Recent studies suggest that coalescing neutron stars are subject to a fluid instability involving the nonlinear coupling of the tide to $p$-modes and $g$-modes. Its influence on the inspiral dynamics and thus the gravitational wave signal is, however, uncertain because we do not know precisely how the instability saturates. Here we construct a simple, physically motivated model of the saturation that allows us to explore the instability's impact as a function of the model parameters. We find that for plausible assumptions about the saturation, current gravitational wave detectors might miss $> 70\%$ of events if only point particle waveforms are used. Parameters such as the chirp mass, component masses, and luminosity distance might also be significantly biased. On the other hand, we find that relatively simple modifications to the point particle waveform can alleviate these problems and enhance the science that emerges from the detection of binary neutron stars.
We study gravitational waves emitted in the late inspiral stage of binary neutron stars by analyzing the waveform obtained in numerical-relativity simulations. For deriving the physical gravitational waveforms from the numerical results, the resolution extrapolation plays an essential role for our simulations. The extrapolated gravitational-wave phases are compared with those calculated in the post-Newtonian (PN) and effective-one-body (EOB) formalisms including corrections of tidal effects. We show that the extrapolated gravitational-wave phases in numerical relativity agree well with those b…
In some short gamma-ray bursts, precursor flares occurring $\sim$ seconds prior to the main episode have been observed. These flares may then be associated with the last few cycles of the inspiral when the orbital frequency is a few hundred Hz. During these final cycles, tidal forces can resonantly excite quasi-normal modes in the inspiralling stars, leading to a rapid increase in their amplitude. It has been shown that these modes can exert sufficiently strong strains onto the neutron star crust to instigate yieldings. Due to the typical frequencies of $g$-modes being $\sim 100\text{ Hz}$, th…
Dynamically formed compact object binaries may still be eccentric while in the LIGO/Virgo band. For a neutron star (NS) in an eccentric binary, the fundamental modes (f-modes) are excited at pericenter, transferring energy from the orbit to oscillations in the NS. We model this system by coupling the evolution of the NS f-modes to the orbital evolution of the binary as it circularizes and moves toward coalescence. NS f-mode excitation generally speeds up the orbital decay and advances the phase of the gravitational wave signal from the system. We calculate how this effect changes the timing of…
We study the resonant tidal excitation of g modes in coalescing superfluid neutron star (NS) binaries and investigate how such tidal driving impacts the gravitational-wave (GW) signal of the inspiral. Previous studies of this type treated the NS core as a normal fluid and thus did not account for its expected superfluidity. The source of buoyancy that supports the g modes is fundamentally different in the two cases: in a normal fluid core the buoyancy is due to gradients in the proton-to-neutron fraction whereas in a superfluid core it is due to gradients in the muon-to-electron fraction. The …
We perform new longterm (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein's equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than 1 radian. We then compare the extrapolated waveforms with those calculated by the latest effec…
Rossby modes (r-modes) of rotating neutron stars can be excited by the gravitomagnetic forces in coalescing binary systems. The previous study by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)] showed that this kind of dynamical tide (DT) can induce phase shifts of 0.1 rad on gravitational waveforms, which is detectable by third-generation (3G) detectors. In this paper, we study the impact of this DT on measuring neutron-star parameters in the era of 3G detectors. We incorporate two universal relations among neutron star properties predicted by different equations of state: (i) the well-k…
The excitation of $f$-mode in a neutron star member of coalescing binaries accelerates the merger course, and thereby introduces a phase shift in the gravitational waveform. Emphasising on the tidal phase shift by aligned, rotating stars, we provide an accurate, yet economical, method to generate $f$-mode-involved, pre-merger waveforms using realistic spin-modulated $f$-mode frequencies for some viable equations of state. We find for slow-rotating stars that the dephasing effects of the dynamical tides can be uniquely, EOS-independently determined by the direct observables (chirp mass ${\cal M…
As evidenced by the coincident detections of GW170817 and GRB 170817A, short gamma-ray bursts are likely associated with neutron star-neutron star merger events. Although rare, some bursts display episodes of early emission, with precursor flares being observed up to $\sim 10$ seconds prior to the main burst. As the stars inspiral due to gravitational wave emission, the exertion of mutual tidal forces leads to the excitation of stellar oscillation modes, which may come into resonance with the orbital motion. Mode amplitudes increase substantially during a period of resonance as tidal energy is…
The possibility that long tidal tails formed during compact object mergers may power optical transients through the decay of freshly synthesized r-process material is investigated. Precise modeling of the merger dynamics allows for a realistic determination of the thermodynamic conditions in the ejected debris. The results of hydrodynamic and full nuclear network calculations are combined to calculate the resultant r-process abundances and the heating of the material by their decays. The subsequent homologous structure is mapped into a radiative transfer code to synthesize emergent model light…
Recently, an instability due to the nonlinear coupling of p-modes to g-modes in tidally deformed neutron stars in coalescing binaries has been studied in some detail. The result is significant because it could influence the inspiral and leave an imprint on the gravitational wave signal that depends on the neutron star equation of state (EOS). Because of its potential importance, the details of the instability should be further elucidated and its sensitivity to the EOS should be investigated. To this end, we carry out a numerical analysis with six representative EOSs for both static and non-sta…
The study of neutron star mergers by the detection of the emitted gravitational waves is one of the most promised tools to study the properties of dense nuclear matter at high densities. It is worth claiming that, at the moment, strong evidence that the temperature of the stars is zero during the last orbits before coalescing does not exist. Contrariwise, there are some theoretical predictions suggesting that the star's temperature might even be a few MeV. According to the main theory, the tides transfer mechanical energy and angular momentum to the star at the expense of the orbit, where fric…
We recently described an instability due to the nonlinear coupling of p-modes to g-modes and, as an application, we studied the stability of the tide in coalescing binary neutron stars. Although we found that the tide is p-g unstable early in the inspiral and rapidly drives modes to large energies, our analysis only accounted for three-mode interactions. Venumadhav, Zimmerman, and Hirata showed that four-mode interactions must also be accounted for as they enter into the analysis at the same order. They found a near-exact cancellation between three- and four-mode interactions and concluded tha…
Observations of gravitational wave (GW) signals produced by coalescing binary neutron stars (NS), like the GW event GW170817, can be exploited to constrain the equation of state (EoS) of matter in the stars' inner core. The information on the internal structure and composition of the stars is encoded in their tidal Love numbers, which leave an imprint in the waveform of the GW signal emitted from the binary during the late inspiral phase. We extended the theory of tidal deformations of compact objects by computing the spin-tidal corrections that affect the dynamics and the GW emission of a bin…
We analyze the LIGO/Virgo GWTC-2 catalog to study the primary mass distribution of the merging black holes. We perform hierarchical Bayesian analysis, and examine whether the mass distribution has a sharp cutoff for primary black hole masses below $65 M_\odot$, as predicted in pulsational pair instability supernova model. We construct two empirical mass functions. One is a piece-wise function with two power-law segments jointed by a sudden drop. The other consists of a main truncated power-law component, a Gaussian component, and a third very massive component. Both models can reasonably fit t…
Recently exploratory studies were performed on the possibility of constraining the neutron star equation of state (EOS) using signals from coalescing binary neutron stars, or neutron star-black hole systems, as they will be seen in upcoming advanced gravitational wave detectors such as Advanced LIGO and Advanced Virgo. In particular, it was estimated to what extent the combined information from multiple detections would enable one to distinguish between different equations of state through hypothesis ranking or parameter estimation. Under the assumption of zero neutron star spins both in signa…
A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency $ω_a$ excites a pair of secondary waves of frequency $ω_b+ω_c \simeq ω_a$. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that $ω_b+ω_c >>ω_a$. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of interaction is …
Nonradial oscillations of stratified neutron stars with solid crusts: Mode characterization and tidal resonances in coalescing binaries
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Yangzhou University（扬州大学）；Kyoto University（京都大学）
Coalescing neutron star (NS)-black hole (BH) binaries are promising sources of gravitational-waves (GWs) to be detected within the next few years by current GW observatories. If the NS is tidally disrupted outside the BH innermost stable circular orbit, an accretion torus may form, and this could eventually power a short gamma-ray burst (SGRB). The observation of an SGRB in coincidence with gravitational radiation from an NS-BH coalescence would confirm the association between the two phenomena and also give us new insights on NS physics. We present here a new method to measure NS radii and th…
We compute the internal modes of a nonspinning neutron star and its tidal metric perturbation in general relativity, and determine the effect of relativistic corrections to the modes on mode coupling. Claims have been made that a new hydrodynamic instability can occur in a neutron star in a binary neutron star system triggered by the nonlinear coupling of the companion's tidal field to pairs of p-modes and g-modes in it as the binary inspirals toward merger. This "PG" instability may be significant since it can influence the binary's inspiral phase by extracting orbital energy, thereby potenti…
Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\approx 63$--86~meter for the neutron-star radius 10.9--13.7\,km. The estimated total error in the gravitational-wave phase is of order 0.1~rad for the total phase of $\gtrsim 210$\,rad in the last $\sim 15$--16 inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effe…
The gravitational wave signal from a binary neutron star merger carries the imprint of the deformability properties of the coalescing bodies, and then of the equation of state of neutron stars. In current models of the waveforms emitted in these events, the contribution of tidal deformation is encoded in a set of parameters, the tidal Love numbers. More refined models include tidal-rotation couplings, described by an additional set of parameters, the rotational tidal Love numbers, which appear in the waveform at $6.5$ post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, we…
We report results of numerical relativity simulations for {\it new} 26 non-spinning binary neutron star systems with 6 grid resolutions using an adaptive mesh refinement numerical re\ lativity code {\tt SACRA-MPI}. The finest grid spacing is $\approx 64$--$85$ m, depending on the systems. First, we derive long-term high-precision inspiral gravitational waveforms and show that the accumulated gravitational-wave phase error due to the finite grid resolution is less than $0.5$ rad during more than $200$ rad phase evolution irrespective of the systems. We also find that the gravitational-wave phas…
Reassessing the Spin of Second-born Black Holes in Coalescing Binary Black Holes and Its Connection to the chi_eff-q Correlation
Anhui Normal University（安徽师范大学）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；Zhejiang University of Technology（浙江工业大学）；Université de Genève（日内瓦大学）；Guizhou University（贵州大学）
Coalescing neutron-star-black-hole (NS-BH) binaries are a promising source of gravitational-wave (GW) signals detectable with large-scale laser interferometers such as Advanced LIGO and Virgo. They are also one of the main short gamma-ray burst (SGRB) progenitor candidates. If the BH tidally disrupts its companion, an SGRB may be ignited when a sufficiently massive accretion disk forms around the remnant BH. Detecting an NS-BH coalescence both in the GW and electromagnetic (EM) spectrum offers a wealth of information about the nature of the source. How much can actually be inferred from a join…
We report the existence of a gravitational-wave-driven secular instability in neutron star binaries, acting on the equilibrium tide. The instability is similar to the classic Chandrasekhar-Friedman-Schutz (CFS) instability of normal modes and is active when the spin of the primary star exceeds the orbital frequency of the companion. Modeling the neutron star as a Newtonian n=1 polytrope, we calculate the instability time scale, which can be as low as a few seconds at small orbital separations but still larger than the inspiral time scale. The implications for orbital and spin evolution are als…
We demonstrate that the compact, thick disc formed in a tidal disruption event may be unstable to non-axisymmetric perturbations in the form of the Papaloizou-Pringle instability. We show this can lead to rapid redistribution of angular momentum that can be parameterised in terms of an effective Shakura-Sunyaev $α$ parameter. For remnants that have initially weak magnetic fields, this may be responsible for driving mass accretion prior to the onset of the magneto-rotational instability. For tidal disruptions around a $10^6$ M$_{\odot}$ black hole, the measured accretion rate is super-Eddington…
On a disk deformed to a non-axisymmetric form, a set of oscillations can be excited by their resonant interaction through the disk deformation (Kato et al. 2011). This resonant instability process has been proposed to suggest a possible cause of the high-frequency quasi-periodic oscillations (HF QPOs) observed in black-hole low-mass X-ray binaries. In the present paper, we examine whether the above-mentioned wave-wave resonant process can describe the tidal instability and superhump in dwarf novae. The results show that the process seems to well describe the observations. If this process is re…
The data analysis of the gravitational wave signals emitted by coalescing neutron star binaries requires the availability of an accurate analytical representation of the dynamics and waveforms of these systems. We propose an effective-one-body (EOB) model that describes the general relativistic dynamics of neutron star binaries from the early inspiral up to merger. Our EOB model incorporates an enhanced attractive tidal potential motivated by recent analytical advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. No fitting parameters are i…
It has recently been suggested that the tidal deformation of a neutron star excites daughter p- and g-modes to large amplitudes via a quasi-static instability. This would remove energy from the tidal bulge, resulting in dissipation and possibly affecting the phase evolution of inspiralling binary neutron stars and hence the extraction of binary parameters from gravitational wave observations. This instability appears to arise because of a large three-mode interaction among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We show that additional four-mode interactions …
Despite their long history and astrophysical importance, some of the key properties of neutron stars are still uncertain. The extreme conditions encountered in their interiors, involving matter of uncertain composition at extreme density and isospin asymmetry, uniquely determine the stars' macroscopic properties within General Relativity. Astrophysical constraints on those macroscopic properties, such as neutron star masses and radii, have long been used to understand the microscopic properties of the matter that forms them. In this article we discuss another astrophysically observable macrosc…
Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral and hence imprint a signature on their gravitational wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve th…
The possible formation mechanisms of massive close binary black holes (BHs) that can merge in the Hubble time to produce powerful gravitational wave bursts detected during advanced LIGO O1 and O2 science runs include the evolution from field low-metallicity massive binaries, the dynamical formation in dense stellar clusters and primordial BHs. Different formation channels produce different source distributions of total masses ${M_\mathrm{tot}}$ and effective spins $χ_\mathrm{eff}$ of coalescing binary BHs. Using a modified \textsc{bse} code, we carry out extensive population synthesis calculat…
We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders $\ell\leq 5$, for planets with spins that are purely aligne…
The direct detection of gravitational waves with upcoming second-generation gravitational wave detectors such as Advanced LIGO and Virgo will allow us to probe the genuinely strong-field dynamics of general relativity (GR) for the first time. We present a data analysis pipeline called TIGER (Test Infrastructure for GEneral Relativity), which is designed to utilize detections of compact binary coalescences to test GR in this regime. TIGER is a model-independent test of GR itself, in that it is not necessary to compare with any specific alternative theory. It performs Bayesian inference on two h…
In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency (< 500 Hz) oscillation modes in the NS, transferring energy between the orbit and the NS. This resonant tide can induce phase shift in the gravitational waveforms, and potentially provide a new window of studying NS interior using gravitational waves. Previous works have considered tidal excitations of pure g-modes (due to stable stratification of the star) and pure inertial modes (due to Coriolis force), with the rotational effect treated in an approximate manner. However, for realistic NSs, the buoyancy…
We present unpublished data from a tidal disruption candidate in NGC 3599 which show that the galaxy was already X-ray bright 18 months before the measurement which led to its classification. This removes the possibility that the flare was caused by a classical, fast-rising, short-peaked, tidal disruption event. Recent relativistic simulations indicate that the majority of disruptions will actually take months or years to rise to a peak, which will then be maintained for longer than previously thought. NGC 3599 could be one of the first identified examples of such an event. The optical spectra…
We propose a procedure to be used in the search for gravitational waves from black hole-neutron star coalescing binaries, in coincidence with short gamma-ray bursts. It is based on two recently proposed semi-analytic fits, one reproducing the mass of the remnant disk surrounding the black hole which forms after the merging as a function of some binary parameters, the second relating the neutron star compactness, i.e. the ratio of mass and radius, with its tidal deformability. Using a Fisher matrix analysis and the two fits, we assign a probability that the emitted gravitational signal is assoc…
Gravitational waves can be emitted by accretion discs if they undergo instabilities that generate a time varying mass quadrupole. In this work we investigate the gravitational signal generated by a thick accretion disc of $1 M_{\odot}$ around a static super-massive black hole of $10^{6}M_{\odot}$, assumed to be formed after the tidal disruption of a solar type star. This torus has been shown to be unstable to a global non-axisymmetric hydrodynamic instability, the Papaloizou-Pringle instability, in the case where it is not already accreting and has a weak magnetic field. We start by deriving a…
Black-hole neutron-star coalescing binaries have been invoked as one of the most suitable scenario to explain the emission of short gamma-ray bursts. Indeed, if the black-hole which forms after the merger, is surrounded by a massive disk, neutrino annihilation processes may produce high-energy and collimated electromagnetic radiation. In this paper, we devise a new procedure, to be used in the search for gravitational waves from black-hole-neutron-star binaries, to assign a probability that a detected gravitational signal is associated to the formation of an accreting disk, massive enough to p…
Gravitational-wave signals from coalescing binary neutron stars can yield important information about the properties of nuclear-matter equation of state from the early part of the signal through tidal effects to the properties and oscillation frequencies of the merger product. We investigate a direct link between the properties of isolated neutron stars and their merger, by comparing the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars with the gravitational-wave frequency associated with the merger of two neutron stars. We calculate the quadrupolar ($l=2$) $f$-mode os…
I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the nonlinear evolution of the elliptical instability. This is observed to produ…
Time-dependent Accretion Disks in Tidal Disruption Events: Long-term Light Curves
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
Applying an equation of state (EOS) with its symmetric nuclear matter (SNM) contribution and low-density symmetry energy $E_{sym}(ρ)$ constrained by heavy-ion reaction data, we calculate the dimensionless tidal deformability $Λ$ of neutron stars in coalescing binary systems. Corresponding to the partially constrained EOS that previously predicted a radius of 11.5 km $\leq R_{1.4} \leq$ 13.6 km for canonical neutron-star configurations, $Λ$ is found to be in the range of 292 $\leqΛ_{1.4}\leq$ 680, consistent with the very recent observation of the GW170817 event. We investigate the effect of th…
In dense star clusters, such as globular and open clusters, dynamical interactions between stars and black holes (BHs) can be extremely frequent, leading to various astrophysical transients. Close encounters between a star and a stellar mass BH make it possible for the star to be tidally disrupted by the BH. Due to the relative low mass of the BH and the small cross section of the tidal disruption event (TDE) for cases with high penetration, disruptions caused by close encounters are usually partial disruptions. The existence of the remnant stellar core and its non-negligible mass compared to …
The study of binary neutron stars mergers by the detection of the emitted gravitational waves is one of the most promised tools to study the properties of dense nuclear matter at high densities. It is worth claiming that, at the moment, strong evidence that the temperature of the stars is zero during the last orbits before coalescing, does not exist. Nevertheless, theoretical studies suggest that the temperature concerning the inspiral phase, could reach even a few MeV. According to the main theory, tides transfer mechanical energy and angular momentum to the star at the expense of the orbit, …
The capture and disruption of stars by supermassive black holes (SMBHs), and the formation and coalescence of binaries, are inevitable consequences of the presence of SMBHs at the cores of galaxies. Pairs of active galactic nuclei (AGN) and binary SMBHs are important stages in the evolution of galaxy mergers, and an intense search for these systems is currently ongoing. In the early and advanced stages of galaxy merging, observations of the triggering of accretion onto one or both BHs inform us about feedback processes and BH growth. Identification of the compact binary SMBHs at parsec and sub…
Short gamma-ray bursts are thought to result from the mergers of two neutron stars or a neutron star and stellar mass black hole. The final stages of the merger are generally accompanied by the production of one or more tidal "tails" of ejecta, which fall back onto the remnant-disc system at late times. Using the results of a linear stability analysis, we show that if the material comprising these tails is modeled as adiabatic and the effective adiabatic index satisfies $γ\ge 5/3$, then the tails are gravitationally unstable and collapse to form small-scale knots. We analytically estimate the …
The destruction of a star by the tides of a supermassive black hole (SMBH) powers a bright accretion flare, and the theoretical modeling of such tidal disruption events (TDEs) can provide a direct means of inferring SMBH properties from observations. Previously it has been shown that TDEs with $β= r_{\rm t}/r_{\rm p} = 1$, where $r_{\rm t}$ is the tidal disruption radius and $r_{\rm p}$ is the pericenter distance of the star, form an in-plane caustic, or ``pancake,'' where the tidally disrupted debris is compressed into a one-dimensional line within the orbital plane of the star. Here we show …
