Equation of state constraints from the threshold binary mass for prompt collapse of neutron star mergers
Andreas Bauswein, Sebastian Blacker, Vimal Vijayan, Nikolaos Stergioulas, Katerina Chatziioannou, James A. Clark, Niels-Uwe F. Bastian, David B. Blaschke, Mateu… 展开作者
Andreas Bauswein, Sebastian Blacker, Vimal Vijayan, Nikolaos Stergioulas, Katerina Chatziioannou, James A. Clark, Niels-Uwe F. Bastian, David B. Blaschke, Mateusz Cierniak, Tobias Fischer
备注：
Accepted for publication in Phys. Rev. Lett.; 14 pages, 5 figures
Using hydrodynamical simulations for a large set of high-density matter equations of state (EoSs) we systematically determine the threshold mass M_thres for prompt black-hole formation in equal-mass and asymmetric neutron star (NS) mergers. We devise the so far most direct, general and accurate method to determine the unknown maximum mass of nonrotating NSs from merger observations revealing M_thres. Considering hybrid EoSs with hadron-quark phase transition, we identify a new, observable signature of quark matter in NS mergers. Furthermore, our findings have direct applications in gravitational wave searches, kilonova interpretations and multi-messenger constraints on NS properties.
Charged-current neutrino opacity within the relativistic Hartree-Fock framework for astrophysical simulations of core-collapse supernovae and binary neutron star mergers
Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学）；University of Wrocław（弗罗茨瓦夫大学）；Silesian University in Opava（奥帕瓦西里西亚大学）
Measuring the collapse time of a binary neutron star merger remnant can inform the physics of extreme matter and improve modelling of short gamma-ray bursts and associated kilonova. The lifetime of the post-merger remnant directly impacts the mechanisms available for the jet launch of short gamma-ray bursts. We develop and test a method to measure the collapse time of post-merger remnants. We show that for a GW170817-like event at $\sim\!40\,$Mpc, a network of Einstein Telescope with Cosmic Explorer is required to detect collapse times of $\sim\!10\,$ms. For a two-detector network at A+ design…
The formation of neutron stars (NSs), both from collapses of massive stars and mergers of compact objects, can be usually indicated by bright transients emitted from explosively-ejected material. In particular, if the newborn NSs can rotate at a millisecond period and have a sufficiently high magnetic field, then the spin-down of the NSs would provide a remarkable amount of energy to the emitting material. As a result, super-luminous supernovae could be produced in the massive stellar collapse cases, while some unusual fast evolving and luminous optical transients could arise from the cases of…
It is known that a binary neutron star merger produces a hypermassive neutron star. The lifetime of this compact remnant depends on the total mass and the equation of state. The collapse of this compact remnant to a black- hole-torus system is expected to give rise to a powerful jet and a short gamma-ray burst. Nevertheless, if the collapse is delayed half a second or so, the surrounding matter would be already accreted and/or expelled and hence no torus will be formed. However, the collapse itself will give rise to a quasi-isotropic magnetized fireball. This magnetic bomb will dissipate much …
We discuss observational strategies to detect prompt bursts associated with gravitational wave events using the Australian Square Kilometre Array Pathfinder (ASKAP). Many theoretical models of binary neutron stars mergers predict that bright, prompt radio emission would accompany the merger. The detection of such prompt emission would greatly improve our knowledge of the physical conditions, environment, and location of the merger. However, searches for prompt emission are complicated by the relatively poor localisation for gravitational wave events, with the 90\% credible region reaching hund…
The threshold mass for prompt collapse in binary neutron star mergers was empirically found to depend on the stellar properties of the maximum-mass non-rotating neutron star model. Here we present a semi-analytic derivation of this empirical relation which suggests that it is rather insensitive to thermal effects, to deviations from axisymmetry and to the exact rotation law in merger remnants. We utilize axisymmetric, cold equilibrium models with differential rotation and determine the threshold mass for collapse from the comparison between an empirical relation that describes the angular mome…
Advanced LIGO detectors at Hanford and Livingston made two confirmed and one marginal detection of binary black holes during their first observing run. The first event, GW150914, was from the merger of two black holes much heavier that those whose masses have been estimated so far, indicating a formation scenario that might differ from "ordinary" stellar evolution. One possibility is that these heavy black holes resulted from a previous merger. When the progenitors of a black hole binary merger result from previous mergers, they should (on average) merge later, be more massive, and have spin m…
Inspiraling and merging binary neutron stars are not only important source of gravitational waves, but also promising candidates for coincident electromagnetic counterparts. These systems are thought to be progenitors of short gamma-ray bursts (sGRBs). We have shown previously that binary neutron star mergers that undergo {\it delayed} collapse to a black hole surrounded by a {\it weighty} magnetized accretion disk can drive magnetically-powered jets. We now perform magnetohydrodynamic simulations in full general relativity of binary neutron stars mergers that undergo {\it prompt} collapse to …
We construct a new equation of state (EOS) for numerical simulations of core-collapse supernovae and neutron-star mergers based on an extended relativistic mean-field model with a small symmetry energy slope $L$, which is compatible with both experimental nuclear data and recent observations of neutron stars. The new EOS table (EOS4) based on the extended TM1 (TM1e) model with $L=40$ MeV is designed in the same tabular form and compared with the commonly used Shen EOS (EOS2) based on the original TM1 model with $L=110.8$ MeV. This is convenient and useful for performing numerical simulations a…
We investigate the properties of the event horizon in the merger between a large black hole and a smaller neutron star. We find that, if the star is compact enough, then, in its rest frame a horizon begins to grow inside the star before it merges with the black hole, in a manner analogous to the growth of the event horizon in stellar collapse. We may say that, ahead of its fall into the larger black hole, the neutron star begins to become a black hole itself. We discuss how the phenomenon, even if not directly observable, can be invariantly characterized. We demonstrate it quantitatively by ex…
Super-Chandrasekhar remnants of double white dwarf mergers could sometimes collapse into a rapidly rotating neutron star (NS), accompanying with a mass ejection of a few times $0.01M_{\odot}$. Bright optical transient emission can be produced by the ejecta due to heating by radioactivities and particularly by energy injection from the NS. Since the merger remnants before collapse resemble a star evolving from the asymptotic giant branch phase to the planetary nebula phase, an intense dusty wind is considered to be driven about several thousand years ago before the collapse and surround the rem…
We study the lifetimes of the remnant produced by the merger of two neutron stars and revisit the determination of the threshold mass to prompt collapse, $M_{\rm th}$. Using a fully general-relativistic numerical approach and a novel method for a rigorous determination of $M_{\rm th}$, we show that a nonlinear universal relation exists between the threshold mass and the maximum compactness. For the temperature-dependent equations of state considered here, our results improve a similar linear relation found recently with methods that are less accurate but yield quantitatively similar results. F…
Inspiraling and merging binary neutron stars (BNSs) are important sources of both gravitational waves and coincident electromagnetic counterparts. If the BNS total mass is larger than a threshold value, a black hole ensues promptly after merger. Through a statistical study in conjunction with recent LIGO/Virgo constraints on the nuclear equation of state, we estimate that up to $\sim 25\%$ of BNS mergers may result in prompt collapse. Moreover, we find that most models of the BNS mass function we study here predict that the majority of prompt-collapse BNS mergers have $q\gtrsim 0.8$. Prompt-co…
Recent observations of short gamma-ray bursts (SGRBs) suggest that binary neutron star (NS) mergers can create highly magnetised, millisecond NSs. Sharp cut-offs in X-ray afterglow plateaus of some SGRBs hint at the gravitational collapse of these remnant NSs to black holes. The collapse of such `supramassive' NSs also describes the blitzar model, a leading candidate for the progenitors of fast radio bursts (FRBs). The observation of an FRB associated with an SGRB would provide compelling evidence for the blitzar model and the binary NS merger scenario of SGRBs, and lead to interesting constra…
We have evolved mergers of equal-mass binary quark stars, the total mass of which is close to the mass shedding limit of uniformly rotating configurations, in fully general relativistic hydrodynamic simulations, aimed at investigating the post-merger outcomes. In particular, we have identified the threshold mass for prompt black hole formation after the merger, by tracing the minimum lapse function as well as the amount of ejected material during the merger simulation. A semi-analytical investigation based on the angular momentum contained in the merger remnant is also performed to verify the …
Recently born magnetars are promising candidates for the engines powering fast radio bursts (FRBs). The focus thus far has been placed on millisecond magnetars born in rare core-collapse explosions, motivated by the star forming dwarf host galaxy of the repeating FRB 121102, which is remarkably similar to the hosts of superluminous supernovae (SLSNe) and long gamma-ray bursts (LGRB). However, long-lived magnetars may also be created in binary neutron star (BNS) mergers, in the small subset of cases with a sufficiently low total mass for the remnant to avoid collapse to a black hole, or in the …
The gravitational-wave GW170817 is associated to the inspiral phase of a binary neutron star coalescence event. The LIGO-Virgo detectors sensitivity at high frequencies was not sufficient to detect the signal corresponding to the merger and post-merger phases. Hence, the question whether the merger outcome was a prompt black hole formation or not must be answered using either the pre-merger gravitational wave signal or electromagnetic counterparts. In this work we present two methods to infer the probability of prompt black hole formation, using the analysis of the inspiral gravitational-wave …
Electromagnetic observations of the first binary Neutron Star (BNS) merger GW170817 has established that relativistic jets can be successfully launched in BNS mergers. Typically, such jets produce emission in two phases: $γ$-ray prompt emission and multi-wavelength afterglow. Due to relativistic de-boosting, the detectability of both these counterparts is dependent on the angle ($θ_v$) between the observer's line of sight and the jet axis. We compare the detectability of prompt and afterglow emission from off-axis jets, assuming standard detector thresholds. We find that for top-hat jets, afte…
We present new numerical relativity results of neutron star mergers with chirp mass $1.188M_\odot$ and mass ratios $q=1.67$ and $q=1.8$ using finite-temperature equations of state (EOS), approximate neutrino transport and a subgrid model for magnetohydrodynamics-induced turbulent viscosity. The EOS are compatible with nuclear and astrophysical constraints and include a new microphysical model derived from ab-initio calculations based on the Brueckner-Hartree-Fock approach. We report for the first time evidence for accretion-induced prompt collapse in high-mass-ratio mergers, in which the tidal…
Most neutron stars (NSs) and black holes (BHs) are believed to be the final remnants in the evolution of massive stars. In this study, we propose a new formation channel for the formation of BHs and peculiar NSs (specifically, magnetars and Thorne-$\dot{\rm Z}$ytkow objects [T$\dot{\rm Z}$Os]), which we refer to as the core merger-induced collapse (CMIC) model. This model involves the merger at the end of a common-envelope phase of an oxygen/neon/magnesium composition white dwarf and the core of a hydrogen-rich or helium-rich non-degenerate star, leading to the creation of peculiar new types o…
We argue that the multiple shells of circumstellar material (CSM) and the supernovae (SN) ejecta interaction with the CSM starting 59 days after the explosion of the Type Ia SN (SN Ia) PTF 11kx, are best described by a violent prompt merger. In this prompt merger scenario the common envelope (CE) phase is terminated by a merger of a WD companion with the hot core of a massive asymptotic giant (AGB) star. In most cases the WD is disrupted and accreted onto the more massive core. However, in the rare cases where the merger takes place when the WD is denser than the core, the core will be disrupt…
If only one family of "neutron stars" exists, their maximum mass must be equal or larger than $2 M_\odot$ and then only in less than about $18\%$ of cases the outcome of the merger of two neutron stars is a direct collapse to a black hole, since the newly formed system can avoid the collapse at least until differential rotation is present. In the so-called two-families scenario, stars made of hadrons are stable only up to about $1.5-1.6 M_\odot$, while the most massive compact stars are entirely made of strange quark matter. We show that in this scenario the outcome of the merger of two neutro…
Using 250 neutron star merger simulations with microphysics, we explore for the first time the role of nuclear incompressibility in the prompt collapse threshold for binaries with different mass ratios. We demonstrate that observations of prompt collapse thresholds, either from binaries with two different mass ratios or with one mass ratio but combined with the knowledge of the maximum neutron star mass or compactness, will constrain the incompressibility at the maximum neutron star density, $K_{\rm max}$, to within tens of percent. This, otherwise inaccessible, measure of $K_{\rm max}$ can po…
Neutron star (NS) mergers provide us with information rich in physics using multi-messenger astrophysical observations. One of the probable remnants of such a merger is a differentially rotating hot hypermassive neutron star. The stability of the merger remnant depends crucially on the underlying Equation of State (EoS) and thus provides a method to probe the nature of dense matter in NSs. In this work, we search for possible signatures of strangeness containing matter in the NS interior on the secular stability of the merger remnant. We also use recently proposed methods to make a rough estim…
A core-collapse supernova occurs when exothermic fusion ceases in the core of a massive star, typically due to exhaustion of nuclear fuel. Theory predicts that fusion could be interrupted earlier, by merging of the star with a compact binary companion. We report a luminous radio transient, VT J121001+495647, found in the Very Large Array Sky Survey. The radio emission is consistent with supernova ejecta colliding with a dense shell of material, potentially ejected by binary interaction in the centuries prior to explosion. We associate the supernova with an archival X-ray transient, which impli…
We examine a triple-star evolution that might lead to core collapse supernovae (CCSNe) in stellar populations that are too old to allow for single or binary evolution to form CCSNe, i.e., where the most massive stars that evolve off the main sequence have masses of ~4-5Mo. In the scenario we examine the most massive star in the triple system, of mass ~4-5Mo, transfers mass to an inner binary system at an orbital separation of ~100-1000Ro. The initial orbital separation of the inner binary is ~10-50Ro. The inner binary accretes most of the mass that the primary star loses and the two stars expa…
We present a systematic study of magnetised neutron star head on collisions. We investigate the resulting magnetic field geometries as the two neutron stars merge. Furthermore, we analyze the luminosity produced in these collisions and monitor the evolution of the magnetic fields from the time of merger until the subsequent production of a black hole. At the time of black hole formation the luminosity peaks and rings-down following the decay of the electromagnetic fields. A comparison is presented for three different cases, one where the initial magnetic field in both neutron stars is aligned,…
We have performed magnetohydrodynamic simulations in general relativity of binary neutron star and binary black hole-neutron star mergers, as well as the magnetorotational collapse of supermassive stars. In many cases the outcome is a spinnng black hole (BH) immersed in a magnetized disk, with a jet emanating from the poles of the BH. While their formation scenarios differ and their BH masses, as well as their disk masses, densities, and magnetic field strengths, vary by orders of magnitude, these features conspire to generate jet Poynting luminosities that all lie in the same, narrow range of…
Pre-merger alert to detect the very-high-energy prompt emission from binary neutron-star mergers: Einstein Telescope and Cherenkov Telescope Array synergy
We present fully general relativistic (GR) simulations of binary white dwarf-neutron star (WDNS) inspiral and merger. The initial binary is in a circular orbit at the Roche critical separation. The goal is to determine the ultimate fate of such systems. We focus on binaries whose total mass exceeds the maximum mass (Mmax) a cold, degenerate EOS can support against gravitational collapse. The time and length scales span many orders of magnitude, making fully general relativistic hydrodynamic (GRHD) simulations computationally prohibitive. For this reason, we model the WD as a "pseudo-white dwar…
We study the statistics and cosmic evolution of massive black hole seeds formed during major mergers of gas-rich late-type galaxies. Generalizing the results of the hydro-simulations from Mayer et al. 2010, we envision a scenario in which a supermassive star can form at the center of galaxies that just experienced a major merger owing to a multi-scale powerful gas inflow, provided that such galaxies live in haloes with masses above 10^{11} Msun, are gas-rich and disc-dominated, and do not already host a massive black hole. We assume that the ultimate collapse of the supermassive star leads to …
We perform three-dimensional hydrodynamic simulations of aspherical core-collapse supernovae focusing on the matter mixing in SN 1987A. The impacts of four progenitor (pre-supernova) models and parameterized aspherical explosions are investigated. The four pre-supernova models include a blue supergiant (BSG) model based on a slow merger scenario developed recently for the progenitor of SN 1987A (Urushibata et al. 2018). The others are a BSG model based on a single star evolution and two red supergiant (RSG) models. Among the investigated explosion (simulation) models, a model with the binary m…
Recent detailed 1D core-collapse simulations have brought new insights on the final fate of massive stars, which are in contrast to commonly used parametric prescriptions. In this work, we explore the implications of these results to the formation of coalescing black-hole (BH) - neutron-star (NS) binaries, such as the candidate event GW190426_152155 reported in GWTC-2. Furthermore, we investigate the effects of natal kicks and the NS's radius on the synthesis of such systems and potential electromagnetic counterparts linked to them. Synthetic models based on detailed core-collapse simulations …
The inspiral and merger of a binary neutron star (NSNS) can lead to the formation of a hypermassive neutron star (HMNS). As the HMNS loses thermal pressure due to neutrino cooling and/or centrifugal support due to gravitational wave (GW) emission, and/or magnetic breaking of differential rotation it will collapse to a black hole. To assess the importance of shock-induced thermal pressure and cooling, we adopt an idealized equation of state and perform NSNS simulations in full GR through late inspiral, merger, and HMNS formation, accounting for cooling. We show that thermal pressure contributes…
We present a seven-minute long $4π$-3D simulation of a shell merger event in a non-rotating $18.88\, M_\odot$ supernova progenitor before the onset of gravitational collapse. The key motivation is to capture the large-scale mixing and asymmetries in the wake of the shell merger before collapse using a self-consistent approach. The $4π$ geometry is crucial as it allows us to follow the growth and evolution of convective modes on the largest possible scales. We find significant differences between the kinematic, thermodynamic and chemical evolution of the 3D and the 1D model. The 3D model shows …
Production of heavy $α$-elements and $^{44}$Ti in Cas A: comparison to abundances from 1D core-collapse supernova models and evidence for Carbon-Oxygen shell mergers
University of California, Berkeley（加州大学伯克利分校）；Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, HUN-REN（孔科利天文台，匈牙利研究与教育网络天文学与地球科学研究中心）；CSFK HUN-REN, MTA Centre of Excellence（匈牙利研究与教育网络孔科利天文学研究所，匈牙利科学院卓越中心）；Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali del Sud（意大利国家核物理研究所 - 南部实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Manitoba（曼尼托巴大学）；Bavarian Geoinstitute (BGI), University of Bayreuth（拜罗伊特大学巴伐利亚地质研究所）
We discuss a scenario of short Gamma-Ray Bursts (GRBs) following a merger of a massive ONeMg white dwarf (WD) with a CO WD, and an ensuing accretion induced collapse (AIC). An initial system with the primary mass $M_1 \sim 6-10 \, M_\odot$ and the secondary mass $M_2 \sim 3-6\, M_\odot$ forms, via two distinct evolutionary channels, a double degenerate CO-ONeMg WD system. For sufficiently large mass ratio $q \equiv M_2/M_1 > q_{crit} \sim 0.25$ the ensuing gravitational wave-driven mass transfer is unstable, whereby the less massive CO WD is disrupted and transfers its mass to the primary ONeM…
Binary neutron star mergers are strong gravitational wave (GW) sources and the leading candidates to interpret short duration gamma-ray bursts (SGRBs). Under the assumptions that SGRBs are produced by double neutron star mergers and that the X-ray plateau followed by a steep decay as observed in SGRB X-ray light curves marks the collapse of a supra-massive neutron star to a black hole (BH), we use the statistical observational properties of {\em Swift} SGRBs and the mass distribution of Galactic double neutron star systems to place constraints on the neutron star equation of state (EoS) and th…
We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at red-shift $z\sim 10$. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within $\sim 5\times 10^5$ yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typ…
Although recent work in numerical relativity has made tremendous strides in quantifying the gravitational wave luminosity of black hole mergers, very little is known about the electromagnetic luminosity that might occur in immediate conjunction with these events. We show that whenever the heat deposited in the gas near a pair of merging black holes is proportional to its total mass, and the surface density of the gas in the immediate vicinity is greater than the (quite small) amount necessary to make it optically thick, the characteristic scale of the luminosity emitted in direct association w…
The first neutron star binary merger detected in gravitational waves, GW170817 and the subsequent detection of its emission across the electromagnetic spectrum showed that these systems are viable progenitors of short $γ$-ray bursts (sGRB). The afterglow signal of GW170817 has been found to be consistent with a structured GRB jet seen off-axis, requiring significant amounts of relativistic material at large angles. This trait can be attributed to the interaction of the relativistic jet with the external wind medium. Here we perform numerical simulations of relativistic jets interacting with re…
During a core-collapse supernova (SN), axionlike particles (ALPs) could be produced through the Primakoff process and subsequently convert into $γ$ rays in the magnetic field of the Milky Way. We do not find evidence for such a $γ$-ray burst in observations of extragalactic SNe with the Fermi Large Area Telescope (LAT). The SN explosion times are estimated from optical light curves and we find a probability of about $\sim$90% that the LAT observed at least one SN at the time of the core collapse. Under the assumption that at least one SN was contained within the LAT field of view, we exclude p…
Multimessenger observations of the binary neutron star merger GW170817 have enabled the discovery of a diverse array of electromagnetic counterparts to compact binary mergers, including an unambiguous kilonova, a short gamma-ray burst, and a late-time radio jet. Beyond these counterparts, compact binary mergers are additionally predicted to be accompanied by prompt low-frequency radio emission. The successful observation of a prompt radio counterpart would be immensely valuable, but is made difficult by the short delay between the gravitational-wave and prompt electromagnetic signals as well a…
Jet-environment interaction after delayed collapse in binary neutron star mergers
Rochester Institute of Technology（罗切斯特理工学院）；INAF, Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Università di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）
We use cosmological, magnetohydrodynamical simulations of Milky Way-mass galaxies from the Auriga project to study their enrichment with rapid neutron capture (r-process) elements. We implement a variety of enrichment models from both binary neutron star mergers and rare core-collapse supernovae. We focus on the abundances of (extremely) metal-poor stars, most of which were formed during the first ~Gyr of the Universe in external galaxies and later accreted onto the main galaxy. We find that the majority of metal-poor stars are r-process enriched in all our enrichment models. Neutron star merg…
A binary neutron star (BNS) merger can lead to various outcomes, from indefinitely stable neutron stars, through supramassive (SMNS) or hypermassive (HMNS) neutron stars supported only temporarily against gravity, to black holes formed promptly after the merger. Up-to-date constraints on the BNS total mass and the neutron star equation of state suggest that a long-lived SMNS may form in $\sim 0.45-0.9$ of BNS mergers. A maximally rotating SMNS needs to lose $\sim 3-6\times 10^{52}$ erg of it's rotational energy before it collapses, on a fraction of the spin-down timescale. A SMNS formation imp…
The recent detection of GW190521 stimulated ideas on how to populate the predicted black hole pair-instability mass gap. One proposed scenario is the dynamical merger of two stars below the pair instability regime forming a star with a small core and an over-sized envelope. We explore this scenario with detailed stellar evolution calculations, starting with ad-hoc initial conditions enforcing no core growth during the merger. We outline the main challenges this scenario has to overcome, in particular the requirement to retain enough of its mass at merger time, in the subsequent evolution, and …
Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating both nucleonic and hyperonic finite-temperature equations of state (EOS) and neutrino cooling for the first time. It is found that even for the hyperonic EOS, a hypermassive neutron star is first formed after the merger for the typical total mass $\approx$ 2.7M\bigodot, and subsequently collapses to a black hole (BH). It is shown that hyperons play a substantial role in the post-merger dynamics, torus formation around the BH, and emission of gravitational waves (GWs). In particul…
Accretion disks around supermassive black holes (SMBH) are promising sites for stellar mass black hole (BH) mergers due to mass segregation and merger acceleration by disk gas torques. Here we show that a GW-kick at BH merger causes ram-pressure stripping of gas within the BH Hill sphere. If $R_{H}\geq H$, the disk height, an off-center UV flare at $a_{\rm BH} \sim 10^{3}r_{g}$ emerges within $t_{\rm UV} \sim \rm{O}(2 {\rm days})(a_{\rm BH}/10^{3}r_{g})(M_{\rm SMBH}/10^{8}M_{\odot})(v_{\rm kick}/10^{2}\rm{km/s})$ post-merger and lasts O$(R_{H}/v_{\rm kick}) \sim \rm{O}(5 t_{\rm UV}$). The flar…
