Estimates of the early EM emission from compact binary mergers
aa r X i v : . [ a s t r o - ph . H E ] F e b Draft version February 10, 2021
Typeset using L A TEX twocolumn style in AASTeX62
Estimates of the early EM emission from compact binary mergers
Yan Li ( 李 彦 ) ∗ and Rong-Feng Shen ( 申 荣 锋 ) † School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai, 519082, P. R. China
ABSTRACTCompact binary mergers that involve at least one neutron star, either binary neutron star or blackhole–neutron star coalescences, are thought to be the potential sources of electromagnetic emissiondue to the material ejected during the merger or those left outside the central object after the merger.Since the intensity of these electromagnetic transients decay rapidly with time, one should pay moreattention to early emissions from such events, which are useful in revealing the nature of these mergers.In this work, we study the early emission of kilonovae, short γ -ray bursts and cocoons that could beproduced in those mergers. We estimate their luminosities and time scales as functions of the chirpmass which is the most readily constrained parameter from the gravitational wave detections of theseevents. We focus on the range of chirp mass as 1 . M ⊙ − . M ⊙ which is compatible with one ofthe merging component being a so-called ‘mass gap’ black hole. We show that the electromagneticobservation of these transients could be used to distinguish the types of the mergers when the detectedchirp mass falls in the range of 1 . M ⊙ − . M ⊙ . Applying our analysis to the sub-threshold GRBGBM-190816, we found that for this particular event the effective spin should be larger than 0.6 andthe mass of the heavier object might be larger than 5.5 M ⊙ for the SFHo equation of state. Keywords:
Stellar mass black holes (1611), Neutron stars (1108), Gamma-ray bursts (629), Gravita-tional wave sources (677), Optical bursts (1164), X-ray bursts (1814) INTRODUCTIONThe first discovery of a binary neutron star (BNS)merger in GWs made by Advanced LIGO & VIRGO,GW170817, opened the muti-message astronomy era(Abbott et al. 2017a). Besides the information encodedin the gravitational wave (GW) strain data alone, theobservation of an electromagnetic (EM) counterpart incoincidence with the GW chirp could reveal a muchricher picture of these events (Bloom et al. 2009).A compact binary merger that involve at least oneneutron star (NS), either BNS or black hole (BH)–NS(BH–NS), would produce a non-negligible fraction ofejecta when the NS is torn apart by the BH’s tidalforces or collides with another NS. There are mainly twocomponents of neutron-rich matter that can be ejected.One is the dynamically ejected matter on the dynami-cal timescales (typically milliseconds) during the merger,which is referred as dynamical ejecta. The other is un-bound from the merger remnant disk by neutrino-drivenand/or viscously-driven winds, which is referred as disk ∗ [email protected] † [email protected] wind. Those neutron-rich ejecta would produce variouskinds of EM emission, as detailed below.The unbound neutron-rich ejecta from a BNS or BH–NS merger undergoes rapid neutron capture (r-process)nucleosynthesis which results in the formation of heavyelements like gold and platinum. The radioactive-decayheating of the ejecta by those unstable isotopes producesso-called kilonova emission (Li & Paczy´nski 1998). Thedetailed emission properties depend on the ejecta mass,velocity, and composition. Heavier elements known aslanthanides (formed in low electron-fraction material)can increase the ejecta opacity by several orders of mag-nitude (Kasen et al. 2013; Tanaka & Hotokezaka 2013),making the kilonova light curve fainter, redder, andlonger-lived (Barnes & Kasen 2013; Grossman et al.2014). The greater the mass of material that is ejected,the brighter the transient that becomes, and the longerthe timescale on which it will peak.BNS and BH–NS mergers with appropriate param-eters (e.g., BH spin, mass ratio, equation of state(EOS), etc.) are likely accompanied by short γ -raybursts (sGRBs) (Eichler et al. 1989; Narayan et al.1992; Fong et al. 2014). The first BNS merger eventGW170817 was followed by a sGRB, i.e., GRB170817A(Abbott et al. 2017b). Shapiro (2017), Paschalidis(2017) and Ruiz et al. (2018) have performed simu-lations of merging systems in full general relativisticmagnetohydrodynamics (MHD) and showed that aftera BH–NS merger a relativistic jet can be launched, pow-ering a sGRB. In the BH–NS merger scenario, the cen-tral engine of the accompanying sGRB is the accretionof disk onto the spinning black hole in the Blandford-Znajeck (BZ) mechanism (Blandford & Znajek 1977).Thus the luminosity and the duration of the burst de-pend on the properties of the disk.A hot, mildly relativistic cocoon surrounding the jetcould be generated by the interaction of the lightersGRB jet with the denser material ejected previously(i.e., magnetic/viscous/neutrino-driven wind from thedisk and/or dynamical ejecta) along the rotation axis ofthe remnant BH formed after a BNS or BH–NS merger(Murguia-Berthier et al. 2014, 2017; Nagakura et al.2014). The energy deposited by the shock in the co-coon diffuses as it expands and escapes to the observer,producing a cooling X-ray, UV and optical emission(Nakar & Piran 2017; Lazzati et al. 2017). The promptemission of the cocoon is detectable for Swift BAT andFermi GBM (Lazzati et al. 2017).The intensity and timescales of these early EM tran-sients strongly depend on the amount of matter thatis ejected during merger, bound in an accretion disk,or ejected in the form of post-merger disk winds, allof which depend on the properties of the coalesc-ing compact objects (Foucart 2012; Kawaguchi et al.2016; Dietrich & Ujevic 2017; Radice et al. 2018).Foucart et al. (2018) introduced a fitting formulathat estimates the remnant mass (including diskas well as dynamical ejecta) for BH–NS mergers.Kr¨uger & Foucart (2020) provided updated fitting for-mulae that estimate the disk mass for BNS and dy-namical ejecta masses for BH–NS and BNS, fitted tothe results of numerical simulations. Combining theirresults, one can make a rough estimate of the two ejectacomponents in different merger events, and hence givesome estimates for those early EM emission, which canbe used (in conjunction with other observations) toconstrain the binary system parameters of an observedmerger event.Due to the large distance and the rapid decaying na-ture of those EM emissions, one should pay more atten-tion to early (several hrs) emissions from such events,which are brighter than that afterward. Therefore, westudy the properties of the early EM emission (e.g., kilo-nova, sGRB, cocoon) from compact binary mergers andderive some estimates of them.As for a detected GW source, the binary chirp mass M ch , which combines the masses of the two components (see Eq. 5 for its definition), is one of the best param-eters constrained from the gravitational signal in low-latency searches. It is the primary parameter used toreveal the nature of the binary, such as whether the sys-tem hosts two NSs, two stellar BHs or a BH and a NS.Barbieri et al. (2019a) pointed out that for some rangeof the chirp mass value, using chirp mass alone cannotdistinguish a BNS merger from a BH–NS merger. Inthis case, for some selected chirp masses, the observa-tion of the kilonova emission from these systems can helpidentify the nature of the merger system (Barbieri et al.2019a).Barbieri et al. (2019a) studied kilonova emissionsfrom mergers of binary whose chirp mass in the range of1 . M ⊙ − . M ⊙ . In this paper, we investigate the dif-ferences in the kilonova emissions between the BNS andBH–NS mergers at given chirp masses which is similarto the approach of Barbieri et al. (2019a). However, ourstudied BNS and BH-NS mergers have a wider rangeof chirp masses, i.e., 1 . M ⊙ − . M ⊙ . Besides kilonovaemission, we investigate the properties of the sGRB andcocoon for the BNS and BH–NS mergers and estimatetheir EM emissions as a function of the chirp mass.For the range of the studied chirp masses, some of theBHs fall in the socalled ‘mass gap’ (Bailyn et al. 1998;¨Ozel et al. 2010; Farr et al. 2011), which is defined em-pirically as 3 M ⊙ − M ⊙ for the absence of low mass blackholes in the Galaxy. Thompson et al. (2019) recentlyreported the discovery of a BH with mass 3 . +2 . − . M ⊙ ina noninteracting binary system with a red giant. Dueto the presence of ‘mass gap’ BH, this work is useful toconstrain the properties of the BH–NS merger systemsand identify whether an observed BH–NS merger eventinvolves a ‘mass gap’ BH or not.This paper is structured as follows. In Section 2 we de-scribe the properties of the two components of ejecta forboth BNS and BH–NS mergers in more detail. Our gen-eral method to derive the masses of dynamical ejecta anddisk for the given chirp masses is described in Section 3.Our calculations for the luminosities and timescales ofkilonova, sGRB, and cocoon are presented and analyzedin Section 4, 5, and 6, respectively. A case study forGRB GBM–190816 is presented in Section 7. In Section8 we summarize the results and discuss the implications. EJECTA PROPERTIESThe EM emissions are determined by the propertiesof the ejecta produced by the BNS or BH–NS merg-ers. Specifically, the greater the mass of the ejecta is,the brighter the EM transient and the longer the peaktimescale will be. Besides, a higher opacity of the ejectawould delay and redden the kilonova transient. For BNSand BH–NS mergers, there are mainly two componentsof neutron-rich ejecta, i.e., dynamical ejecta and diskwind, whose properties are described in the followingsubsections. 2.1.
Dynamical ejecta
In a BNS merger, the tidal force peels matter fromthe surface of the approaching star, producing outwardexpanding tails of debris which are primarily in the equa-torial plane (Rosswog et al. 1999). When the stars comeinto contact, shock heating at the interface could squeezeadditional matter into polar regions (Oechslin et al.2007; Sekiguchi et al. 2016). The ejecta properties de-pend sensitively on the fate of the massive NS rem-nant, the total binary mass, the mass ratio of the bi-nary, and the EOS (see Fern´andez & Metzger (2016);Shibata & Hotokezaka (2019), for recent reviews). ForBNS mergers, the total masses and velocities of dy-namical ejecta typically lie in the range 10 − M ⊙ − − M ⊙ (Hotokezaka et al. 2013a; Radice et al. 2016;Bovard et al. 2017) and 0 . c − . c , respectively.In a BH-NS merger, when the NS is disrupted priorto the merger, there is substantial matter ejected bythe tidal force of the BH. The dynamical ejecta emergesprimarily in the equatorial plane and shows a significantanisotropy, different from a BNS merger whose dynam-ical ejecta is nearly isotropic (Kawaguchi et al. 2015;Just et al. 2015). Foucart et al. (2014), Kyutoku et al.(2015) and Kyutoku et al. (2018) performed numerical-relativity simulations of BH-NS mergers, and found thatthe dynamical ejecta is concentrated in the equato-rial plane with a half opening angle of 10 ◦ − ◦ andsweeps out about a half of the plane. The proper-ties of dynamical ejecta for BH–NS mergers mainly de-pend on the BH spin, the NS EOS and the mass ra-tio (Fern´andez et al. 2015a; Fern´andez & Metzger 2016;Shibata & Hotokezaka 2019). The ejecta mass rangesfrom 0 . M ⊙ to 0 . M ⊙ , and the average velocity ofthe ejecta inferred from the kinetic energy is typically0 . c − . c . This ejecta is highly neutron rich, producingheavy r-process elements (e.g., Lanthanides) which re-sult in a high opacity κ ∼
10 cm / g (Kasen et al. 2017).2.2. Disk wind
For all the BNS mergers and some of the BH–NS merg-ers, the debris of the tidal-disrupted NS(s), which isbound to the central NS or BH remnant, will circular-ize into an accretion disk. The disk mass with typicalvalue of ∼ . M ⊙ − . M ⊙ (Oechslin & Janka 2006;Hotokezaka et al. 2013b; Foucart et al. 2014) dependsprimarily on the total mass and mass ratio of the bi-nary, the spins of the binary components, and the NS EOS (Oechslin et al. 2007; Shibata & Taniguchi 2011).After the merger, those neutron-rich matter hung up inan accretion disk around the central merged remnant ispartially blown away in the form of winds through neu-trino heating and/or viscously driven process (Metzger2017). Referred as disk wind, it is another importantsource of ejecta mass, and often dominate that of thedynamical ejecta. Kiuchi et al. (2015) performed a highresolution magnetohydrodynamic simulation for BH–NSmerger and found that the fraction of the disk mass thatcan be ejected is up to 50%. Notably, the amount of thedisk outflows varies with the spin of the BH remnant(Fern´andez et al. 2015b).As the relatively-slow disk outflows emerge after thedynamical ejecta, they are physically located behind thedynamical ejecta, and possess a more isotropic geom-etry (Metzger 2017). The disk wind is generally lessneutron-rich because of longer exposure to weak inter-actions (Fern´andez et al. 2017). Just et al. (2015) foundthat the majority of the disk wind material ends up inproducing A <
130 r-process elements, and the disk out-flow complements the dynamical ejecta by contributingthe lighter r-process nuclei (
A < METHOD3.1.
Estimations of the ejecta mass
In order to compute the masses of dynamical ejectaand disk from BNS mergers and BH–NS mergers, weadopt the fitting formulae reported in Kr¨uger & Foucart(2020) and Foucart et al. (2018).3.1.1.
Dynamical ejecta for BNS mergers
The dynamical ejecta for BNS mergers can be esti-mated as (Kr¨uger & Foucart 2020) M dyn − M ⊙ = (cid:18) aC + b M n M n + cC (cid:19) M + (1 ↔
2) (1)where C = GM / ( R c ) is the compactness of thelighter of the two NSs, the best-fit coefficients are a = − . b = 114 . c = − .
56 and n = 1 . Disk for BNS mergers
A rather simple fitting formula allows us to predictthe disk mass from BNS mergers to good accuracy(Kr¨uger & Foucart 2020): M disk = M × (cid:2) max (cid:0) aC + c, × − (cid:1)(cid:3) d (2)where a = − . c = 1 . d = 1 . q ranges from0.775 to 1. Figure 1.
Dynamical ejecta (left) and disk (right) masses for given chirp mass M ch whose values are shown in red numbers.From top to bottom, rows of panels correspond to effective BH spin of 0, 0.25, 0.5 and 0.75, respectively. The dashed linesrepresent the parameter space where there is no dynamical ejecta or disk. Dynamical ejecta for BH–NS mergers
Kr¨uger & Foucart (2020) gave a fitting formula forthe dynamical ejecta from BH–NS merger as M dyn M b NS = a Q n − C NS C NS − a Q n ˆ R ISCO + a (3)where M bNS and C NS is the baryonic mass and com-pactness of NS, Q = M BH / M NS , ˆ R ISCO = 3 + Z − sign ( χ eff ) × p (3 − Z ) (3 + Z + 2 Z ), Z =1 + (cid:0) − χ (cid:1) h (1 + χ eff ) + (1 − χ eff ) i , Z = p χ + Z , a = 0.007116, a = 0.001436, a = − n = 0.8636, n = 1.6840, and χ eff = χ BH cos ( i tilt ), and i tilt is the angle between the BHspin and the orbital angular momentum.The value of χ eff is dependent on the formationchannel of the binary system. For binaries formedfrom isolated binary evolution channel, the spin of eachcomponent is almost aligned with the orbital angularmomenta of the binaries, although modest misalign-ment may be caused by adequately strong supernovakicks (O’Shaughnessy et al. 2017; Gerosa rt al. 2018;Bavera et al. 2019). On the other hand, for binariesproduced dynamically in dense stellar environments,their spins have random orientation (Kalogera 2000;Mandel & O’Shaughnessy 2010; Doctor et al. 2019).Abbott et al. (2020) investigate the population prop-erties of the 47 compact binary mergers detected inGWTC-2, of which 44 are binary black hole (BBH)events. They show that the possibility distribution of i tilt of BH component spins with respect to their orbitalangular momenta for BBH systems peaks at i tilt = 0(see figure 10 in their paper). Therefore, in this workwe adopt i tilt = 0 for simplicity, and hence the value of χ eff can be interpreted as the spin of BH.3.1.4. Disk for BH–NS mergers
Foucart et al. (2018) introduced a fitting formula forthe remnant baryon mass in BH–NS mergers: M rem M b NS = (cid:20) max (cid:18) α − C NS η − β ˆ R ISCO C NS η + γ, (cid:19)(cid:21) δ (4)where η = Q/(1+ Q ), α = 0.406, β = 0.139, γ = 0.255, δ = 1.761.Combining Eqs. (3) and (4), as in M disk = M rem − M dyn , one can get the mass of disk for BH–NS merger.3.2. Ejecta mass for a given chirp mass
The binary chirp mass is defined as M ch = ( M M ) / ( M + M ) / (5) where M and M are the masses of the two componentstars. Here we take M > M .LIGO Scientific collaboration & Virgo Collaboration(LVC) classify merging systems as follows: ‘BNS’ whenboth M and M are less than 3 M ⊙ , ‘BBH’ when both M and M are larger than 5 M ⊙ , ‘BHNS’ when M > M ⊙ and M < M ⊙ , or ‘MassGap’ when at least onecomponent possesses a mass between 3 M ⊙ and 5 M ⊙ .NS EOS plays an important role on merger pro-cess and hence on the mass ejection and disk forma-tion. In this paper, we adopt a soft EOS, i.e., SFHoEOS (Steiner et al. 2013), whose maximum mass ofneutron star is M maxNS = 2 . M ⊙ . The NS withstiffer EOS possesses a more uniform density profileand will be more susceptible to mass shedding, tidaldeformation and tidal disruption by the BH tidal field(Shibata & Taniguchi 2011). Thus our calculation actu-ally gives a conservative estimate for the mass ejectioncompared to using other stiffer EOS. Note that for theuse of the SFHo EOS, we have a new classification differ-ent from that of LVC. Specifically, we classify mergingsystems as follows: ‘BNS’ for both M and M less than M maxNS , ‘BH–NS’ for M > M ⊙ and M < M maxNS , ‘Gap–NS’ for M maxNS < M < M ⊙ and M < M maxNS . In thispaper, the minimum NS mass is set to 1 M ⊙ .Adopting the method discussed above, we derive theejecta masses for BNS, BH-NS and Gap-NS mergerswith given chirp masses. The results are plotted inFigure 1, which shows the dynamical ejecta (left) anddisk (right) masses for effective BH spins of 0, 0.25, 0.5and 0.75, respectively. The dashed lines for given chirpmasses are shown for the cases that there is no NS dis-ruption by BH (i.e., no dynamical ejecta or disk).As shown in Figure 1, the masses of disk and dynami-cal ejecta can be up to 0.3 M ⊙ and 0.1 M ⊙ for the SFHoEOS, respectively. The mass of disk is always largerthan that of dynamical ejecta for all cases. For a GAP-NS or BH-NS merger of a given chirp mass, the disrup-tion of NS is more likely to occur in the system withhigher effective spin, lower NS mass or larger BH mass.Meanwhile, the amount of either type of ejecta increaseswith the initial effective spin of the merging system.As the fitting formulae that we used for BNS mergersdo not depend on the spin of the system (see section 3.1.1and 3.1.2), the masses of either dynamical ejecta or diskfor those mergers presented in Figure 1 are independentof the spin. It is worth noting that for a given chirpmass in the range of 1 . M ⊙ − . M ⊙ , the disk massof a BNS merger is far lower than that of a GAP-NSmerger. Besides, all the BNS mergers in those ranges ofchirp masses hardly eject dynamical ejecta while some Figure 2.
Bolometric luminosity light curve for a kilonovafrom a merger with M BH = 4 M ⊙ , M NS = 1 . M ⊙ and χ eff = 0 .
5. The velocity of the dynamical ejecta and diskwind to be 0.3 c and 0.2 c respectively. The opacity of thedynamical ejecta and disk wind is set to 10 cm g − and 1cm g − respectively. of the GAP-NS mergers eject dynamical ejecta (around0.02 M ⊙ ).In the next three sections, we use the results of ejectagiven above to estimate the emissions of kilonova, sGRB,and cocoon. Throughout the paper we assume 50% ofthe disk is driven out as disk wind for all the mergerevents. KILONOVAIn order to investigate the dependence of kilonovaemission on the parameters of the merging system, weadopt a toy model of kilonova presented in Metzger(2017) and apply it to the ejecta mass distribution withgiven chirp masses as shown in Figure 1.Rosswog et al. (2014) performed simulations that fo-cused on the the long-term evolution of the dynamicalejecta of a BNS merger and found that all remnantsexpand in a nearly homologous manner. Therefore, weassume that the merger ejecta is homologously expand-ing. The mean radius of a layer of ejecta with velocity v is R ≈ vt at time t following the merger. Accord-ing to Bauswein et al. (2013), a power-law function canbe used to describe the distribution of ejecta mass withvelocity greater than v (Metzger 2017) M v = M ( > v ) = M ( v / v ) − β (6)where M is the total mass of ejecta, v is the average( ∼ minimum) velocity, and the value of β is set to 3.Initially, the ejecta is extremely hot. However, thisthermal energy cannot escape as radiation due to the high optical depth of ejecta at early time. The opticaldepth is given by the following equation as τ = ρκR = 3 M κ πR ≃ (cid:18) M − M ⊙ (cid:19) (cid:18) κ g − (cid:19) (cid:16) v . c (cid:17) − (cid:18) t (cid:19) − (7)where ρ = 3 M (cid:14)(cid:0) πR (cid:1) is the mean density and κ is theopacity (cross section per unit mass).As the ejecta expands, the diffusion timescale de-creases with time t diff ∝ t − , and eventually radia-tion escapes once t diff = t (Arnett 1982). The diffusiontimescale of the whole ejecta is t diff ≃ Rc τ = 3
M κ πcR = 3 M κ πcvt . (8)For the individual mass layer M v the radiation escapeson the diffusion timescale t d,v ≈ M v κ v πβR v c = R v = vt M v κ v πM v tc (9)where κ v is the opacity of the mass layer v , and thesecond equality makes use of Eq. (6) with β = 3.For the layer whose differential mass is δM v , its loca-tion evolves as dR v dt = v. (10)Its thermal energy δE v evolves as d ( δE v ) dt = − δE v R v dR v dt − L v + ˙ Q (11)where the first term accounts for losses due to PdV ex-pansion in the radiation-dominated ejecta. The secondterm L v = δE v t d,v + t lc,v (12)is the observed luminosity for each mass layer and t lc,v = R v /c serves as a lower limit to the energy loss time.The third term ˙ Q r,v accounts for radioactivity heatingby the radioactive decay of heavy r-process nuclei andcan be expressed as˙ Q r,v = δM v X r,v ˙ e r ( t ) (13)where X r,v is the r-process mass fraction in mass layer M v and ˙ e r is the specific heating rate. Althoughthere is a small amount (up to ∼ Figure 3.
Peak luminosity (left) and peak time (right) of kilonova for given chirp mass M ch whose values are shown in rednumbers. From top to bottom, rows of panels correspond to effective BH spin of 0, 0.25, 0.5 and 0.75, respectively. The velocitiesof the dynamical ejecta and disk wind are set to be 0.3c and 0.2c, respectively. The opacities of the dynamical ejecta and diskwind are set to 10 cm g − and 1 cm g − , respectively. Fern´andez et al. 2019), most of the ejecta follows a rel-atively slow expansion and is dense enough to cause thecapture of all neutrons via the r-process (Metzger et al.2015; Just et al. 2015; Mendoza-Temis et al. 2015). Inthis work, we adopt X r,v = 1 for simplicity. For neutron-rich ejecta, ˙ e r can be approximated by the followingformula (Korobkin et al. 2012)˙ e r =4 × erg s − g − × ǫ th ,v (cid:0) . − π − arctan[( t − t )/ σ ] (cid:1) . (14)where t = 1.3 s, σ = 0.11 s, and ε th,v is the thermal-ization efficiency (see below).The value of the thermal efficiency ε th,v decreasesfrom 0.5 to 0.1 during the first week since the merger(Barnes et al. 2016). In what follows, we adopt the fitprovided in Barnes et al. (2016), ǫ th ,v ( t ) = 0 . exp ( − a v t day ) + ln (cid:16) b v t c v day (cid:17) b v t c v day ] (15)where t day = t /(1 day). According to Metzger (2017),we adopt fixed values of a v = 0.56, b v = 0.17 and c v =0.74.Numerically solving Eqs. (11) and (12) for each layergives L v . Summing L v over all mass shells gives thetotal luminosity L tot ≃ X v L v . (16)In our calculation we set the velocity of the dynamicalejecta and disk wind to be 0.3 c and 0.2 c , respectively.The opacities of the dynamical ejecta and disk wind areapproximated to be 10 cm g − and 1 cm g − , respec-tively (Kasen et al. 2017).Figure 2 shows the bolometric luminosity light curvefor a kilonova from a merger with M BH = 4 M ⊙ , M NS =1 . M ⊙ and χ eff = 0 .
5, which produces ejecta with M wind = 0 . M ⊙ and M dyn = 0 . M ⊙ . Figure 3 il-lustrates the variation of peak luminosity (left) and peaktime (right) of kilonova versus the parameters of merg-ing system. Note that the peak timescales illustratedin Figure 3 corresponds to the time at which the totalluminosity contributed from both wind and dynamicalejecta reaches its maximum value.As shown in Figure 3, the peak luminosities rangefrom 10 to 10 . erg/s, and the peak timescales are ≤
25 hrs. The comparison between Figure 1 and Fig-ure 3 shows that the peak timescales increase with thetotal masses of disk wind and dynamical ejecta. Be-sides, Figure 3 indicates a positive dependence of thepeak timescales on χ eff , as a merger system with higherspin would eject larger amount of dynamical ejecta and disk wind. For most of the GAP-NS mergers, the peaktimescale of the kilonova emission is relatively large(with a median value of ∼
20 hrs, see the right col-umn of Figure 3) due to the sufficient ejection of bothdynamical ejecta and disk wind, thus it should be easierto detect its emission.As we have shown in section 3.2, for a given chirp massat the range of 1 . M ⊙ − . M ⊙ , all the BNS mergerseject negligible dynamical ejecta and relatively massivedisk wind, while the masses of both dynamical ejectaand disk wind ejected from GAP-NS mergers are largerthan those of BNS mergers (see Figure 1). In addition,the opacity of disk wind is lower than that of dynam-ical ejecta (Kasen et al. 2017). Therefore, the kilonovaemission of the BNS mergers with a given chirp mass atthose ranges would be bluer and peak earlier than thatof GAP-NS mergers (see Figure 3). This difference be-tween the BNS merger and GAP-NS merger for a givenchirp mass at the range of 1 . M ⊙ − . M ⊙ would bemore significant if the initial effective BH spin is higher,and hence could be applied to identify a ‘mass gap’ BH. SGRBIn this section we estimate the luminosity and timescale of the sGRB, and their dependence on the binaryparameters. If the merger remnant is a rotating BHwith a massive disk, a sGRB is probably powered byaccretion onto the stellar mass black hole. Due to thelarge accretion rate, the BH can spin up rather quickly.If a strong magnetic field threads the spinning BH and isconnected with an external astrophysical load, the BHspin energy can be tapped via the Blandford–Znajekmechanism (Blandford & Znajek 1977) which launchesa Poynting-flux-dominated jet.The duration of emission in gamma/X-ray bands fromthe sGRB jet is determined by the characteristic viscoustime-scale for accretion of the remnant disk/torus on tothe BH (Fern´andez et al. 2015a; Fern´andez & Metzger2016): t γ = t visc = r ν α ≈ . (cid:16) α . (cid:17) − (cid:16) r
30 km (cid:17) (cid:18) M BH M ⊙ (cid:19) − (cid:18) H . r (cid:19) − s(17)where r is the radial extent of the torus in whichmost of its mass and angular momentum is concen-trated, ν α = αc s H is the disk viscosity due to tur-bulence (Shakura & Sunyaev 1973), α is the viscosityparameter, c s is the sound speed within the disk, and H ≈ c s ( GM BH /r ) − / is the vertical scale height ofthe disk. The ratio of the disk scale height to the diskradius H/r is assumed to be 0.1 for all the mergers inthis work. Note that we set the mass of the promptlyformed BH to be M + M − M disk − M dyn , ignoring theloss by GWs, for simplicity.The total power of Poynting flux from the BZ pro-cess can be estimated as (Lee et al. 2000; Li 2000;Wang et al. 2002; Lei et al. 2005, 2013; McKinney 2005;Lei & Zhang 2011) L BZ =1 . × × χ (cid:18) M BH M ⊙ (cid:19) (cid:18) B G (cid:19) f ( χ BH ) erg/s (18)where χ BH is the dimensionless spin parameter of theBH, and f ( χ BH ) = (cid:2)(cid:0) q (cid:1)(cid:14) q (cid:3) [( q + 1/ q ) arctan q − , (19)here q = χ BH .(cid:16) p − χ (cid:17) .As shown in Eq. (18), L BZ depends on M BH , χ BH and B . A strong magnetic field of the order 10 G isrequired to produce the high luminosity of a sGRB. Theaccumulation of magnetic flux from an accretion flowmay account for such a high magnetic field strength(Tchekhovskoy et al. 2011).Considering the balance between the magnetic pres-sure on the horizon and the ram pressure of the inner-most part of the accretion flow (Moderski et al. 1997),one can estimate the magnetic field strength threadingthe BH horizon as B ≃ . × ˙ M ( M BH M ⊙ ) − (cid:18) q − χ (cid:19) − G. (20)Assuming the accretion time is equal to t visc , the accre-tion rate of BH is˙ M = (1 − ξ wind ) × M disk t visc (21)where ξ wind accounts for the disk mass lost in the formof winds.Substituting Eqs. (20) & (21) into Eq. (18), one canestimate the luminosity of γ -rays for a one-sided jet as L γ = 4 . × ǫ γ χ (1 − ξ wind ) g ( χ BH ) M disk t visc erg / s(22)where g ( χ BH ) = f ( χ BH ) (cid:30)(cid:16) p − χ (cid:17) . The effi-ciency factor ǫ γ accounts for the conversion of Poynting-flux-dominated energy into γ -rays energy. Note that inthis work, we set ǫ γ to be 0.015 (Barbieri et al. 2019b).Considering a simple top-hat jet model, the isotropicequivalent γ -ray luminosity for the sGRB prompt emis-sion is then given by L γ,iso = L γ / (1 − cosθ j ) ≃ L γ / ( θ j /
2) (23)
Figure 4.
The peak isotropic equivalent gamma-rays lumi-nosity for sGRB prompt emission corresponding to initial BHspin of 0.25 (top), 0.5 (middle) and 0.75 (bottom). Note thatfor the BNS mergers whose M ch = 1 . , . , . M ⊙ ,the masses of the remnant objects are all larger than M maxNS ,thus we consider those BNS merger remnants as BHs. Theresult for BNS mergers corresponds to the situation that aBH formed promptly. where θ j is the jet half-opening angle (Frail et al. 2001).It is worth noting that we assume the jet half-openingangle θ j = 0 . L γ,iso for three different BH spins of0.25, 0.5 and 0.75. The results are shown in Figure 4.Since the aforementioned calculation is constructed forthe BZ jet from a rotating BH, it is necessary to iden-tify whether a BNS merger forms a BH. In our calcu-lation, for the BNS mergers whose M ch = 1 . , . , . . M ⊙ , we consider the merger remnant to be aBH as long as the mass of the remnant object is larger0than M maxNS , and hence the results in Figure 4 for BNSmergers correspond to the situation that a BH formspromptly. The dimensionless spin parameter of the BH χ BH is referred to the spin of the promptly formed BH.For the GAP-NS (BH-NS) merger, at the beginning ofaccretion, the spin of the BH is unchanged. Thus in ourcalculation, χ BH is adopted to be the initial BH spin.For a non-spinning BNS, simulations show that the spinof the promptly formed BH ranges from 0.55 to 0.83with a mean value of 0.68 (Coughlin et al. 2019), thushere we adopt the spin of the BH to be 0.68 in all casesfor simplicity.As illustrated in Figure 4, for the sGRB powered byaccretion onto the BH, the isotropic equivalent luminos-ity of γ -rays varies from 10 erg/s to 10 erg/s. Theisotropic luminosities for most of the detected sGRBsare in the range of 10 − erg/s, while there aresome abnormally low events like GRB170817A whose L γ,iso = (1 . ± . × erg/s (Abbott et al. 2017b;Zhang et al. 2018). These observations are consistentwith our predictions. Figure 4 suggests that low L γ,iso ( < erg/s) probably occurs in the BNS systems withthe lighter one larger than 1 . M ⊙ , or in the BH–NS(GAP–NS) systems that involve a heavy NS. Besides,most of the BH–NS (GAP–NS) events probably have a L γ,iso higher than 10 erg/s.Due to the positive dependence of L γ,iso on the ef-fective spin and the disk mass (see eqs. 22 & 23; notethat disk mass increases with the effective spin), a largerspin of the initial system (i.e., of the promptly formedBH) corresponds to a higher sGRB isotropic luminosity(see Figure 4). For the GAP–NS (BH–NS) mergers witha fixed BH spin, the higher isotropic luminosities tendto occur in the systems with lower chirp masses. For agiven chirp mass in the range of M ch = 1 . M ⊙ − . M ⊙ ,as the disk masses of the BNS mergers are three ordersof magnitude lower than that of GAP–NS mergers, theisotropic luminosities from BNS mergers are lower thanthose of GAP–NS mergers by around three to four or-ders of magnitude. This difference in L γ,iso for the chirpmass range of 1 . M ⊙ − . M ⊙ could be applied to iden-tify a ‘mass gap’ BH. COCOONWhen a relativistic jet propagates through the sub-relativistic material that was ejected during and aftermerger (hereafter referred as pre-burst ejecta), the inter-action of the jet with the pre-burst ejecta would result inthe formation of ‘cocoon’, which is a highly-pressured,hot bubble enclosing the jet. If the jet breaks throughthose pre-brust ejecta successfully, the jet and cocoontogether would form a structure which spreads over a much wider opening angle than that of the jet alone.The energy deposited by the shock in the cocoon diffusesas it expands and eventually escapes to the observer,producing an X-ray, UV and optical cooling emission(Nakar & Piran 2017; Lazzati et al. 2017). The promptemission from the cocoon is detectable for Swift BATand Fermi GBM (Lazzati et al. 2017).Lazzati et al. (2017) presented a calculation of possi-ble components of off-axis emission from a sGRB, in-cluding the cocoon prompt emission. Assuming a black-body spectrum they obtain a cocoon emission luminosity L c = 4 × erg/s × (cid:18) E c erg (cid:19) (cid:18) Γ c (cid:19) (cid:18) R a cm (cid:19) − (24)where E c , Γ c and R a correspond to the energy andLorentz factor of the cocoon, and the distance thatthe jet head traverses (see Eq. 32), respectively. Theprompt emission lasts for an angular time-scale as t c ∼ t ang = R ph , c (cid:14)(cid:0) c Γ (cid:1) = 0 .
14 s (cid:18) E c erg (cid:19) (cid:18) Γ c (cid:19) − (25)where R ph , c = (cid:16) E c σ T πm p Γ c (cid:17) is the photospheric radiusof the cocoon (Lazzati et al. 2017; Bhattacharya, Kumar & Smoot2019), σ t is the Thompson cross-section, m p is the massof proton. In the following two subsections, we considerthe interaction of the jet with the pre-bust ejecta toestimate the jet breakout time t b and the Lorentz factorof cocoon Γ c . Then we use them to determine the valueof parameters in Eqs. (24) and (25), and eventuallyestimate L c and t c for the cocoon prompt emission.In the context of BH–NS mergers, the dynamicalejecta are mostly concentrated around the equato-rial plane and the polar-shocked material is absent(Kyutoku et al. 2013). Nevertheless, the presenceof disk winds and sufficient jet-launching time delaycan result in the accumulation of the required ejectamass around the polar regions. Murguia-Berthier et al.(2020) found that the difference in the final structure ofthe jet is not highly sensitive to the exact structure ofthe wind. Thus in what follows, we consider only thedisk wind as the pre-burst ejecta and assume the windejecta is isotropically distributed around the remnant,but bear in mind that this is a crude approximation tothe real geometry of the pre-burst ejecta.6.1. Jet breakout time
The interaction of the relativistic jet with the sub-relativistic pre-burst ejecta have been analytically stud-ied by considering limiting cases for the dynamics1of the ejecta, being either static (Begelman & Cioffi1989; Marti et al. 1994; Matzner 2003; Bromberg et al.2011) or homologously expanding (Duffell et al. 2018).Beniamini et al. (2020) combine these two limits anddescribe the breakout time of a successful jet as t b = t b , e + t b , s (26)where t b,e , t b,s are the jet breakout times in the homol-ogous expansion and static ejecta limits, respectively.In the static ejecta limit, the breakout time is the timethat the jet takes to overpass the merger ejecta t b , s = t w β w β h − β w (27)where β w is the velocity of the pre-brust ejecta (i.e.,disk wind) and β h is the velocity of the jet’s head, t w is the time interval between the merger and the launchof the jet. The velocity of the jet head is related to theratio between the jet’s total luminosity, L j ≡ L γ /ǫ γ , andthe (isotropic equivalent) mass outflow rate of the windejecta, ˙ M w , as follows (Marti et al. 1994; Matzner 2003;Bromberg et al. 2011; Murguia-Berthier et al. 2017) β h = β j + β w ˜ L − L − (28)where˜ L ≡ L j β w ˙ M w c =0 . ǫ γ (cid:18) L γ erg s − (cid:19) (cid:18) β w . (cid:19) (cid:18) − M ⊙ M w (cid:19) (cid:18) t w + t b (cid:19) . (29)As we have discussed above, in our calculation, M w isset to the total mass of disk wind for BH–NS merger.Note that for BNS merger we only consider the diskwind (since there are polar shocked ejecta, the wind-only treatment may be a lower limit to the real M w inthis case).In the homologously expanding limit, Duffell et al.(2018) found that jets are successful when E j & . E w where E w ≈ M w β c / E j denotes the total energy of the jet. Theyidentified two breakout regimes. For energies in therange 0 . E w . E j . E w , jets barely break out anda significant amount of energy is deposited in a cocoon.This regime is dubbed the ‘late breakout’. For higher en-ergies, E j & E w , jets break out easily, and this regimeis dubbed ‘early breakout’. The jet breakout time isgiven by Duffell et al. (2018) as follows t b , e = . t e E w E j =0 . η γ M w ( β w c ) L γ ′ early ′ t e q E j E w − = t e r Lγt e ηγM w( β w c )2 − ′ late ′ (30) where t e ≈ t visc is the duration of the jet engine opera-tion.Beniamini et al. (2020) assume that the self-collimationof sGRB jets does not play a critical role and find thatthe time interval between the binary merger and thelaunching of a typical sGRB jet is ≤ t w is equal to 0.1 s for all thesGRB cases. Then using Eqs. (26)–(30) with t w = 0 . s ,we calculate the jet breakout time, t b , for the mergerswith given chirp masses.It is worth noting that the total energy of the co-coon produced by two-sided jets can be approximatedas (Nakar & Piran 2017) E c ≈ × L j × t b (31)and the distance that the jet has to travel in the ambientejecta can be expressed as (Lazzati et al. 2017) R a = t b × β h,e × c (32)where β h , e = β w + β h β w β h denotes the jet head velocity in theco-moving frame of the medium (Lazzati et al. 2019).Thus using the estimated jet breakout time with themethod discussed above, one can get the value of E c and R a for different merger events.6.2. Lorentz factor of cocoon
Nakar & Piran (2017) studied the cocoon dynamicsfollowing the jet breakout. The terminal Lorentz fac-tor of the cocoon is Γ c = min { n c , η b } , where η b is thecritical baryonic loading, and η c is the usual notation ofbaryonic loading. In our calculation, η b is much largerthan η c therefore we useΓ c = η c ≡ E c m c c (33)to estimate Γ c , where E c is the energy deposited tothe cocoon and m c is its mass. We estimate m c withthe relation m c = ρ w × V c . The cocoon shape atthe time of breakout, as seen in numerical simula-tions (Morsony et al. 2007; Mizuta & Ioka 2013) andpredicted by analytic modeling (Bromberg et al. 2011),is roughly a cone or a cylinder with a height R a , thus thevolume of cocoon can be estimated as (Nakar & Piran2017) V c = 13 πR a θ (34)where θ j is the half-opening angle of jet. The density ofthe wind ejecta is approximated as ρ w = ˙ m w Ω w R a v w whereΩ w is equal to 2 π for the isotropic distribution of windejecta (Lazzati et al. 2019).2 Figure 5.
Peak luminosity (left) and duration (right) of the cocoon prompt emission for initial effective BH spin of 0.25 (top),0.5 (middle) and 0.75 (bottom). The pre-burst ejecta is assumed to be disk wind only for all the merging system. The windejecta is assumed to be isotropically distributed.
Lazzati et al. (2019) derive analytic estimates for thestructure of jets expanding in environments with differ-ent density, velocity, and radial extent. They obtain thejet solid angle asΩ j = s πL j v w Ω w ˙ m w c v h , e sin θ j , inj (35)where θ j,inj is the injection angle of jet. Thus with Ω j =2 π (1 − cosθ j ), the value of θ j for different mergers canbe obtained. Using Eqs. (33) – (35), we derive the valueof Γ c for any given merger.6.3. Results of cocoon prompt emission
Figure 5 shows the variation of peak luminosity L c (left) and duration t c (right) of the cocoon prompt ems-sion versus the parameters of merging system. Note thatfor all mergers, we set the injection angle of jet to be 10 ◦ .As shown in Figure 5, for the cocoon prompt emission,which peaks in X-ray and UV bands, L c is mainly inthe range of 10 to 10 erg/s. The merging systemwith lower effective spin would have a larger t c , as t c decreases with Γ c which is positively related to t b and M w . For a given chirp mass ranging from 1 . M ⊙ to1 . M ⊙ , the peak luminosities of BNS mergers are lowerthan those of GAP-NS mergers by one to three ordersof magnitude. Besides, the duration of cocoon promptemission from BNS mergers are also lower than those of3 Figure 6.
The peak isotropic equivalent gamma-rays luminosity of sGRB prompt emission for EOS SFHo (left) and DD2(right) (see the upper-right corner of each panel for the initial spin of the BH). Note that the maximum mass of neutron starsfor DD2 EOS is 2 . M ⊙ , thus the maximum value of M in the right column is higher than that in the left column. The lightgray region represents 90% confidence interval of the chirp mass for GRB GBM–190816 (see section 7). GAP-NS mergers. These differences would be useful todistinguish the two types of mergers. It is worth notingthat in this range of chirp mass, the cocoon promptemission is likely to be detected only for GAP–NS eventsbecause t c is too short to be detected for other casesaccording to current detection limit. CASE STUDY FOR GRB GBM–190816Fermi GBM-190816, a sub-threshold GRB candi-date, was potentially associated with a sub-thresholdLIGO/Virgo compact binary merger candidate, as re-ported by LIGO/Virgo/Fermi Collaboration. (2019)and Goldstein et al. (2019). According to the GW sig-nal, the lighter compact object is estimated to be lighterthan 3 M ⊙ , which can be either an NS or a low-massBH. The heavier component is a higher-mass BH.Yang et al. (2020) perform an independent analysis ofthe publicly available data and investigate the physi-cal implications of this potential association. Takinginto account the burst distance ∼
428 Mpc, they calcu-late the isotropic γ -ray luminosity as L γ, iso =1 . +3 . − . × erg s − . Based on their assumption that one com-pact object of this CBC event is an NS with a mass of1.4 M ⊙ , using the GW date alone, they further constrainthe mass ratio to be q = 2 . +2 . − . . These component masses give the chirp mass of thisevent M ch = 2 . +0 . − . M ⊙ (90% confidence interval, shownas the light gray region in Figure 6). Thus combin-ing L γ,iso and M ch of GBM-190816 with our estimationscheme above, we find that the effective spin should belarger than 0.6, for the EOS SFHo (see the left columnof Figure 6). For a given χ eff , e.g., χ eff = 0 .
75, the leftbottom panel in Figure 6 suggests that the mass of thelighter one should be smaller than 2 M ⊙ and the mass ofthe BH component should be larger than 5.5 M ⊙ for theEOS SFHo.As the neutron star EOS is a major source ofuncertainty for the ejecta properties, we also takea much stiffer EOS (i.e., DD2, whose maximummass of neutron star is M maxNS = 2 . M ⊙ ) fromHempel & Schaffner-Bielich (2010) and Typel et al.(2010) to approximately capture the edge cases of theparameter space. As a stiffer EOS would result in moreejecta, for the DD2 EOS, the inferred minimum valueof χ eff = 0.45 (see the right column of Figure 6) issmaller than that inferred from the case with SFHoEOS. Besides, compared with the SFHo EOS, for thegiven χ eff = 0 .
75, the DD2 EOS results in a largerupper mass limit of the lighter one (2.4 M ⊙ , close to the4maximum mass of neutron star for the DD2 EOS) and asmaller lower mass limit of the BH component (4.5 M ⊙ ). SUMMARY AND DISCUSSIONThe detection of electromagnetic radiation from acompact binary merger triggered by GWs plays role onstudying the merging system including the properties ofthe outflow, the physics of the relativistic jet and theinteraction between the jet and the pre-burst ejecta. Inthis paper we investigate the early EM emission whichis critical in recognizing the merger and give a detailedestimation for kilonova, sGRB and cocoon prompt emis-sion. We connect our calculation for those early emissioncomponents with the chirp mass M ch which is one of thebest measured parameters encoded in the GW signal.Based on the fitting formulae for the disk and dy-namical ejecta masses of BNS and BH–NS merg-ers from numerical simulations (Foucart et al. 2018;Kr¨uger & Foucart 2020), we found that the mass ofdisk and dynamical ejecta can be up to 0.3 M ⊙ and0.1 M ⊙ for the SFHo EOS, respectively (Figure 1). ForBH–NS mergers, the amount of two types of ejecta in-creases with the initial effective spin of the merging sys-tem. For a given chirp mass, the disruption of NS tendsto occur in the system with lower mass of NS (therefore,larger mass of BH). The mass of disk is larger than thatof dynamical ejecta for any given merger.Barbieri et al. (2019a) pointed out that the chirp massrange of 1 . M ⊙ − . M ⊙ is compatible to both a BNSand a GAP-NS mergers. In this work, we found that fora given chirp mass ranging from 1 . M ⊙ to 1 . M ⊙ , thedisk mass of a BNS merger is far lower than that of aGAP-NS merger. Besides, all the BNS mergers in thisrange of chirp mass hardly eject dynamical ejecta whilesome of the GAP-NS mergers eject significant amountof dynamical ejecta around 0.02 M ⊙ . Due to the depen-dence of the kilonova, sGRB, cocoon on the propertiesof the dynamical ejecta and disk wind, we show thatthose differences in the dynamical ejecta and disk be-tween BNS mergers and GAP-NS mergers for a givenchirp mass at the range of 1 . M ⊙ − . M ⊙ could resultin significant differences in those emissions between thetwo types of mergers.As shown in Figure 3, for a given M ch in the range of1 . M ⊙ − . M ⊙ , the peak luminosities of the kilonovaemission from BNS mergers are nearly tow orders lowerthan those of GAP–NS mergers. Those kilonova emis-sions from BNS mergers tend to be bluer and peak ear-lier than GAP–NS mergers. Therefore, the observationof kilonova (i.e., peak luminosity and timescale) from the mergers whose chirp mass is in the range of about1 . M ⊙ − . M ⊙ can help identify those mergers. Thisis consistent with the result of Barbieri et al. (2019a),in which they studied the light curves of both BNS andBH–NS mergers and pointed out that at the optimalvalue of chirp mass ( M ch = 1 . M ⊙ ) a single observa-tion in the g or K band would be helpful to distinguishthe nature of the merging system.For sGRBs powered by accretion onto the BH, theisotropic equivalent γ -rays luminosity is sensitive to thedisk mass. For M ch = 1 . M ⊙ − . M ⊙ the BNS mergerseject less disk wind compared with GAP–NS mergers,thus L γ of BNS merger is lower than that of GAP–NSmerger by around three to four orders of magnitude (seeFigure 4). Therefore it can be concluded that the ob-servation of sGRB may also be helpful to identify thosemergers when the detected chirp mass falls in the rangeof 1 . M ⊙ − . M ⊙ .As shown in Figure 5, for a given chirp mass rang-ing from 1 . M ⊙ to 1 . M ⊙ , the cocoon prompt emissionwhich peaks in X-ray and UV band form BNS merger isdifferent from that of GAP-NS merger. The peak lumi-nosities of BNS mergers are lower than those of GAP-NSmergers by one to three orders of magnitude (note thatthis difference increases with spin). Besides, the dura-tion of cocoon prompt emission from BNS mergers arealso lower than those of GAP-NS mergers. Therefore,except for the kilonova and sGRB emissions, the cocoonprompt emission can also be used to reveal the natureof a merger.The early emissions estimated in this work are usefulto constrain the properties of merger events (see sec-tion 7 for example). When M ch falls in the range of1 . M ⊙ − . M ⊙ which is compatible to both a BNS anda GAP–NS mergers, we find that the mass of the dy-namical ejecta and disk of the BNS merger is far lowerthan that of the GAP–NS merger, which would result inthe differences in kilonova, sGRB and cocoon betweenBNS mergers and GAP–NS mergers. These are useful indistinguishing the two merger types when the detectedchirp mass falls in the range of 1 . M ⊙ − . M ⊙ .We thank the anonymous referee for useful commentsand suggestions that improve the quality of the pa-per. This work is supported by National Natural Sci-ence Foundation of China (11673078 and 12073091),Guangdong Basic and Applied Basic Research Founda-tion (2019A1515011119) and Guangdong Major Projectof Basic and Applied Basic Research (2019B030302001).REFERENCES5 Abbott, B. P., et al. 2017a, ApJL, 848(2): L12Abbott, B. P., et al., 2017b, ApJL, 848(2): L13Abbott, B. P., et al., 2020b, arXiv:2010.14533Arnett, W. D. 1982, ApJ, 253, 785Bailyn, C. D., Jain, R. K., Coppi, P., & Orosz, J. A. 1998,ApJ, 499, 367Barbieri, C., Salafia, O. S., Colpi, M., Ghirlanda, G.,Perego, A., Colombo, A. 2019, ApJL, 887(2):L35Barbieri, C., Salafia, O. S., Perego, A., Colpi, M., &Ghirlanda, G. 2019, A&A, 625, A152Barnes, J., & Kasen, D. 2013, ApJ, 775(1):18Barnes, J., Kasen, D., Wu, Meng-Ru., Mart´ınez-Pinedo,Gabriel. 2016, 829(2):110Bauswein, A., Goriely, S., Janka, H.T. 2013, ApJ, 773:78Bavera, S. S., Fragos, T., Qin, Y., et al. 2019, A&A, 635,A97Begelman, M. C., & Cioffi, D. F. 1989, ApJL, 345, L21Beniamini, Paz; Duran, Rodolfo Barniol; Petropoulou,Maria; Giannios, Dimitrios. 2020, The ApJL, 895(2):L33Bhattacharya, M., Kumar, P., & Smoot, G. 2019, MNRAS,486, 5289Blandford, R. D., & Znajek, R. L., 1977, MNRAS, 179,433-456Bloom, J. S., Holz, D. E., Hughes, S. A., et al. 2009,e-prints arXiv:0902.1527Bovard, Luke; Martin, Dirk; Guercilena, Federico; et al.2017, PhRvD, 96,12, 124005Bromberg, O., Nakar, E., Piran, T., & Sari, R. 2011, ApJ,740, 100Coughlin M. W.; Dietrich T.; Margalit B.; Metzger B. D.,2019, MNRAS, 489, L91Dietrich, Tim; Ujevic, Maximiliano, 2017, Classical andQuantum Gravity, 34, 10, 105014Doctor, Z., Wysocki, D., O ’ Shaughnessy, R., Holz, D. E.,& Farr, B. 2019, ApJ, 893, 35Paul C. Duffell; Eliot Quataert; Daniel Kasen; HannahKlion, 2018, ApJ, 866:3Eichler D., Livio M., Piran T., Schramm DN. 1989, Nature340:126128.Farr, Will M.; Sravan, Niharika; Cantrell, Andrew; et al.2011, ApJ, 741, 103Fern´andez, R., & Metzger, B. D., 2013, MNRAS, 435, 1,502-517Fern´andez, Rodrigo; Quataert, Eliot; Schwab, Josiah;Kasen, Daniel; Rosswog, Stephan. 2015, MNRAS, 449, 1,390-402Fern´andez, Rodrigo; Kasen, Daniel; Metzger, Brian D.;Quataert, Eliot, 2015, MNRAS 446, 750758Fern´andez, R.; Metzger, B. D., 2016, Annu. Rev. Nucl.Part. Sci., 66, 23 Fern´andez, R., Foucart, F., Kasen, D., et al. 2017, Classicaland Quantum Gravity, 34, 15, 154001Fern´andez, R., Tchekhovskoy, A., Quataert, E., Foucart, F.,Kasen, D. 2018, MNRAS, 482, 3373-3393.Fong W., Berger E., Metzger BD., et al. 2014, ApJ, 780:118.Foucart, Francois, 2012, PhRvD, 86, 12, 124007Foucart, F., Deaton, M. B., Duez, M. D., et al. 2014,PhRvD, 90, 2, 024026Foucart, F., Hinderer, T., & Nissanke, S. 2018, PhRvD, 98,8, 081501Frail, D. A., Kulkarni, S. R., Sari, R. Djorgovski, et al.2001, ApJ, 562, 1, L55-L58.Gerosa, D., Berti, E., O ’ Shaughnessy, R., et al. 2018,PhRvD, 98, 084036Goldstein, A., Hamburg, R., Wood, J., et al. 2019, arXive-prints, arXiv:1903.12597Grossman, D., Korobkin, O., Rosswog, S., Piran, T., 2014,MNRAS, 439, 1, 757-770Hempel, M., & Schaffner-Bielich, J. 2010, NuPhA, 837, 210Hotokezaka, K., Kiuchi, K., Kyutoku, K., et al. 2013,PhRvD, 88, 4, 044026Hotokezaka, K., Kiuchi, K., Kyutoku, K., Okawa, H.,Sekiguchi, Y.i., Shibata, M., Taniguchi, K., 2013,PhRvD, 87, 024001Just, O., et al., 2015, MNRAS, 448, 541Kalogera, V. 2000, ApJ, 541, 319Kasen, D., Badnell, N. R., Barnes, J., 2013, ApJ, 774, 25Kasen, D., Metzger, B.D., Barnes, J., Quataert, E.,Ramirez-Ruiz, E., 2017, Nature, 551, 8084Kawaguchi, K., Kyutoku, K., Nakano, H., Okawa, H.,Shibata, M., Taniguchi, K., 2015, PhRvD, 92, 024014Kawaguchi, K., Kyutoku, K., Shibata, M., Tanaka, M.2016, ApJ, 825, 1, 52Kr¨uger & Foucart, 2020, PhRvD, 101, 10, 103002Kiuchi, K., Sekiguchi, Y., Kyutoku, K., Shibata, M.,Taniguchi, K., Wada, T. 2015, PhRvD, 92, 064034Korobkin, O., Rosswog, S., Arcones, A., Winteler, C. 2012,MNRAS, 426, 3, 1940-1949.Kyutoku, K., Ioka, K., Shibata, M. 2013, PhRvD, 88, 4,041503Kyutoku, K.; Ioka, K.; Okawa, H.; Shibata, M.; Taniguchi,K., 2015, PhRvD, 92, 044028Kyutoku, K., Kiuchi, K., Sekiguchi, Y., Shibata, M.,Taniguchi, K. 2018, PhRvD, 97, 2, 023009Lazzati, D., Deich, A., Morsony, B. J., Workman, J. C.2017, MNRAS, 471, 2, 1652-1661Lazzati, D., Perna, R. 2019, ApJ, 881, 2, 89Lee, H. K., Wijers, R. A. M. J., & Brown, G. E. 2000, PhR,325, 83Lei, W. H., Wang, D. X., & Ma, R. Y. 2005, ApJ, 619, 4206