Multimessenger Binary Mergers Containing Neutron Stars: Gravitational Waves, Jets, and \boldsymbolγ-Ray Bursts
DDraft version February 9, 2021
Typeset using L A TEX default style in AASTeX63
Multimessenger Binary Mergers Containing Neutron Stars: Gravitational Waves, Jets, and γ -RayBursts Milton Ruiz, Stuart L. Shapiro,
1, 2 and Antonios Tsokaros Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 Department of Astronomy & NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (Dated: February 9, 2021)
ABSTRACTNeutron stars (NSs) are extraordinary not only because they are the densest form of matter in thevisible Universe but also because they can generate magnetic fields ten orders of magnitude largerthan those currently constructed on Earth. The combination of extreme gravity with the enormouselectromagnetic (EM) fields gives rise to spectacular phenomena like those observed on August 2017with the merger of a binary neutron star system, an event that generated a gravitational wave (GW)signal, a short γ -ray burst (sGRB), and a kilonova. This event serves as the highlight so far ofthe era of multimessenger astronomy. In this review, we present the current state of our theoreticalunderstanding of compact binary mergers containing NSs as gleaned from the latest general relativisticmagnetohydrodynamic simulations. Such mergers can lead to events like the one on August 2017,GW170817, and its EM counterparts, GRB 170817 and AT 2017gfo. In addition to exploring the GWemission from binary black hole-neutron star and neutron star-neutron star mergers, we also focus ontheir counterpart EM signals. In particular, we are interested in identifying the conditions under whicha relativistic jet can be launched following these mergers. Such a jet is an essential feature of mostsGRB models and provides the main conduit of energy from the central object to the outer radiationregions. Jet properties, including their lifetimes and Poynting luminosities, the effects of the initialmagnetic field geometries and spins of the coalescing NSs and black holes, as well as their governingequation of state, are discussed. Lastly, we present our current understanding of how the Blandford-Znajek mechanism arises from merger remnants as the trigger for launching jets, if, when and how ahorizon is necessary for this mechanism, and the possibility that it can turn on in magnetized neutronergostars, which contain ergoregions, but no horizons. Keywords: black holes, neutron stars, gravitational waves, short gamma-ray bursts, numerical relativity INTRODUCTION
Gravitational wave astronomy was launched in 2015 with the first-ever gravitational wave (GW) detection of theinspiral and merger of a binary black hole (BHBH) system as reported by the LIGO/Virgo (LV) scientific collaboration–event GW150914 (Abbott et al. 2016b,a). Two years later the simultaneous detection of GWs from an inspiralingbinary neutron star (NSNS) system, event GW170817, and its postmerger emission of electromagnetic (EM) radiationspurred the era of multimessenger astronomy (Abbott et al. 2017a; Kozlova et al. 2017; Abbott et al. 2017b,c,d).Although at present the LV scientific collaboration almost weekly announces new GW signals whose progenitors maybe BHBHs, NSNSs, or black hole-neutron star (BHNS) systems there has been no robust discovery of a BHNS systemyet, while the subsequent NSNS candidates have been EM “orphans” i.e. no EM radiation has been associated withthe GWs produced by them. Merging NSNSs and BHNSs are not only important sources of gravitational radiation,but also promising candidates for coincident EM counterparts, which could give new insight into their sources. Namely,GWs are sensitive to the density profile of NSs and their measurement enforces tight constraints on the equation of state(EOS) that governs matter at supranuclear densities (Lattimer & Prakash 2016), while postmerger EM signatures canhelp to explain the phenomenology of short γ -ray bursts (sGRBs), and nucleosynthesis processes powering kilonovae (Li& Paczynski 1998; Metzger 2017). To understand these observations and, in particular, to understand the physics of a r X i v : . [ a s t r o - ph . H E ] F e b matter under extreme conditions, it is crucial to compare them to predictions from theoretical modeling, which, dueto the complexity of the underlying physical phenomena, is largely numerical in nature.Although a spinning BH surrounded by an accretion disk is the remnant of a BHNS merger, this is not necessarilythe case for an NSNS merger. Depending on the total mass of the system, as well as the EOS of the NS companions,the outcome of an NSNS merger can be a stable NS or a spinning BH, surrounded by an accretion disk in either case.Even when a BH is the remnant, the path towards such an outcome is extremely varied and can be decisive for anumber of important issues, like the existence of a sGRB or the production of the heaviest elements in the Universevia a kilonova (Metzger & Fern´andez 2014). The current consensus for the event GW170817 is the formation of atransient NS remnant sustaining itself for a brief period of time (cid:46) (cid:38) . M (cid:12) estimated from the kilonova AT 2017gfo).Assuming that this was the case, it is possible to place strong constraints on the maximum mass of a cold sphericalNS and its EOS (Margalit & Metzger 2017; Shibata et al. 2017a; Rezzolla et al. 2018; Ruiz et al. 2018a; Shibata et al.2019a). These constraints could also provide an explanation for the unidentified 2 . M (cid:12) compact object in GW190814as a rotating or even a nonrotating NS (Most et al. 2020; Tsokaros et al. 2020a). From a different point of view, theabsence of a prompt collapse scenario and the large ejecta mass also puts constraints on NS radii or, equivalently, theirtidal deformability (Bauswein et al. 2017; Radice et al. 2018). These constraints on the NS radius coming directly fromthe postmerger object were further refined by complementary analyses of the GW inspiral signal, which can be usedto estimate the tidal deformability of the inspiraling NSs (Abbott et al. 2017a; Raithel et al. 2018; De et al. 2018).Lattimer & Schramm (1974) and Symbalisty & Schramm (1982) suggested that unstable neutron-rich nuclei can bebuilt in the mergers of BHNS or NSNS systems through rapid neutron bombardment, the r-process. Apart from thedynamical ejecta that emerge within milliseconds after merger, the ejecta that emerge much later are very important inthe determination of whether or not heavier elements through the r-process are being produced. Li & Paczynski (1998)argued that the low mass and high velocity of these ejecta will make them transparent to their own radiation, resultingin emission whose peak will last around one day. Metzger et al. (2010) calculated the luminosity of the radioactively-powered transients in NS mergers and found these transients to be approximately 1000 times brighter than typicalnovae, therefore calling them “kilonovae”. Metzger & Fern´andez (2014) argued that the lifetime of the merger remnantis directly imprinted in their early “blue” emission (from high electron fraction, lanthanide-poor ejecta) or late “red”emission (from low electron fraction, lanthanide-rich ejecta), both of which have been seen in event GW170817. Theblue emission suggested ejecta composed of light r-process elements, while the red emission is consistent with heavierones (lanthanide or actinides). The overall conclusion is the the kilonova AT 2017gfo was a major source of r-processelements (Kasen et al. 2017; Cˆot´e et al. 2017).Another important characteristic associated with event GW170817 was the observation of an sGRB – event GRB170817A (Kozlova et al. 2017; Abbott et al. 2017c). This GRB was unusually weak, and various models have beenproposed to explain this, including a choked-jet cocoon or a successful-jet cocoon (Hallinan et al. 2017; Kasliwalet al. 2017; Mooley et al. 2018). Recently, Mooley et al. (2018) using radio observations from very long-baselineinterferometry were able to break the degeneracy between the choked and successful-jet cocoon models and concludedthat the early-time radio emission was powered by a wide-angle outflow (a cocoon), while the late-time emission wasmost probably dominated by an energetic and narrowly collimated jet with an opening angle of less than five degrees,and observed from a viewing angle of about 20 degrees. This solidified theoretical predictions that NSNS, or at leasta stellar binary where at least one of the companions is a NS, can be the progenitors of the central engine that powersGRBs (Paczynski 1986; Eichler et al. 1989; Narayan et al. 1992).Although GRB 170817A provided the long-sought observational evidence linking sGRBs with NSNS mergers, it didnot reveal the nature of the central engine behind the launching of a relativistic jet. In particular, is a BH horizonnecessary for the existence of a jet or is it just sufficient (Paschalidis et al. 2015; Ruiz et al. 2018b, 2016; Ruiz &Shapiro 2017; Ruiz et al. 2019)? If necessary, then a stable NS remnant cannot be the generator of such jets. If not, isthe jet from a stable NS qualitatively the same as the one launched from a spinning BH immersed in a gaseous disk?In particular, can one describe it as a Blandford & Znajek (1977a) (BZ) jet? Notice that according to Komissarov(2002, 2004, 2005) and Ruiz et al. (2012), the driving mechanism behind a BZ jet is not the horizon but the ergoregion.Thus, while it may be that typical NSs cannot launch a BZ jet, NSs that contain ergoregions –ergostars– might beable to (Ruiz et al. 2020c).Since the pioneering general relativity (GR) simulations of NSNS mergers by Shibata & Ury¯u (2000) and BHNSmergers by Baumgarte et al. (2004), Shibata & Uryu (2006) and Faber et al. (2006a,b), a number of groups haveproduced a large body of work that captures the main characteristics of such events (see reviews by Shibata &Taniguchi (2011); Baiotti & Rezzolla (2017) and Foucart (2020)). Below we will present a brief review of some ofthe important progress in the field, paying special attention to pure hydrodynamical versus magnetohydrodynamicalsimulations. Details regarding the techniques used (either in evolution or in the initial data) will be omitted. Werefer the reader to e.g. Alcubierre (2008); Baumgarte & Shapiro (2010); Shibata (2015) for such details. We also donot treat white dwarf-neutron star (WDNS) mergers, which, though important for GW detections by LISA, are notlikely sources of sGRBs or kilonova. We refer readers interested to the GR simulations of Paschalidis et al. (2011) andreferences therein.We adopt geometrized units with c = G = 1 unless otherwise indicated. BLACK HOLE-NEUTRON STAR MERGERS: REMNANTS AND INCIPIENT JETS
Motivated by the significance of BHNS binaries as copious sources of GW and EM radiation, many numerical studieshave been performed over the past years. Before the pioneering BHBH simulations (Pretorius 2005; Campanelli et al.2006; Baker et al. 2006), most dynamical simulations of BHNS binaries were treated in Newtonian gravity, modelingthe BH as a point mass (Lee 2001; Rosswog et al. 2004; Rosswog 2005; Kobayashi et al. 2004; Rantsiou et al. 2008).Although these studies gave first insights on the basic dynamics of BHNSs, full GR simulations are required to properlymodel the late inspiral, NS disruption, tidal tails, merger remnant, disk mass, fraction of unbound material ejected,sGRB engine, and most significantly the GWs emitted during merger. In the following section, we only review fullGR studies of these binaries. 2.1.
Nonmagnetized evolutions
Most of the close BHNS binary orbits are likely quasi-circular, since gravitational radiation reduces the orbitaleccentricity of the binary as it evolves toward smaller orbits (Peters 1964). However, a small fraction may form indense stellar regions, such as globular cluster or galactic nuclei, through dynamical capture, and they may merge withhigh eccentricities (Kocsis & Levin 2012; Lee et al. 2010; Samsing et al. 2014).Motivated by the above, different groups have generated quasi-equilibrium initial data for BHNSs on quasi-circularorbits (Baumgarte et al. 2004; Taniguchi et al. 2005; Shibata & Uryu 2006, 2007; Grandclement 2006; Taniguchi et al.2007; Foucart et al. 2008). Some of the earliest full GR simulations of these configurations were performed by Shibata& Uryu (2006, 2007), followed by Etienne et al. (2008) and Duez et al. (2008). In all of these studies the binary wasformed by a nonspinning BH with a NS companion modeled as a Γ = 2 polytrope. These simulations showed thatthe fate of BHNS remnants can be classified in two basic categories: 1) the NS is tidally disrupted before reaching theinnermost stable circular orbit (ISCO), inducing a long tidal tail of matter that eventually wraps around the BH andforms a significant accretion disk (typically with a mass (cid:38)
8% of the NS rest-mass); 2) the NS plunges into the BH,leaving a BH surrounded by a negligibly small accretion disk (typically with a mass (cid:46)
2% of the NS rest-mass).Using a Smoothed Particle Hydrodynamics (SPH) code and an approximate “conformal” GR metric, Rantsiou et al.(2008) showed that the mass of the accretion disk remnant strongly depends on the magnitude and direction of theBH spin. In particular, it was found that only systems with a highly spinning BH, and slightly misaligned to the totalangular of the system, yield significant accretion disk remnants. These results were later confirmed by full GR studies(Etienne et al. 2009; Foucart et al. 2011, 2012; Kyutoku et al. 2011) showing that for sufficiently high BH spins, massratios q = M BH /M NS (cid:46)
3, and/or lower NS compactions C = M NS /R NS (cid:46) .
18, a substantial disk can form followingmerger. Here M BH is the Christodoulou (1970) BH mass at infinite separation and M NS the NS rest mass, while M NS and R NS are the gravitational (Arnowitt-Deser-Misner (ADM)) mass and the circumferential radius of the starin isolation, respectively.Using the above numerical simulation results, Foucart (2012) constructed a simple fitting formula to predict theamount of matter remaining outside the BH horizon about 10 ms following merger: M disk M NS ≈ . q / (1 − C ) − . R ISCO R NS . (1)This expression is valid for mass ratios in the range q = 3 −
7, BH spins a BH /M BH = 0 − .
9, and NSs with radii R NS = 11 −
16 km, thereby encompassing the most likely astrophysically relevant parameter space. Here, M disk and R ISCO is the mass of the disk remnant and the radius of the ISCO, respectively. Note that Eq. 1 explicitly shows thatthe mass of the disk remnant depends on the EOS and the BH spin, which determine the mass and radius of the NSand the position of the ISCO, respectively. It should be noticed that BHNSs with nearly-extremal BH spins have beenconsidered by Lovelace et al. (2008); Lovelace et al. (2013). These studies found that upon NS disruption, less thanhalf of the matter is promptly accreted by the BH, around 20% becomes unbound and escapes, and the remainingmass settles into a massive accretion disk.Early population synthesis studies found that the distribution of mass ratios in BHNSs depends on the metallicityand peaks at q = 7 (Belczynski et al. 2008, 2010), but more recent works found that it is generally less than 10,peaking at q ≈ q = 5 in which the NS companion has radius 13 . M NS = 1 . M (cid:12) (compatible with NICERobservations; Miller et al. (2019); Riley et al. (2019)) a BH spin of a BH /M BH (cid:38) .
65 is required to form an accretiondisk with (cid:38)
10% of the NS rest mass. The power available for EM emission is usually taken to be proportional tothe accretion rate. Under this assumption, it is expected that the luminosity of the disk remnant is L EM = (cid:15) ˙ M disk ,where (cid:15) is the efficiency for converting accretion power to EM luminosity and ˙ M disk ∼ M disk /t acc is the rest-massaccretion rate, where t acc is the disk lifetime. Assuming a 1% efficiency and a disk lifetime of ∼ . L EM ∼ erg / s, consistent with typical EM luminosities of sGRBs. This value is also consistent with the “universal”merger scenario for generating EM emission from merger and collapse BH + disk remnants (Shapiro 2017a). Theseresults allow us to conclude that the merger of NSs orbiting highly spinning BHs can be the progenitors of the enginesthat power sGRBs. However, the LV scientific collaboration has reported the observation of BHBHs having highmass and/or low spins (see e.g. Table VI in Abbott et al. (2020b)). If this trend continues for LV-like BHNSs, thenit is expected that LV-like BHNS remnants would have negligible accretion disks, which might disfavor their role asprogenitors of sGRBs and/or observable kilonovae.The previous numerical studies assumed that the NS companion is irrotational. Recently, East et al. (2015) and Ruizet al. (2020a) showed that the NS spin has a strong impact on the disk remnant and the dynamical ejecta. As theprograde NS spin increases, the effective ISCO decreases (Barausse & Buonanno 2010). In addition, as the magnitudeof the NS spin increases, the star becomes less bound and the tidal separation radius r tid (separation at which tidaldisruption begins) increases, also resulting in more pronounced disruption effects. This effect can be easily understoodby estimating r tid by equating the inward gravitational force exerted by the NS on its fluid elements with the BH’soutward tidal and the outgoing centrifugal forces to obtain r tid /M BH (cid:39) q − / C − (cid:2) − Ω M C − (cid:3) − / , (2)(Ruiz et al. 2020a) where Ω = a NS M NS /I . Here a NS is the NS spin parameter and I its moment of inertia. Thissimple Newtonian expression shows that the larger the mass ratio and/or the compaction of the NS, the closer thetidal separation to the ISCO. The NS then experiences tidal disruption effects only during a short time before the bulkof the NS plunges onto the BH. In contrast, the larger the magnitude of the NS spin, the farther away r tid is from theISCO. In this case, the star can be tidally disrupted before being swallowed by the BH which increases the time fordisruption and with it the amount of matter that spreads out to form the disk or escapes to infinity.Recently, Barnes & Kasen (2013) showed that the opacities in r-process ejecta are likely dominated by lanthanides,which induce peak bolometric luminosities for kilonovae of L knova ≈ (cid:18) M eje − M (cid:12) (cid:19) / (cid:16) v eje . c (cid:17) / erg / s , (3)(East et al. 2015) and rise times of t peak ≈ . (cid:18) M eje − M (cid:12) (cid:19) / (cid:16) v eje . c (cid:17) − / days , (4)(East et al. 2015) where v eje and M eje are the mass-averaged velocity and rest-mass of the ejecta. The characteristicspeed of the ejecta is v eje /c (cid:46) . − . (cid:46) − M (cid:12) (see e.g. East et al. (2015); Ruiz et al.(2020a); Foucart et al. (2015); Hayashi et al. (2020)). Therefore, the bolometric luminosity of kilonova signals is L knova (cid:46) erg / s with rise times of (cid:46) ∼
24 mag at200 Mpc inside the aLIGO volume (Abbott et al. 2013), and above the LSST survey sensitivity of 24 . Magnetized evolutions
The previous numerical studies showed that BHNS mergers can create the right conditions to power sGRBs (i.e.a spinning BH + disk). However, they do not account for either magnetic fields or neutrino pair annihilation processes,the most popular components invoked in most sGRB models to drive jets (see e.g. Blandford & Znajek (1977b); Vlahakis& Konigl (2003a,b); Piran (2005); Aloy et al. (2004)). As the lifetime of the neutrino pair annihilation process might betoo small to explain typical sGRBs (Kyutoku et al. 2018), we henceforth focus only on the magnetic process. However,it is worth noting that BH + disk remnants powering sGRBs may be dominated initially by neutrino pair annihilationprocesses followed by the BZ mechanism (Dirirsa 2017), leading to a transition from a thermally-dominated fireball toa Poynting EM-dominated flow, as is inferred for some GRBs, such as GRB 160625B (Zhang et al. 2018).Ideal GR magnetohydrodynamics (GRMHD) studies of magnetized BHNS mergers in which the NS is initiallyendowed with an interior-only poloidal magnetic field generated by the vector potential A i = (cid:18) − y − y c (cid:36) δ xi + x − x c (cid:36) δ yi (cid:19) A ϕ , A ϕ = A b (cid:36) max( P − P cut , n b , (5)were carried out by Chawla et al. (2010), Etienne et al. (2012a) and Kiuchi et al. (2015b), varying the mass ratio, theBH spin, and the strength of the magnetic field. Here the orbital plane is at z = 0, ( x c , y c ,
0) is the coordinate locationof the center of mass of the NS, (cid:36) = ( x − x c ) + ( y − y c ) , and A b , n p and P cut are free parameters. The cutoffpressure parameter P cut confines the magnetic field inside the NS within P > P cut . The parameter n b determines thedegree of central condensation of the magnetic field. Figure 1.
The NS magnetic field lines (green) and rest-mass density ρ (reddish) normalized to the initial NS maximumvalue ρ = 8 . × (1 . M (cid:12) /M NS ) g / cm , at selected times for a BHNS with mass ratio q = 3. The initial BH spin is a BH /M BH = 0 .
75 and the NS is an irrotational Γ = 2 polytrope. Here the BH apparent horizon is shown as a black sphere.Following merger, the field lines are wound into an almost purely toroidal configuration [Adapted from Etienne et al. (2012b)].
These numerical simulations showed that following merger, tidal tails of matter wrap around the BH, forming theaccretion disk and dragging the frozen-in magnetic field into an almost purely toroidal configuration (see Fig. 1).These simulations did not find any evidence of jet launching following the BH + disk formation. Nevertheless, Kiuchiet al. (2015b) reported that in their high-resolution simulations, in which the mass ratio is q = 4, the BH has a spin a BH /M BH = 0 .
75, and the NS is modeled by the APR EOS (Akmal et al. 1998), a thermally-driven wind (but nocollimated) outflow emerges after ∼
50 ms following merger (see Fig. 2).The lack of magnetically-driven jets in these simulations has been attributed to the fact that the magnetic fieldin the disk remnant is almost purely toroidal . Beckwith et al. (2008) showed that BH + disk systems can launchand support magnetically-driven jets only if a net poloidal magnetic flux is accreted onto the BH. Motivated by thisconclusion, Etienne et al. (2012b) endowed the disk remnant from an unmagnetized BHNS simulation with a purelypoloidal field and found that, indeed, under the right conditions , a jet can be launched from BHNS remnants. However,identifying the initial configuration of the seed magnetic field in the NS prior to tidal disruption that could lead tothese conditions remained elusive for many years.Paschalidis et al. (2015) then demonstrated that a more realistic initial magnetic configuration for the NS companion–a dipolar magnetic field extending from the NS interior into the exterior (as in pulsars)– could do the trick. Such afield can be generated by the vector potential A φ = π (cid:36) I r ( r + r ) / (cid:20) r ( r + (cid:36) )8 ( r + r ) (cid:21) , (6)(Paschalidis et al. 2013) which approximately corresponds to a vector potential generated by an interior current loop.Here r is the current loop radius, I is the current, and r = (cid:36) + z , with (cid:36) = ( x − x c ) +( y − y c ) . To reliably evolvethe exterior magnetic field with an ideal GRMHD code and simultaneously mimic the magnetic-pressure dominantenvironment that characterizes a pulsar-like magnetosphere, a low and variable density atmosphere was installedinitially in the exterior where magnetic field stresses dominate over the fluid pressure. Figure 2.
NS rest-mass density with fluid velocity arrows (left) and the gas-to-magnetic-pressure ratio (right) of a q = 4 BHNSremnant after ∼
50 ms following merger. A thermally-driven wind (but no collimated) outflow is observed [From Kiuchi et al.(2015b)].
The above technique was used by Paschalidis et al. (2015) and Ruiz et al. (2018b, 2020a) to perform a series ofBHNS simulations varying the density of the “artificial” atmosphere, the binary mass-ratio, the BH and NS spins,and the orientation of the seed magnetic field axis with respect to the orbital angular momentum. It was foundthat independent of the atmosphere or the NS spin, a magnetically driven, incipient jet is launched once the regionsabove the BH poles become nearly force-free ( B / πρ (cid:29)
1) for small tilt-angle magnetic fields and binary massratios that yield a significant disk remnant. The jet is confined by a collimated, tightly wound, helical magneticfunnel above the BH poles. Following the onset of accretion, the magnetic field in the disk remains predominantlytoroidal as in the previous simulations. However, the external magnetic field maintains a strong poloidal componentthat retains footpoints at the BH poles. Magnetic instabilities (mainly magnetic winding and magnetorotational(MRI)) amplify the magnetic field from ∼ (1 . M (cid:12) /M NS ) G to ∼ (1 . M (cid:12) /M NS ) G at the BH poles, and after∆ t ∼ − M NS / . M (cid:12) ) ms following merger a bonafide jet finally emerges (see Fig. 3). It is worth noting thatthe calculation of Ruiz et al. (2020a) showed that the larger the initial NS prograde spin, the larger the mass of theaccretion disk remnant. Similar behavior was observed for the amount of unbound ejecta. These results suggest thatmoderately high-mass ratio BHNSs ( q (cid:46)
5) that undergo merger, where the NS companion has a non-negligible spin,may give rise to detectable kilonovae even if magnetically-driven jets are not formed.The Lorentz factor in the funnel is Γ L ∼ . − .
3, and hence the jet just above the BH poles is only mildly relativistic.However, the maximum attainable Lorentz factor of a magnetically–powered, nearly axisymmetric jet is comparableto the force-free parameter B / πρ inside the funnel (Vlahakis & Konigl 2003a). Near the end of the simulationsthe force-free parameter in the funnel reaches values (cid:38) L (cid:38)
100 as required by most sGRB models (Zou & Piran 2010).
Figure 3.
NS rest-mass density ρ normalized to its initial maximum value ρ , max = 8 . × (1 . M (cid:12) /M NS ) g / cm (logscale) at selected times for a BHNS with mass ratio q = 3. The initial BH spin is a BH /M BH = 0 .
75 and the NS is an irrotationalΓ = 2 polytrope. Arrows indicate fluid velocities and white lines the magnetic field lines. Bottom panel shows the system afteran incipient jet is launched. Here M = 2 . × − ( M NS / . M (cid:12) ) ms = 7 . NS / . (cid:12) ) km [From Paschalidis et al. (2015)]. The lifetime of the disk is ∆ t ∼ M NS / . M (cid:12) ) − M NS / . M (cid:12) ) ms and the outgoing EM Poynting luminosityis L EM ∼ ± erg / s, and hence consistent with typical sGRBs (Bhat et al. 2016; Lien et al. 2016; Svinkin et al. 2016;Ajello et al. 2019). The luminosity is also consistent with that generated by the BZ mechanism L BZ ∼ (cid:18) a BH M BH (cid:19) (cid:18) M BH . M (cid:12) (cid:19) (cid:18) B G (cid:19) erg / s , (7)(Thorne et al. 1986) as well as with the simple analytic model that seems to apply universally for typically compactbinaries mergers containing magnetized NSs that leave BH + disk remnants (Shapiro 2017a).The above results were obtained with a high initial magnetic field. Paschalidis et al. (2015) argued that a smallerinitial field will yield the same qualitative outcome because the magnetic field amplification following disruption is duelargely to magnetic winding and the MRI. Amplification proceeds until appreciable differential rotational and internalenergy of the plasma in the disk has been converted to magnetic energy. This amplification yields B ∼ G at theBH poles nearly independent of the initial NS magnetic field. Winding occurs on an Alfv´en timescale, so amplificationmay take longer the weaker the initial field.2.3. GW190814: Spin & EOS for a NS companion
One of the most intriguing GW detections to date was event GW190814 (Abbott et al. 2020a), a binary coalescencewhose primary component had mass m = 23 . +1 . − . M (cid:12) and therefore is a BH, while the secondary had mass m =2 . +0 . − . M (cid:12) , placing it at the boundary of the so-called “mass gap” and making its identification uncertain. Furtherambiguity was added by the absence of an EM counterpart. While the nature of this compact object is not yet known, Figure 4.
Two possibilities for the EOS of a NS companion in GW190814. The scenario on the left, which employs the SLy(soft) EOS, fails to provide a model for a uniformly rotating star, even at maximum uniform rotation. On the contrary, thescenario on the right that employs the DD2 (stiff) EOS succeeds and demonstrates the possibility of a slowly rotating NS. Thelower (black) curves represent spherical, nonrotating models, while the upper (red) curves represent uniformly rotation modelsspinning at the Keplerian (mass-shedding) limit [From Tsokaros et al. (2020a)]. it was already suggested by Abbott et al. (2020a) that it can be a rapidly rotating NS, whose dimensionless spinwas estimated to be 0 . (cid:46) a NS /M NS (cid:46) .
68 (Most et al. 2020). For this scenario to be viable the maximum massof a spherical, nonrotating cold NS has to be (cid:38) . M (cid:12) (Most et al. 2020; Tsokaros et al. 2020a). Requiring rapidrotation for a NS companion in GW190814 is a direct consequence of the likely upper limits (2 . − . M (cid:12) ) placedon a spherical, nonrotating NS mass by event GW170817 (Margalit & Metzger 2017; Shibata et al. 2017a; Rezzollaet al. 2018; Ruiz et al. 2018a; Shibata et al. 2019a). These upper limits were mostly based on the assumption that thecompanions in GW170817 were slowly rotating. Assuming rapid uniform NS rotation, instead, the upper limit allowedby event GW170817 increases (Abbott et al. 2017a; Ruiz et al. 2018a) and can explain the 2 . M (cid:12) compact object inGW190814 as a slowly rotating NS. In fact, by allowing for the uncertainties and adopting a sufficiently stiff EOS,even a nonrotating NS can explain GW190814 (Tsokaros et al. 2020a). Note that although no robust discovery of aBHNS exists yet, the NSs in the 20 known NSNS systems (Tauris et al. 2017; Zhu et al. 2018) have low dimensionlessspins. While one cannot draw definitive conclusions from these limited number of observations, one might safely arguethat if spin-down due to EM emission is as efficient as in currently known binaries, then any scenario involving ahighly spinning NS either in an NSNS (like GW170817) or in an BHNS system (like GW190814) is not probable. Insummary, invoking rotation to explain the companion to the BH object in GW190814 depends on the stiffness of theEOS and the assumptions of the maximum mass of a spherical NS. For a soft EOS (low spherical maximum mass) suchas SLy (Douchin & Haensel 2001) rapid rotation is not sufficient, while for sufficiently stiff EOS such as DD2 (Hempel& Schaffner-Bielich 2010) rapid rotation may not even be necessary. Such EOSs are neither rejected nor favored byGW170817, and they are in accordance with the results of NICER (see Fig. 4). NSNS MERGERS: REMNANTS AND INCIPIENT JETS
Numerical simulations of NSNS binaries are somewhat simpler than BHNS binaries, since the latter must treat theBH singularity. Some of the first numerical studies of NSNSs employed Newtonian gravity, modeling the NS as apolytrope (Gilden & Shapiro 1984; Oohara & Nakamura 1989; Rasio & Shapiro 1992, 1994; Shibata et al. 1992, 1993;Xing et al. 1994; New & Tohline 1997). For circular orbit binaries it was found that following the binary merger, a highlydifferentially rotating remnant is formed. However, their simulations could not track its possible collapse to a BH withNewtonian gravity. Motivated by models of sGRBs and the ejection of r-process nuclei, Davies et al. (1994), Ruffertet al. (1996) and Ruffert & Janka (1998) extended the previous results by incorporating a simple treatment of thenuclear physics in their numerical calculations. One of the first approaches used to simulate NSNS coalescence inGR was the “conformal flatness approximation” (CFA) used by Wilson & Mathews (1995), which has been followedby several other treatments with increasing sophistication. Oechslin et al. (2002) evolved NSNS binaries using aLagrangian SPH code with a multigrid elliptic solver to handle the gravitational field equations and corotating initialconfigurations. Faber et al. (2004) subsequently performed SPH simulations in the CFA using a spectral elliptic solverin spherical coordinates and employed the quasi-equilibrium, irrotational binary models of Taniguchi & Gourgoulhon(2002). These models are constructed using the conformal thin-sandwich formalism (York 1999). Oechslin et al. (2007)extended their earlier studies by including the influence of a realistic nuclear EOS. These simulations showed that thedynamics and the final outcome of the merger depend sensitively on the EOS and the binary parameters, such as thegravitational mass of the system and its mass ratio. The first fully GR simulations of NSNS undergoing merger wereperformed by Shibata & Ury¯u (2000); Shibata & Uryu (2002) and Shibata et al. (2003) using a polytropic EOS tomodel the stars. Since then, great progress has been made to model NSNSs incorporating realistic microphysics andmagnetic field effects in full GR and in alternative theories of gravity. In the following we only review full GR studiesof these binaries. For earlier reviews and references, see, e.g., Baumgarte & Shapiro (2010) and Shibata (2015).3.1.
Nonmagnetized evolutions
One of the first questions numerical studies of NSNS mergers in full GR were compelled to address was under whatconditions the highly differentially rotating star remnant collapses to a BH. The uncertainties in the nuclear EOS,combined with theoretical arguments invoking GW170817 and its EM counterparts, allow nonrotating NSs with amaximum mass limit in the range M sphmax ∼ . − . M (cid:12) (Margalit & Metzger 2017; Rezzolla et al. 2018; Ruiz et al.2018a; Shibata et al. 2017a, 2019a). Uniform rotation allows NSs with up to ∼
20% more mass (“supramassive stars”;as coined by Cook et al. (1994a,b)). Even larger masses can be supported against collapse with centrifugal support ifthe star is differentially rotating. Such stars were first constructed and explored by Baumgarte et al. (2000), who builtdynamically stable Γ = 2 polytropic models with masses (cid:38) − M (cid:12) . They coined the label “hypermassive neutronstar” (HMNS) to describe such stars. It was demonstrated by Duez et al. (2004) that shear viscosity drives a HMNS tocollapse to a BH on a (secular) viscous timescale and by Duez et al. (2006) that turbulent magnetic viscosity inducedby MRI can also drive the secular collapse of the latter magnetic HMNSs. These viscous effects compete with neutrinoand GW emission (when the HMNS remnant is nonaxisymmetric) to drive collapse. In NSNS binaries, the fate of theremnant depends on the total mass of the NSNS binary, as we shall now discuss.Shibata & Ury¯u (2000) and Shibata & Taniguchi (2006) found that there is a threshold mass M th above which theremnant collapses immediately on a dynamical timescale to a BH, independently of the initial binary mass ratio. Thisthreshold value depends strongly on the EOS. For Γ = 2 polytropes M th ≈ . M sphmax , while for stiffer EOSs, such asAPR (Akmal et al. 1998) and SLy (Douchin & Haensel 2001), it is ∼ . − . M sphmax . Shibata & Taniguchi (2006) alsofound that in the case of “prompt” collapse to a BH, the mass of the disk remnant increases sharply with increasingmass ratio for a fixed gravitational mass and EOS. In addition, if the mass of the binary is less than M th the diskremnant turns out to be more massive than for those whose mass is larger than M th . For binaries with M < M th theirremnants form a transient, highly deformed HMNS which, after ∼ −
50 ms, undergoes a “delayed” collapse to a BHsurrounded by a significant accretion disk. The collapse occurs due to angular momentum losses from gravitationalradiation in these simulations where neutrino cooling and magnetic fields are absent (Baiotti et al. 2008; Kiuchi et al.2009; Rezzolla et al. 2010; Dietrich et al. 2015; Ruiz et al. 2019). These results have been extended by Hotokezaka et al.(2011) using a piecewise polytropic representation of nuclear EOSs (Read et al. 2009; ¨Ozel & Psaltis 2009). It wasfound that the threshold value is in the range 1 . (cid:46) M th /M sphmax (cid:46) .
7. These results were confirmed also for realisticfinite-temperature EOSs (Bauswein et al. 2013). In addition, the ratio between the threshold mass and maximummass is tightly correlated with the compactness of the M sphmax . Finally, less massive binary mergers form a dynamicallystable NS remnant that may collapse on longer time scales once dissipative processes, such as neutrino dissipation orgravitational radiation, take place (Cook et al. 1994b,a; Lasota et al. 1996; Breu & Rezzolla 2016).Most of the numerical calculations to date have focused on quasi-circular irrotational binaries, though it is expectedthat spin can modify the threshold value of prompt collapse, or at least change the lifetime of the remnant. Preliminaryresults reported by Kastaun & Galeazzi (2015), Dietrich et al. (2017), Ruiz et al. (2019) and Chaurasia et al. (2020)showed that depending on the NS spin, the lifetime of the remnant may change from ∼ (cid:38)
40 ms. Effects of NS spinon the inspiral have been explored by Kiuchi et al. (2017), Bernuzzi et al. (2014), Dietrich et al. (2018) and Tsokaroset al. (2019a). On the other hand, the dynamically captured NSNS mergers that may arise in dense stellar regions,0 f [kHz]01020 P h a s e Φ [ r a d ] R1nsnsR2nsnsRbhbh 250 300 350 400 450 t / M J b h / M b h R1nsnsR1nsns-Kerr RbhbhRbhbh-Kerr
Figure 5.
Left panel: GW phase versus frequency for the NSNS binary using two resolutions (R1nsns,R2nsnsn) and a BHBHbinary having the same gravitational mass. Right panel: Dimensionless spin of the remnant BH for the NSNS (R1nsnsn) andthe BHBH (Rbhbh) binary. Also shown is the dimensionless spin as computed from the Kerr formula for the two systems[From Tsokaros et al. (2020c)]. such as globular clusters, have been studied by East & Pretorius (2012). These results showed that M th and the massof the disk remnant depend not only on the EOS but also on the impact parameter. The calculations by Paschalidiset al. (2015) and East et al. (2016) demonstrated that the HMNS formed through dynamical capture may undergo theone-arm nonaxisymmetric (mode m = 1) instability.During merger, shock heating produces temperatures as high as ∼
100 MeV at the contact layer between the twostars. Subsequent compressions lead to average-temperatures of the order of 10 MeV in the central core of the NSNSremnant (Bauswein et al. 2010), and hence the binary remnant can be a strong emitter of neutrinos. The timescale ofneutrino cooling radiation (typically (cid:46) M = 7 . M (cid:12) , and each star is identical and has a compactness of C = 0 . C max = 0 .
355 set by causality (Lattimer& Prakash 2016). To build these binaries, Tsokaros et al. (2020c) employed the ALF2 EOS (Alford et al. 2005), butreplaced the region where the rest-mass density satisfies ρ ≥ ρ ,s = ρ , nuc = 2 . × gr / cm by the maximally stiffEOS P = ρ − ρ s + P s , (8)with sound speed equal to the speed of light. Here ρ is the total energy density, and P s the pressure at ρ s , assumedknown. The quasi-equilibrium initial data were built using the COCAL code (see e.g. Tsokaros et al. (2015, 2016)).Due to the large compactions of the NSs the binary stars exhibit no tidal disruption up until merger, whereupon aprompt collapse is initiated even before a common core forms. Within the accuracy of the simulations the BH remnantfrom this NSNS binary exhibits ringdown radiation that is not easily distinguishable from a perturbed Kerr BH. Rightpanel of Fig. 5 displays the dimensionless spin from the BH remnant from the NSNS and that from a BHBH binaryhaving the same gravitational (ADM) mass. Also shown are the remnant spins as computed from the analytic Kerrformula whose input is the ratio L p /L e of the polar to equatorial circumference. However, the inspiral leads to phasedifferences of the order of ∼ ∼
81 km separation ( ∼ . Figure 6.
NS rest-mass density ρ (upper left rainbow colorbar) and magnetic field (lower left brownish colorbar) on the orbitalplane at t = 10 . x = 147 m (left), at ∆ x = 74 m (middle), and∆ x = 37 m (right)]. The initial magnetic field strength is 5 × G [Adapted from Aguilera-Miret et al. (2020)].
Magnetized evolutions
Although NS may have very large magnetic fields ( (cid:38) G) at birth, it is expected that cooling processes signifi-cantly reduce their magnitudes (Pons et al. 2009). Pulsar observations indicate that the characteristic surface magneticfield strength of NSs is ∼ − G (Lyne & Graham-Smith 2012; Lorimer 2008; Miller et al. 2019; Semena et al.2019). Nevertheless, magnetic instabilities such as the Kelvin-Helmholtz instability (KHI; see e.g. Price & Rosswog(2006); Anderson et al. (2008); Kiuchi et al. (2015b,a)), MRI (see e.g. Duez et al. (2006); Kiuchi et al. (2015b); Shibataet al. (2006); Siegel et al. (2013)), and magnetic winding (see e.g. Baumgarte et al. (2000); Kiuchi et al. (2015a); Sunet al. (2019)) triggered during and after the NSNS merger can substantially boost the strength of these weak fields.High-resolution simulations are required to properly capture the above instabilities because their fastest growingmodes have short wavelengths. Kiuchi et al. (2015b,a) systematically studied the effects of numerical resolution onthe magnetic field amplification in NSNS mergers and found that, at the unprecedented resolution of ∆ x = 17 . G is amplified to values (cid:38) G in the bulk of the remnant, with local values peakingat ∼ G, after 5 ms following merger. Recently, the calculations by Aguilera-Miret et al. (2020) reported that ata resolution of ∆ x = 37 m an initial magnetic field of 5 × G is amplified to values of ∼ G after about 10 msfollowing merger (see Fig. 6). These extremely high-resolution simulations are computationally quite expensive andcurrently inaccessible for general studies. Typical NSNS simulations use a resolution (cid:38)
120 m (see e.g. Ciolfi et al.(2019a); Ruiz et al. (2019); Weih et al. (2020); Vincent et al. (2020); Bernuzzi et al. (2020)). To overcome the lack ofresolution, some works have adopted subgrid models to mimic the effect of magnetic instabilities (see .e.g. Giacomazzoet al. (2015); Palenzuela et al. (2015); Aguilera-Miret et al. (2020); Radice (2020)), while others have employed high,but dynamically weak initial magnetic fields to mimic the resulting magnetic field following the merger (see e.g. Ruizet al. (2016); Ciolfi et al. (2019a); M¨osta et al. (2020)). These two approaches allow the tracking of the secular evolutionof the a quasi-stationary NSNS remnant consisting of a HMNS that ultimately undergoes delayed collapse to a highlyspinning BH surrounded by an accretion disk with a strong magnetic field with finite computational resources.Some of the first long-term ideal GRMHD studies of NSNS mergers were performed by Anderson et al. (2008) and Liuet al. (2008) using Γ = 2 polytropes endowed with a 10 G polodial magnetic field confined to the NS interior (seeEq. 5). The simulations of Anderson et al. (2008) reported the formation of a long-lived HMNS. During this phase,turbulent magnetic fields transport angular momentum away from the center, inducing the formation an axisymmetriccentral core that eventually collapses to a spinning BH. Liu et al. (2008) reported the evolution of equal and unequalbinaries that promptly collapse to a BH following merger, surrounded by a disk with (cid:46)
2% of the total rest mass ofthe binary. Neither an outflow nor a magnetic field collimation were found.The calculations of Rezzolla et al. (2011) reported that ∼
12 ms after the collapse of a HMNS remnant, MHDinstabilities develop and form a central, low-density, poloidal-field funnel, though there were no evidences of an outflow.The initial data consist of a binary polytrope initially endowed with a 10 G poloidal magnetic field confined to the2
Figure 7.
NS rest-mass density and magnetic field lines at t − t mrg ≈ . t − t mrg ≈ . t − t mrg ≈ . t mrg is the merger time. Cyan color on the left panel displays magnetic fieldsstronger than 10 . G. Yellow, green, and dark blue colors on the middle panel show rest-mass densities of 10 , 10 , and10 g / cm , respectively. Light and dark blue colors on the right panel indicate rest-mass densities of 10 . , and 10 g / cm ,respectively [From Kiuchi et al. (2015b)]. stellar interior. The highest resolution used in these studies was ∆ x ≈
221 m. A subsequent high-resolution studyby Kiuchi et al. (2015b), employing an H4 EOS (Glendenning & Moszkowski 1991) with seed poloidal magnetic fieldsconfined to the stellar interior, found that during merger, the magnetic field is steeply amplified due to the KHI.In their high-resolution case (∆ x = 70 m) the amplification is 40 −
50 times larger than that in the low-resolutioncase (∆ x = 150 m). In contrast to the results of Rezzolla et al. (2011), the ram pressure of the fall-back debris preventsthe formation of a coherent poloidal field. As the frozen-in magnetic field lines are anchored to the fluid elements, anoutflow, which was not seen after 40 ms following merger (see Fig. 7), is presumably necessary to generate a coherentpoloidal magnetic field.Ruiz et al. (2016) evolved the same NSNS configuration as in Rezzolla et al. (2011) but using higher resolution(∆ x = 152 m). As this resolution is still not enough to properly capture the growth of the magnetic field due to theKHI, Ruiz et al. (2016) endowed the initial NSs with dynamically weak, purely poloidal magnetic fields with strengths B pole (cid:39) . × (1 . M (cid:12) /M NS ) G at the poles of the stars, which matches the values of the field strength inthe HMNS reached in Kiuchi et al. (2015b). It was found that by ∼ ∼ M NS / . M (cid:12) ) ms following BHformation, the magnetic field above the BH poles has been wound into a tight, helical funnel inside of which fluidelements begin to flow outward: this is an incipient jet (see Fig. 8). The lack of a jet in Kiuchi et al. (2015b) can beattributed to the persistent fall-back debris in the atmosphere, which increases the ram pressure above the BH poles.Therefore, a longer simulation like the one in Ruiz et al. (2016) is required for jet launching. Notice that jet launchingmay not be possible for all EOSs if the matter fall-back timescale is longer than the disk accretion timescale (Paschalidis2017).In addition, Ruiz et al. (2016) studied the impact of the magnetic configuration on the jet launching time. For thisthe NSs were endowed with the pulsar-like interior + exterior magnetic field generated by the vector field in Eq. 6.To reliable evolve the exterior magnetic field, Ruiz et al. (2016) adopted the atmosphere treatment previously usedby Paschalidis et al. (2015). As illustrated in Fig. 8, a magnetically-driven jet is launched on the same time scale (seesecond column in Fig. 9). Unlike in the BHNS case in Paschalidis et al. (2015), where the magnetic field grows followingBH formation, the MRI and magnetic winding in the HMNS already amplifies the magnetic field to saturation levelsbefore the onset of collapse to a BH. The incipient jet is then launched by the BH + disk remnant due to the emptyingof the funnel as matter accretes onto the BH, thereby driving the magnetic field regions above the BH poles to nearlyforce-free values ( B / πρ (cid:29) ∼ ◦ , while for the magnetic fieldconfined to the stellar interior it is ∼ ◦ . The Lorentz factor in the outflow is Γ L ∼ .
2. Thus, the incipient jetis only mildly relativistic. However, the force-free parameter inside the funnel is B / πρ ∼
100 (see bottom panelof the second column in Fig. 9), and therefore fluid elements can be accelerated to Γ L ∼
100 (Vlahakis & Konigl2003a). The lifetime of the accretion disk (jet’s fuel) is ∼ M NS / . M (cid:12) ) ms and hence consistent with sGRBlifetimes (Bhat et al. 2016; Lien et al. 2016; Svinkin et al. 2016; Ajello et al. 2019). The outgoing Poynting luminosityis L EM ∼ . − . erg / s, roughly consistent with the luminosity expected from the BZ effect (see Eq. 7) and the3 Figure 8.
NS rest-mass density ρ normalized to its initial maximum value ρ , max = 5 . × (1 . M (cid:12) /M NS ) g/cm (logscale) at selected times for an NSNS merger. Arrows display plasma velocities and white lines show magnetic field lines. Here M = 1 . × − ( M NS / . M (cid:12) ) ms = 4 . M NS / . M (cid:12) ) km [Snapshots from case IH in Ruiz et al. (2016)]. universal merger model (Shapiro 2017b). As this equation is strictly valid for highly force-free magnetospheres, it islikely that any deviation from the expected Poynting luminosity is due to partial baryon-loaded surroundings.To further assess the robustness of the emergence of the incipient jet in NSNS mergers, numerical studies by Ruizet al. (2019, 2020b) probed the impact of the NS spin and the orientation of the seed poloidal magnetic field on theformation and lifetime of the HMNS, BH + disk remnant, and the jet launching time. Ruiz et al. (2019) found thatthe larger the corotating NS spin, the more massive the accretion disk, and hence the longer the jet’s lifetime. Inaddition, the larger the NS spin, the shorter the time delay between the peak GW and the emergence of the incipientjet. On the other hand, the simulations of Ruiz et al. (2020b) suggest that there is a threshold value of the inclinationof magnetic dipole moment with respect to the orbital angular momentum (cid:126)L of the binary beyond which jet launchingis suppressed. A jet is launched whenever a net poloidal magnetic flux with a consistent sign along (cid:126)L is accreted ontothe BH once B / πρ (cid:29) ∼ − G. The NSNS binarieswere evolved with a resolution ∆ x (cid:38)
177 m. These calculations found that after 22 ms following merger, an organizedmagnetic field structure above the BH emerges, though magnetically-driven outflow was not observed (see Fig. 10). Thelack of an incipient jet is likely due to insufficient resolution to properly capture the magnetic instabilities that boostthe magnetic field strength to (cid:38) . G, an essential ingredient for jet launching, and/or to too short evolutions times.Notice that the ram-pressure of the fall-back debris depends strongly on the EOS. More baryon-loaded surroundingsrequire stronger magnetic fields to overcome the ram-pressure, delaying the launch of the jet while the fields amplify.The previous numerical studies involved NSNS mergers leading to the formation of a transient HMNS undergoingdelayed collapse to a BH. The possibility of jet launching from a stable supramassive NS remnant has recently beeninvestigated by Ruiz et al. (2018a), Ciolfi et al. (2019b) and Ciolfi (2020). The calculation of Ruiz et al. (2018a) reporteda long-term ( ∼
200 ms) simulation of a supramassive NS remnant initially threaded by a pulsar-like magnetic field. Itwas found that magnetic winding induces the formation of a tightly-wound-magnetic-field funnel within which somematter begins to flow outward (see first column in Fig. 9). The maximum Lorentz factor in the outflow is Γ L ∼ . B / πρ (cid:28)
1. The Poynting luminosity is ∼ erg / s, and roughlymatches the GR pulsar spindown luminosity (Ruiz et al. 2014). These calculations suggest that a supramassive NSremnant probably cannot be the progenitor of a sGRB. This has been confirmed by the simulations of Ciolfi et al.(2019b) and Ciolfi (2020), which reported the emergence of an outflow with a maximum Lorentz factor of Γ L (cid:46) . (cid:38)
212 ms following the merger of a magnetized, low-mass NSNS. Recently, the calculation of M¨osta et al. (2020)suggested that neutrino effects may help reduce the baryon-load in the region above the poles of the NS, inducing agrowth of the force-free parameter in the funnel. They found a maximum Lorentz factor of Γ L (cid:46) . Figure 9.
NS rest-mass density ρ normalized to its initial maximum value (log scale) for a NSNS binary that forms:a stable, supramassive remnant (left column); a HMNS remnant that undergoes delayed collapse (middle column); and aremnant that undergoes prompt collapse (right column). Top row displays the NSs at the time of magnetic field insertion, whilemiddle row displays the outcome once the remnant has reached quasi-equilibrium. Bottom row shows the force-free parameter B / (8 πρ ) (log scale). White lines represent magnetic field lines, while arrows represent fluid velocity flow vectors. The fieldlines form a tightly wound helical funnel and drive a jet following delayed collapse, but not in the other two cases. Here M = 0 . M tot / . M (cid:12) ) ms = 4 . M tot / . M (cid:12) ) km; therefore quasi-equilibrium for the supramassive case (left column) isachieved at t ∼
200 ms [From Ruiz et al. (2018a)].
Although supramassive NS or prompt collapse remnants may not launch magnetically-driven jets, they may bethe progenitors of fast radio bursts (FRBs) –a new class of radio transients lasting less than a few tens of mil-liseconds (Lorimer et al. 2007; Thornton et al. 2013). Falcke & Rezzolla (2014) have suggested that magnetic fieldreconfigurations during the collapse of a supramassive NS can induce a burst of EM radiation consistent with thatof typical FRBs. Palenzuela et al. (2013) studied EM counterparts from the inspiral and merger of a NSNS binariesusing full GR resistive MHD simulations. They found that the interaction between the stellar magnetospheres extractskinetic energy from the binary and powers radiative Poynting fluxes as large as L EM (cid:39) − ( B/ G ) erg / s in afew milliseconds. Motivated by these results, Paschalidis & Ruiz (2018) performed numerical simulations of promptcollapse NSNS mergers in which the NSs are initially endowed with a pulsar-like magnetic field. Combining their nu-merical results with population studies, they concluded that FRBs may be the most likely EM counterpart of promptcollapse NSNSs, as previously claimed by Totani (2013).3.3. GW170817 and the NS maximum mass
Event GW170817 (Abbott et al. 2017a) marked not only the first direct detection of a NSNS binary undergoingmerger via GWs but also the simultaneous detection of the sGRB GRB 170817A, and kilonova AT 2017gfo, the latterwith its afterglow radiation in the radio, optical/IR, and X-ray bands (von Kienlin et al. 2017; Kozlova et al. 2017).These observations have been used to impose constraints on the physical properties of a NS, and in particular, on themaximum mass of a nonrotating spherical NS, M sphmax .Margalit & Metzger (2017) argued that following the merger of the NSNS progenitor of GW170817, a transient HMNSis formed which collapses to a BH on a timescale of ∼ −
100 ms, producing the observed kilonova ejecta expanding5
Figure 10.
Magnetic field lines at ∼
22 ms (left) and ∼
32 ms (right) following an NSNS merger, along with two isosurfacesof rest-mass density 10 (yellow) and 10 g / cm (cyan), cut off for y < at mildly relativistic velocities. This conclusion combined with the GW observation, led to their tight predictionthat M sphmax (cid:46) . M (cid:12) with 90% confidence. On the other hand, Shibata et al. (2017b) summarized a number of theirrelativistic hydrodynamic simulations favoring a long-lived, massive NS remnant surrounded by a torus to supporttheir inferred requirement of a strong neutrino emitter that has a sufficiently high electron fraction ( Y e (cid:38) .
25) toavoid an enhancement of the ejecta opacity. This argument led then to the results that M sphmax ∼ . − . M (cid:12) . Arecently review of these calculations by Shibata et al. (2019b) using energy and angular momentum conservation lawsagain lead to M sphmax (cid:46) . M (cid:12) . Rezzolla et al. (2018) assumed that the transient GW170817 remnant collapsed to aspinning BH once it had reached a mass close to but below the maximum mass of a supramassive star. This assumptioncombined with their quasi-universal rotating NS model relations led to M sphmax (cid:46) . +0 . − . M (cid:12) . Ruiz et al. (2018a) usedthe existence of the sGRB GRB170817A, combined with their conclusion that only a NSNS merger that forms anHMNS that undergoes delayed collapse to a BH can be the progenitor of an engine that powers an sGRB (see Fig. 9),to impose the bound M sphmax (cid:46) . /β (for low spin priors), where β is s the ratio of the maximum mass of an uniformlyrotating NS (supramassive limit) to the maximum mass of a nonrotating star. Causality arguments allow β to beas high as 1 .
27, while most realistic candidate EOSs predict β (cid:39) .
2, yielding M sphmax in the range ∼ . − . M (cid:12) .If instead one assumes high spin priors in interpreting the data for GW170817 their maximum mass limit becomes ∼ . − . M (cid:12) . Thus the different analyses seem to converge on a value for M sphmax ∼ . − . M (cid:12) . ERGOSTARS: POTENTIAL MULTIMESSENGER ENGINES
In the previous two sections, we summarized GRMHD simulations showing that the key requirement for the emer-gence of a magnetically-driven jet is the existence of a spinning BH remnant surrounded by an appreciable disk. Inaddition, these simulations also suggest that the BZ process is the driving mechanism to power them.The BZ process can be explained using the membrane paradigm (Thorne et al. 1986), in which the BH horizonis treated as a spherical, rotating conductor of finite resistivity. The magnetic field lines threading the BH horizontransfer rotational kinetic energy from a spinning BH to an outgoing Poynting and matter flux. However, Komissarov(2002, 2004, 2005) has argued that the BH horizon is not the “driving force” behind the BZ mechanism, but ratherit is the ergoregion. To disentangle the effects of the BH horizon and the ergoregion, Ruiz et al. (2012) performedforce-free, numerical evolutions of magnetic fields on the fixed matter + metric background of an “ergostar” (a starwith an internal ergoregion but no horizon) modeled by the EOS of incompressible, homogeneous matter with constanttotal mass-energy density. In addition, the same magnetic fields were evolved on the fixed background of a spinningBH. Ruiz et al. (2012) found that once the system reaches quasi-equilibrium, the configuration of the EM fields and6
Figure 11.
Initial and final profiles of a dynamically stable ergostar modeled with the ALF2cc EOS (see Eq. 8). The rest-massdensity ρ is normalized to its initial maximum value. The inner shaded torus indicates the position of the ergoregion. Here P c is the initial rotation period measured at the point where the rest-mass density is maximum [From Tsokaros et al. (2019b)]. Figure 12.
Final profiles of the rest-mass density ρ normalized to the initial maximum density (top), and the force-freeparameter inside the helical magnetic funnel (bottom) for a standard HMNS (left), an ergostar (middle row), and BH + disk(right). White lines depict the magnetic field lines, while the arrows display fluid velocities. P c is the rotation period measureat the point where the rest-mass density is maximum. Here M = 5 . b = B / π . [Fig. 1 from Ruiz et al. (2020c)]. currents on both backgrounds are the same, in agreement with Komissarov (2002, 2004, 2005). These preliminaryresults suggest that the BZ process is a mechanism driven by the ergoregion, and not by the BH horizon.Recently, Tsokaros et al. (2019b, 2020b) constructed the first dynamically stable ergostars using compressible, causalEOSs based on the ALF2 and SLy EOSs, but with their inner core replaced by the maximally stiff EOS in Eq. 8. Thesolutions are highly differentially rotating HMNSs with a corresponding spherical compaction of C = 0 .
3. In principle,such objects may form during NSNS mergers. Their stability was demonstrated by evolving them in full GR for overa hundred dynamical times ( (cid:38)
30 rotational periods) and observing their quasi-stationary behavior (see Fig. 11). Thisstability was in contrast to earlier Γ = 3 polytropic models (Komatsu et al. 1989), which proved radially unstable tocollapse (Tsokaros et al. 2019b).Using the above models, Ruiz et al. (2020c) performed the first fully GRMHD simulations of dynamically stable er-gostars to assess the impact of ergoregions on launching magnetically–driven outflows. In addition, and for comparisonpurposes, the evolution of a standard magnetic HMNS without an ergoregion and a highly spinning BH surrounded bya magnetized accretion disk were also considered. The ergostar and the standard HMNS were initially endowed witha pulsar-like magnetic field generated by the vector potential in Eq. 6, while the accretion disk was endowed with apoloidal magnetic field confined to the interior (see Eq. 5). In all cases, after a few Alfv´en times, the seed magnetic field7is wound into a helical structure from which matter begins to flow outward (see Fig. 12). In the HMNS cases (ergostarand standard star), the maximum Lorentz factor in the outflow is Γ L ∼ .
5, while in the BH + disk case Γ L ∼ . B / πρ (cid:38) L (cid:38)
100 asrequired by sGRB models (Zou & Piran 2010). These simulations suggest that the BZ process only operates when aBH is present, though the Poynting luminosity in all cases is comparable. Further studies are required to confirm thistentative conclusion. ACKNOWLEDGMENTSWe thank T. Baumgarte, C. Gammie, V. Paschalidis, and N. Yunes for useful discussions, and members of theIllinois Relativity group undergraduate research team (K. Nelli, M. N.T Nguyen, and S. Qunell) for assistance withsome of the visualizations. This work was supported by National Science Foundation Grant No. PHY-1662211 andthe National Aeronautics and Space Administration (NASA) Grant No. 80NSSC17K0070 to the University of Illinoisat Urbana-Champaign. This work made use of the Extreme Science and Engineering Discovery Environment, whichis supported by National Science Foundation Grant No. TG-MCA99S008. This research is part of the Blue Waterssustained-petascale computing project, which is supported by the National Science Foundation (Grants No. OCI-0725070 and No. ACI-1238993) and the State of Illinois. Blue Waters is a joint effort of the University of Illinois atUrbana-Champaign and its National Center for Supercomputing Applications. Resources supporting this work werealso provided by the NASA High-End Computing Program through the NASA Advanced Supercomputing Division atAmes Research Center. REFERENCES
Abbott, B., et al. 2016a, Phys. Rev. Lett., 116, 241103,doi: 10.1103/PhysRevLett.116.241103Abbott, B. P., et al. 2013, doi: 10.1007/lrr-2016-1—. 2016b, Phys. Rev. Lett., 116, 061102,doi: 10.1103/PhysRevLett.116.061102—. 2017a, Phys. Rev. Lett., 119, 161101,doi: 10.1103/PhysRevLett.119.161101—. 2017b, Astrophys. J., 848, L12,doi: 10.3847/2041-8213/aa91c9—. 2017c, Astrophys. J., 848, L13,doi: 10.3847/2041-8213/aa920c—. 2017d, Astrophys. J., 850, L39,doi: 10.3847/2041-8213/aa9478—. 2018. https://arxiv.org/abs/1805.11581Abbott, R., et al. 2020a, Astrophys. J., 896, L44,doi: 10.3847/2041-8213/ab960f—. 2020b. https://arxiv.org/abs/2010.14527Aguilera-Miret, R., Vigan`o, D., Carrasco, F., Mi˜nano, B., &Palenzuela, C. 2020, Phys. Rev. D, 102, 103006,doi: 10.1103/PhysRevD.102.103006Ajello, M., et al. 2019, Astrophys. J., 878, 52,doi: 10.3847/1538-4357/ab1d4eAkmal, A., Pandharipande, V., & Ravenhall, D. 1998,Phys. Rev. C, 58, 1804, doi: 10.1103/PhysRevC.58.1804Alcubierre, M. 2008, Introduction to 3 + 1 NumericalRelativity (New York: Oxford Univ. Press) Alford, M., Braby, M., Paris, M., & Reddy, S. 2005,Astrophys. J., 629, 969, doi: 10.1086/430902Aloy, M. A., Janka, H.-T., & Muller, E. 2004, eConf,C041213, 0109, doi: 10.1051/0004-6361:20041865Anderson, M., Hirschmann, E. W., Lehner, L., et al. 2008,Phys. Rev. Lett., 100, 191101,doi: 10.1103/PhysRevLett.100.191101Antoniadis, J., Freire, P. C. C., Wex, N., et al. 2013,Science, 340, 448, doi: 10.1126/science.1233232Baiotti, L., Giacomazzo, B., & Rezzolla, L. 2008, Phys.Rev., D78, 084033, doi: 10.1103/PhysRevD.78.084033Baiotti, L., & Rezzolla, L. 2017, Rept. Prog. Phys., 80,096901, doi: 10.1088/1361-6633/aa67bbBaker, J. G., Centrella, J., Choi, D.-I., Koppitz, M., & vanMeter, J. 2006, Phys. Rev. Lett., 96, 111102,doi: 10.1103/PhysRevLett.96.111102Barausse, E., & Buonanno, A. 2010, Phys. Rev. D, 81,084024, doi: 10.1103/PhysRevD.81.084024Barnes, J., & Kasen, D. 2013, Astrophys. J., 775, 18,doi: 10.1088/0004-637X/775/1/18Baumgarte, T. W., & Shapiro, S. L. 2010, NumericalRelativity: Solving Einstein’s Equations on the Computer(Cambridge University Press)Baumgarte, T. W., Shapiro, S. L., & Shibata, M. 2000,Astrophys. J. Lett., 528, L29, doi: 10.1086/312425 Baumgarte, T. W., Skoge, M. L., & Shapiro, S. L. 2004,Phys. Rev. D, 70, 064040,doi: 10.1103/PhysRevD.70.064040Bauswein, A., Baumgarte, T. W., & Janka, H. T. 2013,Phys. Rev. Lett., 111, 131101,doi: 10.1103/PhysRevLett.111.131101Bauswein, A., Janka, H.-T., & Oechslin, R. 2010, Phys.Rev. D, 82, 084043, doi: 10.1103/PhysRevD.82.084043Bauswein, A., Just, O., Janka, H.-T., & Stergioulas, N.2017, Astrophys. J., 850, L34,doi: 10.3847/2041-8213/aa9994Beckwith, K., Hawley, J. F., & Krolik, J. H. 2008,Astrophys. J., 678, 1180, doi: 10.1086/533492Belczynski, K., Dominik, M., Bulik, T., et al. 2010,Astrophys. J., 715, L138,doi: 10.1088/2041-8205/715/2/L138Belczynski, K., Taam, R. E., Rantsiou, E., & van der Sluys,M. 2008, Astrophys. J., 682, 474, doi: 10.1086/589609Bernuzzi, S., Dietrich, T., Tichy, W., & Br¨ugmann, B.2014, Phys. Rev., D89, 104021,doi: 10.1103/PhysRevD.89.104021Bernuzzi, S., et al. 2020, Mon. Not. Roy. Astron. Soc., 497,1488, doi: 10.1093/mnras/staa1860Bhat, P. N., et al. 2016, Astrophys. J. Suppl., 223, 28,doi: 10.3847/0067-0049/223/2/28Blandford, R. D., & Znajek, R. L. 1977a, Mon. Not. Roy.Astron. Soc., 179, 433, doi: 10.1093/mnras/179.3.433—. 1977b, mnras, 179, 433Breu, C., & Rezzolla, L. 2016, Mon. Not. Roy. Astron. Soc.,459, 646, doi: 10.1093/mnras/stw575Campanelli, M., Lousto, C. O., Marronetti, P., &Zlochower, Y. 2006, Phys. Rev. Lett., 96, 111101,doi: 10.1103/PhysRevLett.96.111101Chaurasia, S. V., Dietrich, T., Ujevic, M., et al. 2020, Phys.Rev. D, 102, 024087, doi: 10.1103/PhysRevD.102.024087Chawla, S., Anderson, M., Besselman, M., et al. 2010,Phys.Rev.Lett., 105, 111101,doi: 10.1103/PhysRevLett.105.111101Christodoulou, D. 1970, Phys. Rev. Lett., 25, 1596,doi: 10.1103/PhysRevLett.25.1596Ciolfi, R. 2020, Mon. Not. Roy. Astron. Soc., 495, L66,doi: 10.1093/mnrasl/slaa062Ciolfi, R., Kastaun, W., Giacomazzo, B., et al. 2017, Phys.Rev., D95, 063016, doi: 10.1103/PhysRevD.95.063016Ciolfi, R., Kastaun, W., Kalinani, J. V., & Giacomazzo, B.2019a, Phys. Rev. D, 100, 023005,doi: 10.1103/PhysRevD.100.023005—. 2019b, Phys. Rev. D, 100, 023005,doi: 10.1103/PhysRevD.100.023005 Cook, G. B., Shapiro, S. L., & Teukolsky, S. A. 1992,Astrophys. J., 398, 203, doi: 10.1086/171849Cook, G. B., Shapiro, S. L., & Teukolsky, S. A. 1994a,Astrophys.J., 424, 823, doi: 10.1086/173934—. 1994b, Astrophys. J., 422, 227Cˆot´e, B., Belczynski, K., Fryer, C. L., et al. 2017,Astrophys. J., 836, 230, doi: 10.3847/1538-4357/aa5c8dCromartie, H. T., et al. 2019, Nature Astron., 4, 72,doi: 10.1038/s41550-019-0880-2Davies, M. B., Benz, W., Piran, T., & Thielemann, F. K.1994, Astrophys. J., 431, 742, doi: 10.1086/174525De, S., Finstad, D., Lattimer, J. M., et al. 2018, ArXive-prints. https://arxiv.org/abs/1804.08583Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts,M. S. E., & Hessels, J. W. T. 2010, Nature, 467, 1081,doi: 10.1038/nature09466Dietrich, T., Bernuzzi, S., Br¨ugmann, B., Ujevic, M., &Tichy, W. 2018, Phys. Rev., D97, 064002,doi: 10.1103/PhysRevD.97.064002Dietrich, T., Bernuzzi, S., Ujevic, M., & Bruegmann, B.2015, arXiv e-prints. https://arxiv.org/abs/1504.01266Dietrich, T., Bernuzzi, S., Ujevic, M., & Tichy, W. 2017,Phys. Rev., D95, 044045,doi: 10.1103/PhysRevD.95.044045Dirirsa, F. F. 2017, PoS, HEASA2016, 004,doi: 10.22323/1.275.0004Douchin, F., & Haensel, P. 2001, Astron. Astrophys., 380,151, doi: 10.1051/0004-6361:20011402Duez, M. D., Foucart, F., Kidder, L. E., et al. 2008, Phys.Rev. D, 78, 104015, doi: 10.1103/PhysRevD.78.104015Duez, M. D., Liu, Y. T., Shapiro, S. L., Shibata, M., &Stephens, B. C. 2006, Physical Review Letters, 96,031101, doi: 10.1103/PhysRevLett.96.031101Duez, M. D., Liu, Y. T., Shapiro, S. L., & Stephens, B. C.2004, Phys. Rev., D69, 104030,doi: 10.1103/PhysRevD.69.104030East, W. E., Paschalidis, V., & Pretorius, F. 2015,Astrophys. J., 807, L3, doi: 10.1088/2041-8205/807/1/L3East, W. E., Paschalidis, V., Pretorius, F., & Shapiro, S. L.2016, Phys. Rev. D, 93, 024011,doi: 10.1103/PhysRevD.93.024011East, W. E., & Pretorius, F. 2012, Astrophys. J. Letters,760, L4, doi: 10.1088/2041-8205/760/1/L4Eichler, D., Livio, M., Piran, T., & Schramm, D. N. 1989,Nature, 340, 126, doi: 10.1038/340126a0Etienne, Z. B., Faber, J. A., Liu, Y. T., et al. 2008, Phys.Rev., D77, 084002, doi: 10.1103/PhysRevD.77.084002Etienne, Z. B., Liu, Y. T., Paschalidis, V., & Shapiro, S. L.2012a, Phys.Rev., D85, 064029,doi: 10.1103/PhysRevD.85.064029 Etienne, Z. B., Liu, Y. T., Shapiro, S. L., & Baumgarte,T. W. 2009, Phys. Rev. D, 79, 044024,doi: 10.1103/PhysRevD.79.044024Etienne, Z. B., Paschalidis, V., & Shapiro, S. L. 2012b,Phys.Rev., D86, 084026,doi: 10.1103/PhysRevD.86.084026Faber, J. A., Baumgarte, T. W., Shapiro, S. L., &Taniguchi, K. 2006a, Astrophys. J. Lett., 641, L93,doi: 10.1086/504111Faber, J. A., Baumgarte, T. W., Shapiro, S. L., Taniguchi,K., & Rasio, F. A. 2006b, Phys. Rev. D, 73, 024012,doi: 10.1103/PhysRevD.73.024012Faber, J. A., Grandclement, P., & Rasio, F. A. 2004, Phys.Rev. D, 69, 124036, doi: 10.1103/PhysRevD.69.124036Falcke, H., & Rezzolla, L. 2014, Astron. Astrophys., 562,A137, doi: 10.1051/0004-6361/201321996Foucart, F. 2012, Phys. Rev., D86, 124007,doi: 10.1103/PhysRevD.86.124007—. 2020, Front. Astron. Space Sci., 7, 46,doi: 10.3389/fspas.2020.00046Foucart, F., Duez, M., Kidder, L., et al. 2015, Phys. Rev.Lett., 115, 171101, doi: 10.1103/PhysRevLett.115.171101Foucart, F., Duez, M. D., Kidder, L. E., et al. 2012, Phys.Rev. D, 85, 044015, doi: 10.1103/PhysRevD.85.044015Foucart, F., Duez, M. D., Kidder, L. E., & Teukolsky, S. A.2011, Phys.Rev., D83, 024005,doi: 10.1103/PhysRevD.83.024005Foucart, F., Kidder, L. E., Pfeiffer, H. P., & Teukolsky,S. A. 2008, Phys. Rev. D, 77, 124051,doi: 10.1103/PhysRevD.77.124051Friedman, J. L., & Ipser, J. R. 1987, Astrophys. J., 314,594, doi: 10.1086/165088Friedman, J. L., Ipser, J. R., & Sorkin, R. D. 1988,Astrophys. J., 325, 722, doi: 10.1086/166043Giacobbo, N., & Mapelli, M. 2018, Mon. Not. Roy. Astron.Soc., 480, 2011, doi: 10.1093/mnras/sty1999Giacomazzo, B., Zrake, J., Duffell, P., MacFadyen, A. I., &Perna, R. 2015, Astrophys. J., 809, 39,doi: 10.1088/0004-637X/809/1/39Gilden, D. L., & Shapiro, S. L. 1984, Astrophys. J., 287,728, doi: 10.1086/162731Glendenning, N. K., & Moszkowski, S. A. 1991, Phys. Rev.Lett., 67, 2414, doi: 10.1103/PhysRevLett.67.2414Grandclement, P. 2006, Phys. Rev. D, 74, 124002,doi: 10.1103/PhysRevD.74.124002Hallinan, G., Corsi, A., Mooley, K. P., et al. 2017, Science,358, 1579, doi: 10.1126/science.aap9855Hayashi, K., Kawaguchi, K., Kiuchi, K., Kyutoku, K., &Shibata, M. 2020. https://arxiv.org/abs/2010.02563 Hempel, M., & Schaffner-Bielich, J. 2010, Nuclear PhysicsA, 837, 210 ,doi: https://doi.org/10.1016/j.nuclphysa.2010.02.010Hessels, J. W. T., Ransom, S. M., Stairs, I. H., et al. 2006,Science, 311, 1901, doi: 10.1126/science.1123430Hotokezaka, K., Kyutoku, K., Okawa, H., Shibata, M., &Kiuchi, K. 2011, Phys. Rev., D83, 124008,doi: 10.1103/PhysRevD.83.124008Just, O., Obergaulinger, M., Janka, H. T., Bauswein, A., &Schwarz, N. 2016, Astrophys. J., 816, L30,doi: 10.3847/2041-8205/816/2/L30Kasen, D., Metzger, B., Barnes, J., Quataert, E., &Ramirez-Ruiz, E. 2017, Nature, 551, 80,doi: 10.1038/nature24453Kasliwal, M., et al. 2017, Science, 358, 1559,doi: 10.1126/science.aap9455Kastaun, W., & Galeazzi, F. 2015, Phys. Rev. D, 91,064027, doi: 10.1103/PhysRevD.91.064027Kawamura, T., Giacomazzo, B., Kastaun, W., et al. 2016,Phys. Rev., D94, 064012,doi: 10.1103/PhysRevD.94.064012Kiuchi, K., Cerd´a-Dur´an, P., Kyutoku, K., Sekiguchi, Y., &Shibata, M. 2015a, Phys. Rev., D92, 124034,doi: 10.1103/PhysRevD.92.124034Kiuchi, K., Kawaguchi, K., Kyutoku, K., et al. 2017, Phys.Rev. D, 96, 084060, doi: 10.1103/PhysRevD.96.084060Kiuchi, K., Sekiguchi, Y., Kyutoku, K., et al. 2015b, Phys.Rev. D, 92, 064034, doi: 10.1103/PhysRevD.92.064034Kiuchi, K., Sekiguchi, Y., Shibata, M., & Taniguchi, K.2009, Phys. Rev. D, 80, 064037,doi: 10.1103/PhysRevD.80.064037Kobayashi, S., Laguna, P., Phinney, E. S., & M´esz´aros, P.2004, Astrophys. J., 615, 855, doi: 10.1086/424684Kocsis, B., & Levin, J. 2012, Phys. Rev. D, 85, 123005,doi: 10.1103/PhysRevD.85.123005Komatsu, H., Eriguchi, Y., & Hachisu, I. 1989, MNRAS,239, 153, doi: 10.1093/mnras/239.1.153Komissarov, S. 2002, in 3rd International SakharovConference on Physics.https://arxiv.org/abs/astro-ph/0211141Komissarov, S. S. 2004, Mon. Not. Roy. Astron. Soc., 350,407, doi: 10.1111/j.1365-2966.2004.07446.xKomissarov, S. S. 2005, mnras, 359, 801,doi: 10.1111/j.1365-2966.2005.08974.xKoranda, S., Stergioulas, N., & Friedman, J. L. 1997,Astrophys. J., 488, 799, doi: 10.1086/304714Kozlova, A., Golenetskii, S., Aptekar, R., et al. 2017, GRBCoordinates Network, Circular Service, No. 21517, Kyutoku, K., Kiuchi, K., Sekiguchi, Y., Shibata, M., &Taniguchi, K. 2018, Phys. Rev. D, 97, 023009,doi: 10.1103/PhysRevD.97.023009Kyutoku, K., Okawa, H., Shibata, M., & Taniguchi, K.2011, Phys. Rev. D, 84, 064018,doi: 10.1103/PhysRevD.84.064018Lasota, J.-P., Haensel, P., & Abramowicz, M. A. 1996,Astrophys. J., 456, 300, doi: 10.1086/176650Lattimer, J. M., & Prakash, M. 2016, Phys. Rept., 621,127, doi: 10.1016/j.physrep.2015.12.005Lattimer, J. M., & Schramm, D. N. 1974, Astrophys. J.Lett., 192, L145, doi: 10.1086/181612Lee, W. H. 2001, Mon. Not. R. Astron. Soc., 328, 583,doi: 10.1046/j.1365-8711.2001.04898.xLee, W. H., Ramirez-Ruiz, E., & van de Ven, G. 2010,Astrophys. J., 720, 953,doi: 10.1088/0004-637X/720/1/953Lehner, L., Liebling, S. L., Palenzuela, C., et al. 2016,Class. Quant. Grav., 33, 184002,doi: 10.1088/0264-9381/33/18/184002Li, L.-X., & Paczynski, B. 1998, Astrophys. J., 507, L59,doi: 10.1086/311680Lien, A., et al. 2016, Astrophys. J., 829, 7,doi: 10.3847/0004-637X/829/1/7Liu, Y. T., Shapiro, S. L., Etienne, Z. B., & Taniguchi, K.2008, Phys. Rev. D, 78, 024012,doi: 10.1103/PhysRevD.78.024012Lorimer, D. R. 2008, Living Reviews in Relativity, 11,doi: 10.12942/lrr-2008-8Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic,D. J., & Crawford, F. 2007, Science, 318, 777,doi: 10.1126/science.1147532Lovelace, G., Duez, M. D., Foucart, F., et al. 2013,Class.Quant.Grav., 30, 135004,doi: 10.1088/0264-9381/30/13/135004Lovelace, G., Owen, R., Pfeiffer, H. P., & Chu, T. 2008,Phys. Rev. D, 78, 084017,doi: 10.1103/PhysRevD.78.084017Lyne, A. G., & Graham-Smith, F. 2012, Pulsar astronomy(Cambridge University Press)Margalit, B., & Metzger, B. D. 2017, Astrophys. J. Letters,850, L19, doi: 10.3847/2041-8213/aa991cMargalit, B., & Metzger, B. D. 2017, Astrophys. J. Lett.,850, L19, doi: 10.3847/2041-8213/aa991cMetzger, B. D. 2017, Living Rev. Rel., 20, 3,doi: 10.1007/s41114-017-0006-zMetzger, B. D., & Fern´andez, R. 2014, Mon. Not. R.Astron. Soc., 441, 3444, doi: 10.1093/mnras/stu802 Metzger, B. D., Mart´ınez-Pinedo, G., Darbha, S., et al.2010, Mon. Not. R. Astron. Soc., 406, 2650,doi: 10.1111/j.1365-2966.2010.16864.xMiller, M., et al. 2019, Astrophys. J. Lett., 887, L24,doi: 10.3847/2041-8213/ab50c5Mooley, K. P., Nakar, E., Hotokezaka, K., et al. 2018,Nature, 554, 207, doi: 10.1038/nature25452Most, E. R., Papenfort, L. J., Weih, L. R., & Rezzolla, L.2020, Mon. Not. R. Astron. Soc., 499, L82,doi: 10.1093/mnrasl/slaa168M¨osta, P., Radice, D., Haas, R., Schnetter, E., & Bernuzzi,S. 2020, Astrophys. J. Lett., 901, L37,doi: 10.3847/2041-8213/abb6efNarayan, R., Paczynski, B., & Piran, T. 1992, Astrophys. J.Letter, 395, L83, doi: 10.1086/186493New, K. C. B., & Tohline, J. E. 1997, Astrophys. J., 490,311, doi: 10.1086/304861Oechslin, R., Janka, H. T., & Marek, A. 2007, A&A, 467,395, doi: 10.1051/0004-6361:20066682Oechslin, R., Rosswog, S., & Thielemann, F. K. 2002, Phys.Rev. D, 65, 103005, doi: 10.1103/PhysRevD.65.103005Oohara, K., & Nakamura, T. 1989, Progress of TheoreticalPhysics, 82, 535, doi: 10.1143/PTP.82.535¨Ozel, F., & Psaltis, D. 2009, Phys. Rev. D, 80, 103003,doi: 10.1103/PhysRevD.80.103003Paczynski, B. 1986, Astrophys. J. Lett, 308, L43,doi: 10.1086/184740Palenzuela, C., Lehner, L., Liebling, S. L., et al. 2013,Phys.Rev., D88, 043011,doi: 10.1103/PhysRevD.88.043011Palenzuela, C., Liebling, S. L., Neilsen, D., et al. 2015,Phys. Rev., D92, 044045,doi: 10.1103/PhysRevD.92.044045Palenzuela, C., Pani, P., Bezares, M., et al. 2017, Phys.Rev., D96, 104058, doi: 10.1103/PhysRevD.96.104058Paschalidis, V. 2017, Class. Quant. Grav., 34, 084002,doi: 10.1088/1361-6382/aa61cePaschalidis, V., East, W. E., Pretorius, F., & Shapiro, S. L.2015, Phys. Rev., D92, 121502,doi: 10.1103/PhysRevD.92.121502Paschalidis, V., Etienne, Z. B., & Shapiro, S. L. 2013,Phys.Rev., D88, 021504,doi: 10.1103/PhysRevD.88.021504Paschalidis, V., Liu, Y. T., Etienne, Z., & Shapiro, S. L.2011, Phys. Rev. D, 84, 104032,doi: 10.1103/PhysRevD.84.104032Paschalidis, V., & Ruiz, M. 2018.https://arxiv.org/abs/1808.04822Paschalidis, V., Ruiz, M., & Shapiro, S. L. 2015, Astrophys.J., 806, L14, doi: 10.1088/2041-8205/806/1/L14 Peters, P. C. 1964, Phys. Rev., 136, B1224,doi: 10.1103/PhysRev.136.B1224Piran, T. 2005, Reviews of Modern Physics, 76, 1143,doi: 10.1103/RevModPhys.76.1143Pons, J., Miralles, J., & Geppert, U. 2009, Astron.Astrophys., 496, 207, doi: 10.1051/0004-6361:200811229Pretorius, F. 2005, Phys. Rev. Lett., 95, 121101,doi: 10.1103/PhysRevLett.95.121101Price, D., & Rosswog, S. 2006, Science, 312, 719,doi: 10.1126/science.1125201Radice, D. 2020, Symmetry, 12, 1249,doi: 10.3390/sym12081249Radice, D., Bernuzzi, S., & Perego, A. 2020,doi: 10.1146/annurev-nucl-013120-114541Radice, D., Galeazzi, F., Lippuner, J., et al. 2016, Mon.Not. Roy. Astron. Soc., 460, 3255,doi: 10.1093/mnras/stw1227Radice, D., Perego, A., Zappa, F., & Bernuzzi, S. 2018,Astrophys. J., 852, L29, doi: 10.3847/2041-8213/aaa402Raithel, C., ¨Ozel, F., & Psaltis, D. 2018, Astrophys. J.Lett., 857, L23, doi: 10.3847/2041-8213/aabcbfRantsiou, E., Kobayashi, S., Laguna, P., & Rasio, F. A.2008, Astrophys. J., 680, 1326, doi: 10.1086/587858Rasio, F. A., & Shapiro, S. L. 1992, Astrophys. J., 401, 226,doi: 10.1086/172055—. 1994, Astrophys. J., 432, 242, doi: 10.1086/174566Read, J. S., Lackey, B. D., Owen, B. J., & Friedman, J. L.2009, Phys. Rev., D79, 124032,doi: 10.1103/PhysRevD.79.124032Rezzolla, L., Baiotti, L., Giacomazzo, B., Link, D., & Font,J. A. 2010, Class. Quant. Grav., 27, 114105,doi: 10.1088/0264-9381/27/11/114105Rezzolla, L., Giacomazzo, B., Baiotti, L., et al. 2011,Astrophys. J. Letters, 732, L6,doi: 10.1088/2041-8205/732/1/L6Rezzolla, L., Most, E. R., & Weih, L. R. 2018, TheAstrophysical Journal, 852, L25,doi: 10.3847/2041-8213/aaa401Riley, T. E., et al. 2019, Astrophys. J. Lett., 887, L21,doi: 10.3847/2041-8213/ab481cRosswog, S. 2005, Astrophys. J., 634, 1202,doi: 10.1086/497062Rosswog, S., Speith, R., & Wynn, G. A. 2004, Mon. Not.R. Astron. Soc., 351, 1121,doi: 10.1111/j.1365-2966.2004.07865.xRuffert, M., & Janka, H. T. 1998, A&A, 338, 535.https://arxiv.org/abs/astro-ph/9804132Ruffert, M., Janka, H. T., & Schaefer, G. 1996, Astrophys.J., 311, 532. https://arxiv.org/abs/astro-ph/9509006 Ruiz, M., Lang, R. N., Paschalidis, V., & Shapiro, S. L.2016, Astrophys. J., 824, L6,doi: 10.3847/2041-8205/824/1/L6Ruiz, M., Palenzuela, C., Galeazzi, F., & Bona, C. 2012,Mon.Not.Roy.Astron.Soc., 423, 1300Ruiz, M., Paschalidis, V., & Shapiro, S. L. 2014, Phys.Rev., D89, 084045, doi: 10.1103/PhysRevD.89.084045Ruiz, M., Paschalidis, V., Tsokaros, A., & Shapiro, S. L.2020a. https://arxiv.org/abs/2011.08863Ruiz, M., & Shapiro, S. L. 2017, Phys. Rev., D96, 084063,doi: 10.1103/PhysRevD.96.084063Ruiz, M., Shapiro, S. L., & Tsokaros, A. 2018a, Phys. Rev.,D97, 021501, doi: 10.1103/PhysRevD.97.021501—. 2018b, Phys. Rev., D98, 123017,doi: 10.1103/PhysRevD.98.123017Ruiz, M., Tsokaros, A., Paschalidis, V., & Shapiro, S. L.2019, Phys. Rev., D99, 084032,doi: 10.1103/PhysRevD.99.084032Ruiz, M., Tsokaros, A., & Shapiro, S. L. 2020b, Phys. Rev.D, 101, 064042, doi: 10.1103/PhysRevD.101.064042Ruiz, M., Tsokaros, A., Shapiro, S. L., Nelli, K. C., &Qunell, S. 2020c, Phys. Rev. D, 102, 104022,doi: 10.1103/PhysRevD.102.104022Samsing, J., MacLeod, M., & Ramirez-Ruiz, E. 2014,Astrophys. J., 784, 71, doi: 10.1088/0004-637X/784/1/71Sekiguchi, Y., Kiuchi, K., Kyutoku, K., & Shibata, M.2011, Phys. Rev. Lett., 107, 051102,doi: 10.1103/PhysRevLett.107.051102—. 2015, Phys. Rev. D, 91, 064059,doi: 10.1103/PhysRevD.91.064059Semena, A. N., Lutovinov, A. A., Mereminskiy, I. A., et al.2019, Mon. Not. Roy. Astron. Soc., 490, 3355,doi: 10.1093/mnras/stz2722Shapiro, S. L. 2017a, Phys. Rev. D, 95, 101303,doi: 10.1103/PhysRevD.95.101303—. 2017b, Phys. Rev., D95, 101303,doi: 10.1103/PhysRevD.95.101303Shibata, M. 2005, Phys. Rev. Lett., 94, 201101,doi: 10.1103/PhysRevLett.94.201101Shibata, M. 2015, 100 Years of General Relativity–Numerical Relativity (Singapure: World ScientificPublishing Company)Shibata, M., Duez, M. D., Liu, Y. T., Shapiro, S. L., &Stephens, B. C. 2006, Phys. Rev. Lett., 96, 031102,doi: 10.1103/PhysRevLett.96.031102Shibata, M., Fujibayashi, S., Hotokezaka, K., et al. 2017a,Phys. Rev. D, 96, 123012,doi: 10.1103/PhysRevD.96.123012—. 2017b, Phys. Rev., D96, 123012,doi: 10.1103/PhysRevD.96.1230122