Post-merger Gravitational Wave Signal Research Articles

General relativistic moving-mesh hydrodynamic simulations with arepo and applications to neutron star mergers

ABSTRACT We implement general relativistic hydrodynamics in the moving-mesh code arepo. We also couple a solver for the Einstein field equations employing the conformal flatness approximation. The implementation is validated by evolving isolated static neutron stars using a fixed metric or a dynamical space–time. In both tests, the frequencies of the radial oscillation mode match those of independent calculations. We run the first moving-mesh simulation of a neutron star merger. The simulation includes a scheme to adaptively refine or derefine cells and thereby adjusting the local resolution dynamically. The general dynamics are in agreement with independent smoothed particle hydrodynamics and static-mesh simulations of neutron star mergers. Coarsely comparing, we find that dynamical features like the post-merger double-core structure or the quasi-radial oscillation mode persist on longer time scales, possibly reflecting a low numerical diffusivity of our method. Similarly, the post-merger gravitational wave emission shows the same features as observed in simulations with other codes. In particular, the main frequency of the post-merger phase is found to be in good agreement with independent results for the same binary system, while, in comparison, the amplitude of the post-merger gravitational wave signal falls off slower, i.e. the post-merger oscillations are less damped. The successful implementation of general relativistic hydrodynamics in the moving-mesh arepo code, including a dynamical space–time evolution, provides a fundamentally new tool to simulate general relativistic problems in astrophysics.

On the possibility to detect gravitational waves from post-merger supermassive neutron stars with a kilohertz detector

ABSTRACT The detection of a secular post-merger gravitational wave (GW) signal in a binary neutron star (BNS) merger serves as strong evidence for the formation of a long-lived post-merger neutron star (NS), which can help constrain the maximum mass of NSs and differentiate NS equations of state. We specifically focus on the detection of GW emissions from rigidly rotating NSs formed through BNS mergers, using several kilohertz GW detectors that have been designed. We simulate the BNS mergers within the detecting limit of LIGO-Virgo-KARGA O4 and attempt to find out on what fraction the simulated sources may have a detectable secular post-merger GW signal. For kilohertz detectors designed in the same configuration of LIGO A+, we find that the design with peak sensitivity at approximately 2 kHz is most appropriate for such signals. The fraction of sources that have a detectable secular post-merger GW signal would be approximately $0.94{\!-\!}11~{{ \rm per\ cent}}$ when the spin-downs of the post-merger rigidly rotating NSs are dominated by GW radiation, while it would be approximately $0.46{\!-\!}1.6~{{ \rm per\ cent}}$ when the contribution of electromagnetic (EM) radiation to the spin-down processes is non-negligible. We also estimate this fraction based on other well-known proposed kilohertz GW detectors and find that, with advanced design, it can reach approximately $12{\!-\!}45~{{ \rm per\ cent}}$ for the GW-dominated spin-down case and $4.7{\!-\!}16~{{\rm per\ cent}}$ when both the GW and EM radiations are considered.

Thermal Effects in Binary Neutron Star Mergers

We study the impact of finite-temperature effects in numerical-relativity simulations of binary neutron star mergers with microphysical equations of state and neutrino transport in which we vary the effective nucleon masses in a controlled way. We find that, as the specific heat is increased, the merger remnants become colder and more compact due to the reduced thermal pressure support. Using a full Bayesian analysis, we demonstrate that this effect will be measurable in the postmerger gravitational wave signal with next-generation observatories at signal-to-noise ratios of 15.

Flares, Jets, and Quasiperiodic Outbursts from Neutron Star Merger Remnants

Using numerical relativity simulations with a subgrid dynamo prescription to generate strong initial magnetic fields, we investigate the possibility of launching a jet-like outflow from the hypermassive neutron star (HMNS) during the early stages of the merger, prior to the remnant’s collapse to a black hole. We demonstrate that buoyant instabilities in the strongly magnetized HMNS can lead to a periodic emission of powerful electromagnetic flares shortly after the merger. These are followed by a collimated mildly relativistic outflow. Both types of outflows feature quasiperiodic kilohertz substructure. These early-time outflows may power precursors to short-duration gamma-ray bursts (sGRBs) or in some cases the entire sGRB. While the overall temporal power spectrum we find broadly agrees with the one recently reported for quasiperiodic oscillations in the sGRB GRB910711, our simulations suggest that the periodic electromagnetic substructure is dominated by magnetohydrodynamic shearing processes rather than correlating with the corresponding postmerger gravitational-wave signal.

Probing neutron stars with the full premerger and postmerger gravitational wave signal from binary coalescences

The gravitational wave signal emitted during the coalescence of two neutron stars carries information about the stars' internal structure. During the long inspiral phase the main matter observable is the tidal interaction between the binary components, an effect that can be parametrically modeled with compact-binary solutions to general relativity. After the binary merger the main observable is frequency modes of the remnant, most commonly giving rise to a short-duration signal accessible only through numerical simulations. The complicated morphology and the decreasing detector sensitivity in the relevant frequencies currently hinder detection of the postmerger signal and motivate separate analyses for the premerger and postmerger data. However, planned and ongoing detector improvements could soon put the postmerger signal within reach. In this study we target the whole premerger and postmerger signal without an artificial separation at the binary merger. We construct a hybrid analysis that models the inspiral with templates based on analytical calculations and calibrated to numerical relativity and the postmerger signal with a flexible morphology-independent analysis. Applying this analysis to GW170817 we find, as expected, that the postmerger signal remains undetected. We further study simulated signals and find that we can reconstruct the full signal and simultaneously estimate both the premerger tidal deformation and the postmerger signal frequency content. Our analysis allows us to study neutron star physics using all the data available and directly test the premerger and postmerger signal for consistency thus probing effects such as the onset of the hadron-quark phase transition.

Can a binary neutron star merger in the vicinity of a supermassive black hole enable a detection of a post-merger gravitational wave signal?

ABSTRACT The post-merger gravitational-wave (GW) signal of a binary neutron star (BNS) merger is expected to contain valuable information that could shed light on the equation of state (EOS) of NSs, the properties of the matter produced during the merger, as well as the nature of any potential intermediate merger product such as hypermassive or supramassive NSs. However, the post-merger lies in the high frequency regime (≳1000 Hz) where current LIGO-Virgo detectors are insensitive. While proposed detectors such as NEMO, Cosmic Explorer and Einstein Telescope could potentially detect the post-merger for BNSs within $\mathcal {O}(10~\mathrm{Mpc})$, such events are likely to be rare. In this work, we speculate on the possibility of detecting the post-merger from BNSs coalescing in the vicinity of supermassive black holes (SMBHs). The redshift produced by the gravitational field of the SMBH, as well as the BNS’s proper motion around the SMBH, could effectively ‘stretch’ the post-merger signal into the band of the detectors. We demonstrate, using a phenomenological model, that such BNS coalescences would enable constraints on the peak of the post-merger signal that would otherwise have not been possible, provided the degree of redshifting due to the SMBH can be independently acquired. Further, using numerical simulations of binary neutron stars, we show how such mergers would improve EOS model selection using the post-merger signal. We discuss the mechanisms that might deliver such events and the limitations of this work.

Realistic finite-temperature effects in neutron star merger simulations

Binary neutron star mergers provide a unique probe of the dense-matter equation of state (EoS) across a wide range of parameter space, from the zero-temperature EoS during the inspiral to the high-temperature EoS following the merger. In this paper, we implement a new model for calculating parametrized finite-temperature EoS effects into numerical relativity simulations. This "M* model" is based on a two-parameter approximation of the particle effective mass and includes the leading-order effects of degeneracy in the thermal pressure and energy. We test our numerical implementation by performing evolutions of rotating single stars with zero- and non-zero temperature gradients, as well as evolutions of binary neutron star mergers. We find that our new finite-temperature EoS implementation can support stable stars over many dynamical timescales. We also perform a first parameter study to explore the role of the M* parameters in binary neutron star merger simulations. All simulations start from identical initial data with identical cold EoSs, and differ only in the thermal part of the EoS. We find that both the thermal profile of the remnant and the post-merger gravitational wave signal depend on the choice of M* parameters, but that the total merger ejecta depends only weakly on the finite-temperature part of the EoS across a wide range of parameters. Our simulations provide a first step toward understanding how the finite-temperature properties of dense matter may affect future observations of binary neutron star mergers.

Sub-radian-accuracy gravitational waves from coalescing binary neutron stars in numerical relativity. II. Systematic study on the equation of state, binary mass, and mass ratio

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 phase error for a binary system with a tabulated equation of state (EOS) is comparable to that for a piecewise polytropic EOS. Then we validate the SACRA inspiral gravitational waveform template, which will be used to extract tidal deformability from gravitational wave observation, and find that accuracy of \ our waveform modeling is $\lesssim 0.1$ rad in the gravitational-wave phase and $\lesssim 20 \%$ in the gravitational-wave amplitude up to the gravitational-wave frequency $1000$ Hz.\ Finally, we calibrate the proposed universal relations between a post-merger gravitational wave signal and tidal deformability/neutron star radius in the literature and show that th\ ey suffer from systematics and many relations proposed as universal are not very universal. Improved fitting formulae are also proposed.

Binary neutron star mergers: Effects of spin and post-merger dynamics

Spin can have significant effects on the electromagnetic transients accompanying binary neutron star mergers. The measurement of spin can provide important information about binary formation channels. In the absence of a strong neutron star spin prior, the degeneracy of spin with other parameters leads to significant uncertainties in their estimation, in particular limiting the power of gravitational waves to place tight constraints on the nuclear equation of state. Thus detailed studies of highly spinning neutron star mergers are essential to understand all aspects of multimessenger observation of such events. We perform a systematic investigation of the impact of neutron star spin---considering dimensionless spin values up to $a_{\rm NS}=0.33$---on the merger of equal mass, quasicircular binary neutron stars using fully general-relativistic simulations. We find that the peak frequency of the post-merger gravitational wave signal is only weakly influenced by the neutron star spin, with cases where the spin is aligned (antialigned) with the orbital angular momentum giving slightly lower (higher) values compared to the irrotational case. We find that the one-arm instability arises in a number of cases, with some dependence on spin. Spin has a pronounced impact on the mass, velocity, and angular distribution of the dynamical ejecta, and the mass of the disk that remains outside the merger remnant. We discuss the implications of these findings on anticipated electromagnetic signals, and on constraints that have been placed on the equation of state based on multimessenger observations of GW170817.

Echoes from the abyss: a highly spinning black hole remnant for the binary neutron star merger GW170817

The first direct observation of a binary neutron star (BNS) merger was a watershed moment in multi-messenger astronomy. However, gravitational waves from GW170817 have only been observed prior to the BNS merger, but electromagnetic observations all follow the merger event. While post-merger gravitational wave signal in general relativity is too faint (given current detector sensitivities), here we present the first tentative detection of post-merger gravitational wave “echoes” from a highly spinning “black hole” remnant. The echoes may be expected in different models of quantum black holes that replace event horizons by exotic Planck-scale structure and tentative evidence for them has been found in binary black hole merger events. The fact that the echo frequency is suppressed by log M (in Planck units) puts it squarely in the LIGO sensitivity window, allowing us to build an optimal model-agnostic search strategy via cross-correlating the two detectors in frequency/time. We find a tentative detection of echoes at fecho ≃ 72 Hz, around 1.0 sec after the BNS merger, consistent with a 2.6–2.7 M⊙ “black hole” remnant with dimensionless spin 0.84–0.87. Accounting for all the “look-elsewhere” effects, we find a significance of 4.2 σ, or a false alarm probability of 1.6× 10−5, i.e. a similar cross-correlation within the expected frequency/time window after the merger cannot be found more than 4 times in 3 days. If confirmed, this finding will have significant consequences for both physics of quantum black holes and astrophysics of binary neutron star mergers.

Modeling the postmerger gravitational wave signal and extracting binary properties from future binary neutron star detections

Gravitational wave astronomy has established its role in measuring the equation of state governing cold supranuclear matter. To date and in the near future, gravitational wave measurements from neutron star binaries are likely to be restricted to the inspiral. However, future upgrades and the next generation of gravitational wave detectors will enable us to detect the gravitational wave signatures emitted after the merger of two stars, at times when densities beyond those in single neutron stars are reached. Therefore, the postmerger gravitational wave signal enables studies of supranuclear matter at its extreme limit. To support this line of research, we present new and updated phenomenological relations between the binary properties and characteristic features of the postmerger evolution. Most notably, we derive an updated relation connecting the mass-weighted tidal deformability and the maximum neutron star mass to the dominant emission frequency of the postmerger spectrum. With the help of a configuration-independent Bayesian analysis using simplified Lorentzian model functions, we find that the main emission frequency of the postmerger remnant, for signal-to-noise ratios of $8$ and above, can be extracted within a 1-sigma uncertainty of about 100 Hz for Advanced LIGO and Advanced Virgo's design sensitivities. In some cases, even a postmerger signal-to-noise ratio of $4$ can be sufficient to determine the main emission frequency. This will enable us to measure binary and equation-of-state properties from the postmerger, to perform a consistency check between different parts of the binary neutron star coalescence, and to put our physical interpretation of neutron star mergers to the test.

Detecting the Hadron-Quark Phase Transition with Gravitational Waves

The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the post-merger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numerical-relativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadron-quark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted post-merger gravitational wave signal from a future binary compact star merger event.

The Allowed Parameter Space of a Long-lived Neutron Star as the Merger Remnant of GW170817

Abstract Due to the limited sensitivity of the current gravitational wave (GW) detectors, the central remnant of the binary neutron star (NS) merger associated with GW170817 remains an open question. In view of the relatively large total mass, it is generally proposed that the merger of GW170817 would lead to a short-lived hypermassive NS or directly produce a black hole (BH). There is no clear evidence to support or rule out a long-lived NS as the merger remnant. Here, we utilize the GW and electromagnetic (EM) signals to comprehensively investigate the parameter space that allows a long-lived NS to survive as the merger remnant of GW170817. We find that for some stiff equations of state, the merger of GW170817 could, in principle, lead to a massive NS, which has a millisecond spin period. The post-merger GW signal could hardly constrain the ellipticity of the NS. If the ellipticity reaches 10−3, in order to be compatible with the multi-band EM observations, the dipole magnetic field of the NS (B p ) is constrained to the magnetar level of ∼1014 G. If the ellipticity is smaller than 10−4, B p is constrained to the level of ∼109–1011 G. These conclusions weakly depend on the adoption of the NS equation of state.

Not quite a black hole

Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection with quantum gravity. Asymptotically free quadratic gravity is considered here as the UV completion of general relativity. A classical theory that captures its main features is used to search for solutions as sourced by matter. We find that sufficiently dense matter produces a novel horizonless configuration, the 2-2-hole, which closely matches the exterior Schwarzschild solution down to about a Planck proper length of the would-be horizon. The 2-2-hole is characterized by an interior with a shrinking volume and a seemingly innocuous timelike curvature singularity. The interior also has a novel scaling behavior with respect to the physical mass of the 2-2-hole. This leads to an extremely deep gravitational potential in which particles get efficiently trapped via collisions. As a generic static solution, the 2-2-hole may then be the nearly black endpoint of gravitational collapse. There is a considerable time delay for external probes of the 2-2-hole interior, and this determines the spacing of echoes in a post-merger gravitational wave signal.

Exploring properties of high-density matter through remnants of neutron-star mergers

Remnants of neutron-star mergers are essentially massive, hot, differentially rotating neutron stars, which are initially strongly oscillating. They represent a unique probe for high-density matter because the oscillations are detectable via gravitational-wave measurements and are strongly dependent on the equation of state. The impact of the equation of state is apparent in the frequency of the dominant oscillation mode of the remnant. For a fixed total binary mass a tight relation between the dominant postmerger frequency and the radii of nonrotating neutron stars exists. Inferring observationally the dominant postmerger frequency thus determines neutron star radii with high accuracy of the order of a few hundred meters. By considering symmetric and asymmetric binaries of the same chirp mass, we show that the knowledge of the binary mass ratio is not critical for this kind of radius measurements. We summarize different possibilities to deduce the maximum mass of nonrotating neutron stars. We clarify the nature of the three most prominent features of the postmerger gravitational-wave spectrum and argue that the merger remnant can be considered to be a single, isolated, self-gravitating object that can be described by concepts of asteroseismology. The understanding of the different mechanisms shaping the gravitational-wave signal yields a physically motivated analytic model of the gravitational-wave emission, which may form the basis for template-based gravitational-wave data analysis. We explore the observational consequences of a scenario of two families of compact stars including hadronic and quark stars. We find that this scenario leaves a distinctive imprint on the postmerger gravitational-wave signal. In particular, a strong discontinuity in the dominant postmerger frequency as function of the total mass will be a strong indication for two families of compact stars. (abridged)

Low mass binary neutron star mergers: Gravitational waves and neutrino emission

Neutron star mergers are among the most promising sources of gravitational waves for advanced ground-based detectors. These mergers are also expected to power bright electromagnetic signals, in the form of short gamma-ray bursts, infrared/optical transients, and radio emission. Simulations of these mergers with fully general relativistic codes are critical to understand the merger and post-merger gravitational wave signals and their neutrinos and electromagnetic counterparts. In this paper, we employ the SpEC code to simulate the merger of low-mass neutron star binaries (two $1.2M_\odot$ neutron stars) for a set of three nuclear-theory based, finite temperature equations of state. We show that the frequency peaks of the post-merger gravitational wave signal are in good agreement with predictions obtained from simulations using a simpler treatment of gravity. We find, however, that only the fundamental mode of the remnant is excited for long periods of time: emission at the secondary peaks is damped on a millisecond timescale in the simulated binaries. For such low-mass systems, the remnant is a massive neutron star which, depending on the equation of state, is either permanently stable or long-lived. We observe strong excitations of l=2, m=2 modes, both in the massive neutron star and in the form of hot, shocked tidal arms in the surrounding accretion torus. We estimate the neutrino emission of the remnant using a neutrino leakage scheme and, in one case, compare these results with a gray two-moment neutrino transport scheme. We confirm the complex geometry of the neutrino emission, also observed in previous simulations with neutrino leakage, and show explicitly the presence of important differences in the neutrino luminosity, disk composition, and outflow properties between the neutrino leakage and transport schemes.

One-arm spiral instability in hypermassive neutron stars formed by dynamical-capture binary neutron star mergers

Using general-relativistic hydrodynamical simulations, we show that merging binary neutron stars can form hypermassive neutrons stars that undergo the one-arm spiral instability. We study the particular case of a dynamical capture merger where the stars have a small spin, as may arise in globular clusters, and focus on an equal-mass scenario where the spins are aligned with the orbital angular momentum. We find that this instability develops when post-merger fluid vortices lead to the generation of a toroidal remnant - a configuration whose maximum density occurs in a ring around the center-of-mass - with high vorticity along its rotation axis. The instability quickly saturates on a timescale of $\sim 10$ ms, with the $m=1$ azimuthal density multipole mode dominating over higher modes. The instability also leaves a characteristic imprint on the post-merger gravitational wave signal that could be detectable if the instability persists in long-lived remnants.

Neutron-star properties from the postmerger gravitational wave signal of binary neutron stars

We discuss the equation-of-state dependence of the gravitational-wave signal of neutron-star mergers. For a given binary mass the dominant oscillation frequency of the postmerger remnant scales tightly with neutron star radii of a given mass. This relation means that a measurement of the dominant GW frequency, when combined with information from the inspiral phase, implies a simultaneous mass and radius measurement. Moreover, we derive a procedure by which the detection of two merger events with somewhat different binary masses can be employed for an estimate of the maximum mass of nonrotating neutron stars, the radius of the maximum-mass configuration and the maximum central density of neutron stars. Compared to our method recently described in [7] we here employ a slightly modified procedure.

Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers

Neutron star (NS) merger simulations are conducted for 38 representative microphysical descriptions of high-density matter in order to explore the equation-of-state (EoS) dependence of the postmerger ring-down phase. The formation of a deformed, oscillating, differentially rotating very massive NS is the typical outcome of the coalescence of two stars with $1.35{M}_{\ensuremath{\bigodot}}$ for most candidate EoSs. The oscillations of this object imprint a pronounced peak in the gravitational wave (GW) spectra, which is used to characterize the emission for a given model. The peak frequency of this postmerger GW signal correlates very well with the radii of nonrotating NSs, and thus allows us to constrain the high-density EoS by a GW detection. In the case of $1.35\mathrm{\text{\ensuremath{-}}}1.35{M}_{\ensuremath{\bigodot}}$ mergers the peak frequency scales particularly well with the radius of an NS with $1.6{M}_{\ensuremath{\bigodot}}$, where the maximum deviation from this correlation is only 60 m for fully microphysical EoSs which are compatible with NS observations. Combined with the uncertainty in the determination of the peak frequency it appears likely that a GW detection can measure the radius of a $1.6{M}_{\ensuremath{\bigodot}}$ NS with an accuracy of about 100--200 m. We also uncover relations of the peak frequency with the radii of nonrotating NSs with $1.35{M}_{\ensuremath{\bigodot}}$ or $1.8{M}_{\ensuremath{\bigodot}}$, with the radius or the central energy density of the maximum-mass Tolman-Oppenheimer-Volkoff configuration, and with the pressure or sound speed at a fiducial rest mass density of about twice the nuclear saturation density. Furthermore, it is found that a determination of the dominant postmerger GW frequency can provide an upper limit for the maximum mass of nonrotating NSs. The effect of variations of the binary setup are investigated and corresponding functional dependences between the peak frequency and radii of nonrotating NSs are derived. With higher total binary masses, correlations are tighter for radii of nonrotating NSs with higher masses. The prospects for a detection of the postmerger GW signal and a determination of the dominant GW frequency are estimated to be in the range of 0.015--1.2 events per year with the upcoming Advanced Laser Interferometer Gravitational Wave Observatory detector.

Measuring Neutron-Star Properties via Gravitational Waves from Neutron-Star Mergers

We demonstrate by a large set of merger simulations for symmetric binary neutron stars (NSs) that there is a tight correlation between the frequency peak of the postmerger gravitational-wave (GW) emission and the physical properties of the nuclear equation of state (EoS), e.g., expressed by the radius of the maximum-mass Tolman-Oppenheimer-Volkhoff configuration. Therefore, a single measurement of the peak frequency of the postmerger GW signal will constrain the NS EoS significantly. For optimistic merger-rate estimates a corresponding detection with Advanced LIGO is expected to happen within an operation time of roughly a year.