglows were mainly observed at relatively late times. The observed light curves were consistent with simple power-law in time, in agreement with the basic afterglow theory. However, the X-Ray telescope (XRT) on board the Swift shed new light onto the afterglow emission, revealing in the energy range of 0.3–10 keV complex behaviours which deviate from the simple blast wave deceleration profile (Tagliaferri et al. Reference Tagliaferri, Goad, Chincarini, Moretti, Campana, Burrows, Perri, Barthelmy, Gehrels and Krimm2005; Nousek et al. Reference Nousek, Kouveliotou, Grupe, Page, Granot, Ramirez-Ruiz, Patel, Burrows, Mangano and Barthelmy2006; O'Brien et al. Reference O'Brien, Willingale, Osborne, Goad, Page, Vaughan, Rol, Beardmore, Godet and Hurkett2006; Zhang et al. Reference Zhang, Fan, Dyks, Kobayashi, Mészáros, Burrows, Nousek and Gehrels2006).
The earliest phase of the GRB X-ray emission consists of a steep decay. The flux temporal index 
$\alpha$ (
$F \propto t^{-\alpha }$) is much larger than 2, which means that the emission fades much faster than predicted by the classical afterglow theory. Moreover, after the steep decay, several X-ray afterglows show a plateau phase characterized by a shallow (
$\alpha \sim 0.5$) temporal decay that can last for hours. This phase can be followed by an abrupt flux suppression or by a new decay phase, which resembles the standard afterglow decay. This broken power-law behaviour observed in X-ray is inconsistent with the simple forward shock scenario. Afterglows presenting this feature are all but rare, since it is observed in 
${\sim }80\,\%$ of LGRB (Evans et al. Reference Evans, Beardmore, Page, Osborne, O'Brien, Willingale, Starling, Burrows, Godet and Vetere2009; Margutti et al. Reference Margutti, Zaninoni, Bernardini, Chincarini, Pasotti, Guidorzi, Angelini, Burrows, Capalbi and Evans2013; Melandri et al. Reference Melandri, Covino, Rogantini, Salvaterra, Sbarufatti, Bernardini, Campana, D'Avanzo, D'Elia and Fugazza2014) and 
${\sim }50\,\%$ of SGRB (Rowlinson et al. Reference Rowlinson, O'Brien, Metzger, Tanvir and Levan2013; D'Avanzo et al. Reference D'Avanzo, Salvaterra, Bernardini, Nava, Campana, Covino, D'Elia, Ghirlanda, Ghisellini and Melandri2014).
At late time (
${>}10^{3}\ \textrm {s}$), X-ray flares are often observed (Chincarini et al. Reference Chincarini, Mao, Margutti, Bernardini, Guidorzi, Pasotti, Giannios, Della Valle, Moretti and Romano2010). Their temporal behaviour is similar to the prompt emission pulses. Therefore, if produced by internal energy dissipation, late-time X-ray flares require a reactivation of the GRB central engine.
The X-ray afterglow without the above features behaves as the standard theory predict; a decay phases with 
$\alpha \sim 1$, followed by a late-time fading with 
$\alpha \sim 2$ when the jet break occur.
The reason why the X-ray lightcurves behave so differently with respect to the lightcurves in the other energy ranges, while standard afterglow theory would predict a similar trend, is still an open issue in the field.
At present, the most understood feature is the steep decay, which is interpreted as the tail of the prompt emission and, as such, not related to the forward shock that powers the afterglow. This occurs because the emission region (approximated with a surface) is curved, and the photons emitted at the same time in different parts of the region reach the observer at different times. Considering the observer is supposedly aligned with the jet axis, the photons emitted close to the axis arrive earlier than those at higher latitude. Moreover, since the jet is expanding relativistically, the emission is beamed around the (radial) direction of motion. This means that photons emitted farther from the axis will be more debeamed from the observer line of sight with respect to those emitted close to the axis. Since the latter arrive before the former, the observer detects a flux rapidly fading in time. This effect, usually referred as high latitude emission (HLE) is able to account for the X-ray steep decay (Fenimore et al. Reference Fenimore, Madras and Nayakshin1996; Kumar & Panaitescu Reference Kumar and Panaitescu2000).
On the contrary, the interpretation of X-ray plateaus is still debated. The more explored scenario invokes the presence of a long-lasting central engine, that remains active for hours after the GRB prompt emission (Rees & Mészáros Reference Rees and Mészáros1998; Zhang et al. Reference Zhang, Fan, Dyks, Kobayashi, Mészáros, Burrows, Nousek and Gehrels2006). Since such a long period of activity is difficult to attain by an accreting BH (but see Kumar, Narayan & Johnson (Reference Kumar, Narayan and Johnson2008)), millisecond magnetars have been proposed as a more suitable central engine candidate (Dai & Lu Reference Dai and Lu1998; Zhang & Mészáros Reference Zhang and Mészáros2001). As already mentioned in § 4.2.1, a millisecond magnetar loses rotational energy via magnetic dipole spindown emission. This energy can be injected into the forward shock (external dissipation), or dissipated in proximity of the central engine (internal dissipation), sustaining in this way the X-ray emission.
A key feature of the magnetar central engine is that the magnetic dipole spindown emission is characterized by a constant luminosity up to a certain time, the characteristic spindown time when half of the energy is radiated, and then the luminosity is expected to decline as 
$t^{-2}$. Interestingly, for a millisecond magnetar, the spindown time scale is of the same order of magnitude of the typical plateau duration. Therefore, this well-defined temporal behaviour can straightforwardly account for the plateau in X-ray afterglow lightcurves and the successively decay phase. Moreover, if the magnetar is metastable, it may collapse into a BH when the spindown deprives it from centrifugal support. When this happens, the energy outflow ceases abruptly, and if the X-ray radiation is generated by internal dissipation this can explain the sharp drop in flux sometimes observed (see, e.g. Troja et al. Reference Troja, Cusumano, O'Brien, Zhang, Sbarufatti, Mangano, Willingale, Chincarini, Osborne and Marshall2007; Sarin, Lasky & Ashton Reference Sarin, Lasky and Ashton2020). The magnetar model can successfully fit those GRB lightcurves that present a plateau (Lyons et al. Reference Lyons, O'Brien, Zhang, Willingale, Troja and Starling2010; Dall'Osso et al. Reference Dall'Osso, Stratta, Guetta, Covino, De Cesare and Stella2011; Bernardini et al. Reference Bernardini, Margutti, Mao, Zaninoni and Chincarini2012, Reference Bernardini, Campana, Ghisellini, D'Avanzo, Burlon, Covino, Ghirlanda, Melandri, Salvaterra and Vergani2013; Rowlinson et al. Reference Rowlinson, O'Brien, Metzger, Tanvir and Levan2013) and can also account for an observed anticorrelation between plateau luminosity and duration (Dainotti, Cardone & Capozziello Reference Dainotti, Cardone and Capozziello2008).
Although promising, the magnetar central engine, as already explained, cannot guarantee the formation of the jet, due to the large number of baryons in the surrounding medium expected when a long-lived NS results from the merger. Since the jet is essential to explain both the prompt emission and the afterglow, this constitutes a very important issue for the magnetar model.
A different class of model that avoids the problems of the long-lasting central engines invokes a more refined description of the GRB jet. Beniamini et al. (Reference Beniamini, Duque, Daigne and Mochkovitch2020) recently developed a model in which the X-ray plateau is generated by the forward shock driven by a structured jet,Footnote 11 when the observer is located slightly outside the jet axis. Another model has been proposed recently by Oganesyan et al. (Reference Oganesyan, Ascenzi, Branchesi, Salafia, Dall'Osso and Ghirlanda2020), in which both the steep-decay and the plateau in X-ray can be explained by the prompt high-latitude emission when the jet is structured. Therefore, according to Oganesyan et al. (Reference Oganesyan, Ascenzi, Branchesi, Salafia, Dall'Osso and Ghirlanda2020), the X-ray plateau is part of the tail of the prompt emission, while the forward shock is responsible for the optical and radio afterglow. This scenario is able to explain why the afterglow follows the standard theory in the optical band but often does not in the X-ray.
Concerning the X-ray flares, a late-time activity of the central engine is often invoked. This may be provided either by a magnetar central engine (Dai et al. Reference Dai, Wang, Wu and Zhang2006; Metzger et al. Reference Metzger, Giannios, Thompson, Bucciantini and Quataert2011; Bernardini et al. Reference Bernardini, Campana, Ghisellini, D'Avanzo, Burlon, Covino, Ghirlanda, Melandri, Salvaterra and Vergani2013) either by mechanisms similar to those responsible for the prompt emission or by dissipation of magnetic field as occurs in Galactic magnetars or by a BH accreting at late time (Perna, Armitage & Zhang Reference Perna, Armitage and Zhang2006; Proga & Zhang Reference Proga and Zhang2006; Lee, Ramirez-Ruiz & López-Cámara Reference Lee, Ramirez-Ruiz and López-Cámara2009; Dall'Osso et al. Reference Dall'Osso, Perna, Tanaka and Margutti2017).
4.3. Kilonova
As was already stated, during an NS–NS or an NS–BH coalescence an amount of NS matter is expected to be unbound from the central remnant and ejected with mildly relativistic velocity. Since these expanding ejecta, as formed by NS decompressed matter, are neutron rich, they constitute a natural environment for r-process nucleosynthesis. This chain of nuclear reactions is characterized by the rapid capture of a number of free neutrons by neutron-rich nuclei, leading to the formation of very heavy elements. Due to the excess of neutrons, these elements are metastable and they eventually decay (mainly through 
$\beta$-decay) turning some neutrons into protons.Footnote 12 The radioactive decay of the newly synthesized heavy nuclei deposits energy within the ejecta via non-thermal particles such as 
$\gamma$-rays, 
$\alpha$ and 
$\beta$ particles, and fission fragments, which then thermalizes efficiently and turns into ejecta internal energy. This energy excess is finally radiated away and produces the thermal transient which is commonly referred to as kilonova or macronova (Li & Paczyński Reference Li and Paczyński1998; Kulkarni Reference Kulkarni2005; Metzger et al. Reference Metzger, Martínez-Pinedo, Darbha, Quataert, Arcones, Kasen, Thomas, Nugent, Panov and Zinner2010; Metzger Reference Metzger2017).Footnote 13
Within the context of a single component isotropic model (a model characterized by a single isotropic ejecta with uniform composition), it is possible to obtain an estimate for the main KN observational features, such as the peak luminosity, time at which the peak occur and brightness temperature at the peak. In this context the governing parameters are: the mass 
$M_{\textrm {ej}}$; the velocity 
$v_{\textrm {ej}}$; and the opacity 
$k$ of the ejecta. A simple realistic model can be built using these three parameters. In fact, the first parameter, representing the total amount of matter undergoing radioactive decay, constitutes the ‘fuel’ of the KN, while all the three parameters determine the characteristic photon diffusion time scale. Taking into account a homogeneous composition and assuming that the peak of the emission occurs when the time scale of expansion equals the diffusion time scale (Arnett Reference Arnett1982), it is possible to obtain the following equations (Metzger et al. Reference Metzger, Martínez-Pinedo, Darbha, Quataert, Arcones, Kasen, Thomas, Nugent, Panov and Zinner2010):
\begin{align} \left. \begin{array}{c@{}} t_{\textrm{peak}}=\left(\dfrac{3kM_{\textrm{ej}}}{4{\rm \pi} c v_{\textrm{ej}}} \right)^{1/2}\simeq2.7\ \textrm{days} \left(\dfrac{M_{\textrm{ej}}}{10^{{-}2}\ \textrm{M}_\odot}\right)^{1/2} \left(\dfrac{v_{\textrm{ej}}}{0.1c}\right)^{{-}1/2} \left(\dfrac{k}{\textrm{cm}^2\ \textrm{g}^{{-}1}}\right)^{1/2}\nonumber\\ L_{\textrm{peak}}=M_{\textrm{ej}}\dot{\epsilon}_{n}(t_{\textrm{peak}}) \simeq5\times10^{40}\dfrac{\textrm{erg}}{\textrm{s}}\epsilon_{\textrm{th}} \left(\dfrac{M_{\textrm{ej}}}{10^{{-}2}\ \textrm{M}_\odot}\right)^{0.35} \left(\dfrac{v_{\textrm{ej}}}{0.1c}\right)^{0.65}\left(\dfrac{k}{\textrm{cm}^2\ \textrm{g}^{{-}1}} \right)^{{-}0.65}\\ T_{\textrm{peak}}=\left(\dfrac{L_{\textrm{peak}}}{4{\rm \pi}\sigma R^{2}_{\textrm{peak}}}\right)^{1/4}\simeq 3460\ \textrm{K} \epsilon^{1/4}_{\textrm{th}}\left(\dfrac{M_{\textrm{ej}}}{10^{{-}2}\ \textrm{M}_\odot} \right)^{{-}0.17}\left(\dfrac{v_{\textrm{ej}}}{0.1c}\right)^{{-}0.09} \left(\dfrac{k}{\textrm{cm}^2\ \textrm{g}^{{-}1}}\right)^{{-}0.41} \end{array}\right\}, \end{align}
where 
$\dot {\epsilon }_n$ is the specific radioactive heating rate, 
$\epsilon _{\textrm {th}}\le 1$ is the thermalization efficiency and 
$R_p=v_{\textrm {ej}}t_p$ is the ejecta typical size at time 
$t_p$.
The opacity is determined by the composition of the matter. It depends on whether elements of the group of lanthanides are synthesized or not during r-process nucleosynthesis. These elements, due to the numerous transition lines in the optical bands, give rise to an opacity which can be even two order of magnitude higher than that of the iron group elements. If they are present, they dominate the net opacity of the ejecta (Barnes & Kasen Reference Barnes and Kasen2013; Tanaka & Hotokezaka Reference Tanaka and Hotokezaka2013). Their synthesis depends on the electron fraction of the ejected matter, which is defined as 
$Y_e \equiv n_p/(n_n + n_p)$ – where 
$n_p$ and 
$n_n$ are the proton and neutron number densities – and measures how much the matter is neutron rich. In particular, considering a threshold of 
$Y_e \simeq 0.25$, low 
$Y_e$ ensures the synthesis of lanthanides, while high 
$Y_e$ prevents it (Wu et al. Reference Wu, Fernández, Martínez-Pinedo and Metzger2016). Equations (4.2) show that the effect of increasing opacity is to shift the peak of the lightcurve at later time, to make the emission fainter, and to decrease its peak temperature making the transient redder in colour.
Figure 6(a) shows an example of a simple kilonova model outlined in Metzger (Reference Metzger2017) characterized by mass of the ejecta 
$M_{\textrm {ej}} = 0.01\ \textrm {M}_\odot$, 
$v_{\textrm {ej}} = 0.1\,c$ and 
$k = 10\ \textrm {cm}^2\ \textrm {g}^{-1}$.
(a) The KN lightcurve in different photometric filters (optical and NIR) from a single component model characterized by 
$M_{\textrm {ej}} = 0.01\ \textrm {M}_\odot$, 
$v_{\textrm {ej}} = 0.1\,c$ and 
$k = 10\ \textrm {cm}^2\ \textrm {g}^{-1}$. Lightcurves obtained with the code in https://github.com/mcoughlin/gwemlightcurves. (b) The SDPT lightcurve from the fiducial model in Siegel & Ciolfi (Reference Siegel and Ciolfi2016b) characterized by 
$M_{\textrm {ej}} = 5\times 10^{-3}\ \textrm {M}_\odot$ and 
$B= 10^{16}\ \textrm {G}$. In this case the NS does not collapse. The black curve represents the bolometric luminosity, the dark blue curve is the lightcurve in the energy range of Swift-XRT (0.3–10 keV), the red curve in Swift-BAT range (15–150 keV), the green curve in Swift-UVOT range (170–650 nm). Light blue and purple curves represent lightcurves above BAT range and below UVOT range, respectively. Figure adapted from Siegel & Ciolfi (Reference Siegel and Ciolfi2016b).
Although the single component model is instructive in understanding the qualitative impact of the parameters on the KN lightcurve and to have an indication of the brightness and spectral range of the emission (at an order of magnitude level), it is too simple for a comparison with the data. In fact, as it was anticipated in § 3, hydrodynamical simulations showed that in a CBM, several ejection mechanisms occur at different times leading to multiple ejecta components, with different mass, velocity and chemical composition (i.e. opacity). This prediction was confirmed by the detection of AT2017gfo, whose lightcurve is very hard to explain with a single component model (Perego, Radice & Bernuzzi Reference Perego, Radice and Bernuzzi2017a; Pian et al. Reference Pian, D'Avanzo, Benetti, Branchesi, Brocato, Campana, Cappellaro, Covino, D'Elia and Fynbo2017; Tanaka et al. Reference Tanaka, Utsumi, Mazzali, Tominaga, Yoshida, Sekiguchi, Morokuma, Motohara, Ohta and Kawabata2017).
In an NS–NS merger, an amount of matter of 
$M_{ej} \sim 10^{-3}-10^{-2}\ \textrm {M}_\odot$ is expelled via dynamical mass ejection during the merger itself with a velocity of 
$v_{\textrm {ej}} \sim 0.1\text {--}0.3\ \textrm {c}$ and an electron fraction 
$Y_e \sim 0.05-0.4$. Tidal ejecta are responsible for the lower 
$Y_e$ component and are located on the binary equatorial plane. Shock-driven ejecta, which cover the polar region, have higher 
$Y_e$, due to the fact that the matter is heated by the shocks and this leads to pair production and consequently to the capture of positrons by neutrons (Rosswog Reference Rosswog2015). In the case of NS–BH merger only the tidal component is present and the unbound mass can reach 
$M_{\textrm {ej}} \sim 10^{-1}\ \textrm {M}_\odot$ (Rosswog Reference Rosswog2005; Foucart et al. Reference Foucart, Deaton, Duez, O'Connor, Ott, Haas, Kidder, Pfeiffer, Scheel and Szilagyi2014).
The presence of a (meta) stable massive NS, only for NS–NS mergers, would produce further mass outflow in the form of neutrino-driven (e.g. Dessart et al. Reference Dessart, Ott, Burrows, Rosswog and Livne2009; Perego et al. Reference Perego, Rosswog, Cabezón, Korobkin, Käppeli, Arcones and Liebendörfer2014; Martin et al. Reference Martin, Perego, Arcones, Thielemann, Korobkin and Rosswog2015) and/or magnetically driven (e.g. Siegel, Ciolfi & Rezzolla Reference Siegel, Ciolfi and Rezzolla2014; Ciolfi et al. Reference Ciolfi, Kastaun, Giacomazzo, Endrizzi, Siegel and Perna2017; Ciolfi & Kalinani Reference Ciolfi and Kalinani2020) baryon-loaded winds, with a potentially high electron fraction due to the effect of neutrino irradiation from the NS itself, a mass of up to a few 
${\sim }10^{-2}\ \textrm {M}_\odot$, and a velocity of 
${\sim }0.1\text {--}0.2\ \textrm {c}$ (where the higher end can be achieved in the polar region in presence of a strong magnetic field; Ciolfi & Kalinani Reference Ciolfi and Kalinani2020).
Furthermore, after the collapse to a BH for NS–NS systems, or simply after merger for NS–BH systems, up to 
$40\,\%$ of the accretion disk mass can be ejected via MHD turbulence and neutrino heating within the disk itself (e.g. Siegel & Metzger Reference Siegel and Metzger2018; Fernández et al. Reference Fernández, Tchekhovskoy, Quataert, Foucart and Kasen2019). These disk wind ejecta are characterized by a wide range of electron fractions (
$Y_e\sim 0.1\text {--}0.5$) and low velocity 
$v_{\textrm {ej}} \lesssim 0.1\ \textrm {c}$ (e.g. Perego et al. Reference Perego, Rosswog, Cabezón, Korobkin, Käppeli, Arcones and Liebendörfer2014; Fernández et al. Reference Fernández, Quataert, Schwab, Kasen and Rosswog2015; Martin et al. Reference Martin, Perego, Arcones, Thielemann, Korobkin and Rosswog2015; Wu et al. Reference Wu, Fernández, Martínez-Pinedo and Metzger2016; Siegel & Metzger Reference Siegel and Metzger2017, Reference Siegel and Metzger2018; Fujibayashi et al. Reference Fujibayashi, Kiuchi, Nishimura, Sekiguchi and Shibata2018; Radice et al. Reference Radice, Perego, Hotokezaka, Bernuzzi, Fromm and Roberts2018).
The presence of different matter components, with different mass, velocity and electron fraction, results in more complicated lightcurves with fast evolving bluer components (blue KN) and slower evolving redder components (red KN). Moreover, since each of the components have a different geometrical/angular distribution, the resulting KN lightcurve also depends on the orientation of the system with respect to the observer (e.g. Perego et al. Reference Perego, Radice and Bernuzzi2017a; Wollaeger et al. Reference Wollaeger, Korobkin, Fontes, Rosswog, Even, Fryer, Sollerman, Hungerford, van Rossum and Wollaber2018).
4.4. Spindown-powered transients
When the outcome of an NS–NS merger is another NS (stable or metastable), the newborn NS is expected to spin very fast with rotational periods of 
${\sim }1\ \textrm {ms}$, and to have a strong magnetic field – up to 
${\sim }10^{16}\ \textrm {G}$ in the interior – due to amplification mechanisms. During the first 
$O(100)\ \textrm {ms}$ the NS is hot and in differential rotation. In this phase, the strong neutrino irradiation and the gradient of magnetic pressure generated by the field winding due the action of differential rotation are responsible for a baryon-loaded wind (see also previous section). If the NS is a stable NS or SMNS it does not collapse when the core differential rotation is quenched, and it has a sufficient amount of time to lose its huge amount of rotational energy (
$O(10^{52}\ \textrm {erg})$) through magnetic dipole spindown emission (Pacini Reference Pacini1967). The energy emitted at first as a Poynting flux is converted close to the source (by dissipation mechanisms not fully understood) in a electron–positron pair rich wind, analogous to a pulsar wind, expanding with relativistic velocities.Footnote 14 When the fast pulsar wind encounters the previously emitted and much slower baryon wind it drives a shock through it increasing its temperature and boosting its expansion. The thermal radiation from these hot expanding ejecta, gives origin to a spindown powered transient (SDPT) which is expected to be observable in X-ray, UV and optical bands (e.g. Yu, Zhang & Gao Reference Yu, Zhang and Gao2013; Metzger & Piro Reference Metzger and Piro2014; Siegel & Ciolfi Reference Siegel and Ciolfi2016a,Reference Siegel and Ciolfib).
So far, a compelling detection of this type of transients is still missing, although potential associations have been discussed in the literature (e.g. Ciolfi Reference Ciolfi2016; Xue et al. Reference Xue, Zheng, Li, Brandt, Zhang, Luo, Zhang, Bauer, Sun and Lehmer2019). SDPTs are of particular interest since they are the only EM counterparts of CBM whose detection is a clear signature of the formation of a long-lived NS after the merger. The formation of such a type of NS would allow us to further constrain the NS EOS. Moreover, an SDPT detection would represent a secure way to distinguish a NS–NS merger from an NS–BH merger.
So far SDPT have been studied only through one-dimensional semianalytical approaches. These models consider a central NS, radiating via magnetic dipole emission, embedded in a PWN surrounded by an expanding spherical baryon wind. One of the first models of this kind was developed by Yu et al. (Reference Yu, Zhang and Gao2013), who found a peak luminosity in the range 
$10^{44}\text {--}10^{45}\ \textrm {erg}\ \textrm {s}^{-1}$ occurring 
$10^4\text {--}10^5\ \textrm {s}$ after the merger. Later Gao et al. (Reference Gao, Ding, Wu, Dai and Zhang2015) applied this model to the SGRB GRB080503 to explain feature observed in its lightcurve. A similar model was developed by Metzger & Piro (Reference Metzger and Piro2014), who provided a deeper focus on PWN physics in particular adding a self-consistent treatment of PWN opacity and baryon ejecta degree of ionization and albedo. They predict in this way a dimmer transient with respect to the Yu et al. (Reference Yu, Zhang and Gao2013) model with peak luminosity in range 
$10^{43}\text {--}10^{44}\ \textrm {erg}\ \textrm {s}^{-1}$ peaking at 
$10^4\text {--}10^5\ \textrm {s}$ after merger. Siegel & Ciolfi (Reference Siegel and Ciolfi2016a) advanced further the complexity of the treatment by including a relativistic dynamics, and starting the evolution from the baryon wind ejection, thus before the pulsar wind launching. In this way they followed three phases of the transient evolution: the baryon wind emitting phase; a second phase characterized by the pulsar wind and baryon wind interaction and the crossing of the shock through the latter; and a final phase in which the baryon wind expands under the pressure of an inner PWN. They predict that the transient peaks in the soft X-rays at 
${\sim }10^2\text {--}10^4\ \textrm {s}$ after the merger, with a luminosity ranging in the interval 
$10^{46}\text {--}10^{48}\ \textrm {erg}\ \textrm {s}^{-1}$ (Siegel & Ciolfi Reference Siegel and Ciolfi2016b). In figure 6(b) an example of an SPDT model from Siegel & Ciolfi (Reference Siegel and Ciolfi2016b) is shown.
5. Final remarks
The merger of a binary system composed by two NSs or an NS and a BH is a powerful source of gravitational radiation that can also be followed by an intense emission of photons across the whole EM spectrum. So far, only one event of this kind, the NS–NS merger named GW170817, has been observed through these two different messengers. However, the information we gained by this single detection increased considerably our understanding in many different fields of astrophysics and fundamental physics.
The observation of a flash in 
$\gamma$-rays (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2017e; Goldstein et al. Reference Goldstein, Veres, Burns, Briggs, Hamburg, Kocevski, Wilson-Hodge, Preece, Poolakkil and Roberts2017; Savchenko et al. Reference Savchenko, Ferrigno, Kuulkers, Bazzano, Bozzo, Brandt, Chenevez, Courvoisier, Diehl and Domingo2017) along with a collimated outflow moving relativistically from the centre of explosion (Mooley et al. Reference Mooley, Deller, Gottlieb, Nakar, Hallinan, Bourke, Frail, Horesh, Corsi and Hotokezaka2018; Ghirlanda et al. Reference Ghirlanda, Salafia, Paragi, Giroletti, Yang, Marcote, Blanchard, Agudo, An and Bernardini2019) allowed us to confirm that (at least some) SGRBs are generated after an NS–NS merger. The multiwavelength observation of the afterglow showed that GRB relativistic jets are structured (Troja et al. Reference Troja, Piro, van Eerten, Wollaeger, Im, Fox, Butler, Cenko, Sakamoto and Fryer2017, Reference Troja, Piro, Ryan, van Eerten, Ricci, Wieringa, Lotti, Sakamoto and Cenko2018; Alexander et al. Reference Alexander, Margutti, Blanchard, Fong, Berger, Hajela, Eftekhari, Chornock, Cowperthwaite and Giannios2018; D'Avanzo et al. Reference D'Avanzo, Campana, Salafia, Ghirlanda, Ghisellini, Melandri, Bernardini, Branchesi, Chassande-Mottin and Covino2018).
The first NS–NS observation coincides also with the observation of a KN. The brightness and properties of the KN demonstrated that CBMs are favourable site of r-processes, which is the synthesis channel with whom the heaviest elements form in the universe.
The GW170817 has been also used to measure the Hubble constant (Fishbach et al. Reference Fishbach, Gray, Magaña Hernandez, Qi, Sur, Acernese, Aiello, Allocca, Aloy and Amato2019), and the limits on the tidal deformability of the NSs have been used to constrain the dense matter EOS (Abbott et al. Reference Abbott, Abbott, Abbott, Acernese, Ackley, Adams, Adams, Addesso, Adhikari and Adya2018).
Although the scientific outcome of GW170817 have been wide, many open questions concerning CBMs and their EM counterparts still remains unsolved. For example, at present, it is not clear how much the magnetic field can be amplified during an NS–NS merger (see, e.g. Ciolfi (Reference Ciolfi2020b) for a recent review). The magnitude of the magnetic field, in turn, impacts the amount of matter ejected during the merger, the possibility to launch a jet and/or to form a magnetar as the result of the coalescence (and thus whether SDPTs occur in nature or not).
Concerning GRBs, many aspects of their physics are still not clear: Is a magnetar able to launch a GRB jet? Is the jet more similar to a hot fireball or to a cold Poynting flux dominated outflow? What are the dissipation mechanisms responsible for converting the jet kinetic energy in 
$\gamma$-ray radiation? What is the origin of the X-ray plateaus and X-ray flares often observed to occur in GRB afterglows? These are among the principal questions that astrophysicist need to address in the near future. Plasma physics is expected to play a key role in addressing them.
In the near future, the gravitational interferometers, the X-ray surveys such as eROSITA (Merloni et al. Reference Merloni, Predehl, Becker, Böhringer, Boller, Brunner, Brusa, Dennerl, Freyberg and Friedrich2012), the wide field X-ray telescopes such as THESUS-SXI (Amati et al. Reference Amati, O'Brien, Götz, Bozzo, Tenzer, Frontera, Ghirlanda, Labanti, Osborne and Stratta2018; Stratta et al. Reference Stratta, Ciolfi, Amati, Bozzo, Ghirlanda, Maiorano, Nicastro, Rossi, Vinciguerra and Frontera2018), and the optical surveys such as the VEra Rubin Observatory (Ivezić et al. Reference Ivezić, Kahn, Tyson, Abel, Acosta, Allsman, Alonso, AlSayyad, Anderson and Andrew2019), are going to provide us more and more joint GW-EM detections of CBMs. This represents a unique opportunity to unveil the physical mechanism at the base of the most energetic events in the universe and to study extreme environments characterized by intense gravity, strong magnetic fields, high densities and temperatures which cannot be reproduced in terrestrial laboratory. Observations of CBMs will allow us to get new insights into the physics of astrophysical plasmas.
Acknowledgements
The authors thank the PLUS collaboration (coordinator G. Montani). We thank A. Panaitescu for the plot in figure 4. We thank G. Ghisellini and O. S. Salfia for fruitful discussion. S.A. acknowledges the PRIN-INAF ‘Towards the SKA and CTA era: discovery, localization and physics of transient sources’ and the ERC Consolidator Grant ‘MAGNESIA’ (nr.817661). S.A. acknowledges the GRAvitational Wave Inaf TeAm – GRAWITA (P.I. E. Brocato).
Editor William Dorland thanks the referees for their advice in evaluating this article.
Declaration of interests
The authors report no conflict of interest.
Funding
G.O. and M.B. acknowledge financial contribution from the agreement ASI-INAF n.2017-14-H.0. M.B. acknowledge financial support from MIUR (PRIN 2017 grant 20179ZF5KS).
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