Post-merger Gravitational Wave 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.

Effects of onset of phase transition on binary neutron star mergers

ABSTRACT Quantum Chromodynamics predicts phase transition from hadronic matter to quark matter at high density, which is highly probable in astrophysical systems like binary neutron star mergers. To explore the critical density where such phase transition can occur, we performed numerical relativity simulations of binary neutron star mergers with various masses (equal and unequal binaries). We aim to understand the effect of the onset of phase transition on the merger dynamics and gravitational wave spectra. We generated a set of equations of states by agnostically changing the onset of phase transition, having the hadronic matter part and quark matter part fixed. This particular arrangement of the equation of states explores the scenario of mergers where mixed phases of matter are achieved before or during the merger. Under these circumstances, if the matter properties with hadronic and quark degrees differ significantly, it is reflected in the stability of the final merger product for the intermediate mass binary. We performed a case study on mixed species merger, where one of the binary companions is hybrid star. If quark matter appears at low densities, we observe significant change in post-merger gravitational wave analysis in terms of higher peak frequencies and post-merger frequencies in power spectral density. We report indications expressed as spikes in phase difference plots at merger time for mixed mergers. We found that the expression of phase transition in post-merger gravitational wave signals is more significant for unequal mass binary than for equal mass binary having the same total baryonic mass.

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.

Morphology-independent characterization method of postmerger gravitational wave emission from binary neutron star coalescences

Gravitational waves (GWs) emitted during the coalescence of binary neutron star (BNS) systems carry information about the equation of state (EoS) describing the extremely dense matter inside neutron stars (NSs). In particular, the EoS determines the fate of the binary after the merger: a prompt collapse to black hole (BH), or the formation of a NS remnant that is either stable or survives up to a few seconds before collapsing to a BH. Determining the evolution of a BNS system will therefore place strong constraints on the EoS. We present a morphology-independent method, developed in the framework of the coherentWaveBurst analysis of signals from ground-based interferometric detectors of GWs. The method characterizes the time-frequency postmerger GW emission from a BNS system, and determines whether, after the merger, it formed a remnant NS or promptly collapsed to a BH. We measure the following quantities to characterize the postmerger emission: ratio of signal energies and match of luminosity profile in different frequency bands, weighted central frequency and bandwidth. From these quantities, based on the study of signals simulated through injections of numerical relativity waveforms, we build a statistics to discriminate between the different scenarios after the merger. Finally, we test our method on a set of signals simulated with new models, to estimate its efficiency as a function of the source distance.

Search for postmerger gravitational waves from binary neutron star mergers using a matched-filtering statistic

In this paper, we present a new method to search for a short, a few tens of millis long, postmerger gravitational-wave (GW) signal following the merger of two neutron stars. Such a signal could follow the event GW170817 observed by Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors. Our method is based on a matched filtering statistic and an approximate template of the postmerger signal in the form of a damped sinusoid. We test and validate our method using postmerger numerical simulations from the CoRe database. We find no evidence of the short postmerger signal in the LIGO data following the GW170817 event and we obtain upper limits. For short postmerger signals investigated, our best upper limit on the root sum square of the GW strain emitted from 1.15 kHz to 4 kHz is at 50% detection efficiency. The distance corresponding to this best upper limit is 4.64 Mpc.

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.

Compact dark objects in neutron star mergers

We estimate the long-lasting gravitational wave (GW) emission of compact dark objects following a binary neutron-star (NS) merger. We consider compact dark objects, which initially reside in the centers of NSs and which may consist of self-interacting dark matter (DM). By approximating the compact dark objects as test particles, we model the merging of NS binaries hosting DM components with three-dimensional relativistic simulations. Our simulation results suggest that the DM components remain gravitationally bound and orbit inside the merger remnant with orbital separations of typically a few km. The subsequent orbital motion of the DM components generates a GW signal with frequencies in the range of a few kHz. When considering a range of different binary masses and high-density equations of state (EOS), we find that the GW frequency of the orbiting DM components scales with the compactness of NSs. Similarly, we find relations between the DM GW frequency and the dominant postmerger GW frequency of the stellar fluid or the tidal deformability, which quantifies EOS effects during the binary inspiral. Hence, a measurement of these quantities can be used to specify the frequency range of the GW emission by DM. Under the assumption that GW back reaction is the only relevant dissipative process, the GW signal may last between seconds and years depending on the mass of the DM component. We estimate the detectibility of the GW signals and find that DM components in NS mergers may only be detectable with existing and projected GW instruments if the dark objects are as massive as about 0.01 to $0.1{M}_{\ensuremath{\bigodot}}$. We emphasize that the GW emission is limited by the lifetime of the remnant. A forming black hole will immediately swallow the DM objects because their orbits are smaller than the innermost stable circular orbit of the black hole.

Hierarchical Bayesian method for constraining the neutron star equation of state with an ensemble of binary neutron star postmerger remnants

Binary neutron star (BNS) post-merger gravitational-wave emission can occur in the aftermath of a BNS merger -- provided the system avoids prompt collapse to a black hole -- as a quasistable hypermassive remnant experiences quadrupolar oscillations and non-axisymmetric deformations. The post-merger gravitational-wave spectrum possesses a characteristic peak frequency that has been shown to be dependent on the binary chirp mass and the neutron star equation of state (EoS), rendering post-merger gravitational waves a powerful tool for constraining neutron star composition. Unfortunately, the BNS post-merger signal is emitted at high ($\gtrsim 1.5$ kHz) frequencies, where ground-based gravitational wave detectors suffer from reduced sensitivity. It is therefore unlikely that post-merger signals will be detected with sufficient signal-to-noise ratio (SNR) until the advent of next-generation detectors. However, by employing empirical relations derived from numerical relativity simulations, we can combine information across an ensemble of BNS mergers, allowing us to obtain EoS constraints with many low-SNR signals. We present a hierarchical Bayesian method for deriving constraints on $R_{1.6}$, the radius of a 1.6$\mathrm{M_{\odot}}$ neutron star, through an ensemble analysis of binary neutron star mergers. We apply this method to simulations of the next two LIGO-Virgo-KAGRA observing runs, O4 and O5, as well as an extended 4-year run at A+ sensitivity, demonstrating the potential of our approach to yield EoS information from the post-merger signal with current-generation detectors. The A+ 4-year scenario is predicted to improve the constraint on $R_{1.6}$ from the currently available multimessenger-based 95\% credible interval (C.I.) uncertainty of $R_{1.6}=12.07^{+0.98}_{-0.77}$ km to $R_{1.6}=11.91^{+0.80}_{-0.56}$ km, a 22% reduction of the 95% C.I. width.

The gravitational afterglow of boson stars

In this work we study the long-lived post-merger gravitational wave signature of a boson-star binary coalescence. We use full numerical relativity to simulate the post-merger and track the gravitational afterglow over an extended period of time. We implement recent innovations for the binary initial data, which significantly reduce spurious initial excitations of the scalar field profiles, as well as a measure for the angular momentum that allows us to track the total momentum of the spatial volume, including the curvature contribution. Crucially, we find the afterglow to last much longer than the spin-down timescale. This prolonged gravitational wave afterglow provides a characteristic signal that may distinguish it from other astrophysical sources.

Gravitational Wave Radiation from Newborn Accreting Magnetars

The observed electromagnetic radiation from some long and short gamma-ray bursts, and neutron stars (NSs), and the theoretical models proposed to interpret these observations together point to a very interesting but confusing problem, namely, whether fall-back accretion could lead to dipole field decay of newborn NSs. In this paper, we investigate the gravitational wave (GW) radiation of newborn magnetars with a fall-back disk formed in both the core-collapse of massive stars and the merger of binary NSs. We make a comparison of the results obtained with and without fall-back accretion-induced dipole-field decay (FADD) involved. Depending on the fall-back parameters, initial parameters of newborn magnetars, and models used to describe FADD, FADD may indeed occur in newborn magnetars. Because of the low dipole fields caused by FADD, the newborn magnetars will be spun up to higher frequencies and have larger masses in comparison with the non-decay cases. Thus the GW radiation of newborn accreting magnetars would be remarkably enhanced. We propose that observation of GW signals from newborn magnetars using future GW detectors may help to reveal whether FADD could occur in newborn accreting magnetars. Our model is also applied to the discussion of the remnant of GW170817. From the post-merger GW searching results of Advanced LIGO and Advanced Virgo we cannot confirm the remnant is a low-dipole-field long-lived NS. Future detection of GWs from GW170817-like events using more sensitive detectors may help to clarify the FADD puzzle.

Finite-temperature effects in dynamical spacetime binary neutron star merger simulations: validation of the parametric approach

ABSTRACT Parametric equations of state (EoSs) provide an important tool for systematically studying EoS effects in neutron star merger simulations. In this work, we perform a numerical validation of the M*-framework for parametrically calculating finite-temperature EoS tables. The framework, introduced by Raithel et al., provides a model for generically extending any cold, β-equilibrium EoS to finite temperatures and arbitrary electron fractions. In this work, we perform numerical evolutions of a binary neutron star merger with the SFHo finite-temperature EoS, as well as with the M*-approximation of this same EoS, where the approximation uses the zero-temperature, β-equilibrium slice of SFHo and replaces the finite-temperature and composition-dependent parts with the M*-model. We find that the approximate version of the EoS is able to accurately recreate the temperature and thermal pressure profiles of the binary neutron star remnant, when compared to the results found using the full version of SFHo. We additionally find that the merger dynamics and gravitational wave signals agree well between both cases, with differences of $\lesssim 1\!-\!2\,{\textrm{per cent}}$ introduced into the post-merger gravitational wave peak frequencies by the approximations of the EoS. We conclude that the M*-framework can be reliably used to probe neutron star merger properties in numerical simulations.

Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers

The postmerger gravitational wave (GW) emission from a binary neutron star merger is expected to provide exciting new constraints on the dense-matter equation of state (EoS). Such constraints rely, by and large, on the existence of quasi-universal relations, which relate the peak frequencies of the postmerger GW spectrum to properties of the neutron star structure in a model-independent way. In this work, we report on violations of existing quasi-universal relations between the peak spectral frequency, f 2, and the stellar radius, for EoS models with backwards-bending slopes in their mass–radius relations (such that the radius increases at high masses). The violations are extreme, with variations in f 2 of up to ∼600 Hz between EoSs that predict the same radius for a 1.4 M ⊙ neutron star but that have significantly different radii at higher masses. Quasi-universality can be restored by adding in a second parameter to the fitting formulae that depends on the slope of the mass–radius curve. We further find strong evidence that quasi-universality is better maintained for the radii of very massive stars (with masses 2 M ⊙). Both statements imply that f 2 is mainly sensitive to the high-density EoS. Combined with observations of the binary neutron star inspiral, these generalized quasi-universal relations can be used to simultaneously infer the characteristic radius and slope of the neutron star mass–radius relation.

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.

Constraints on the Maximum Densities of Neutron Stars from Postmerger Gravitational Waves with Third-Generation Observations.

Using data from 289 numerical relativity simulations of binary neutron star mergers, we identify, for the first time, a robust quasiuniversal relation connecting the postmerger peak gravitational-wave frequency and the value of the density at the center of the maximum mass nonrotating neutron star. This relation offers a new possibility for precision equation-of-state constraints with next-generation ground-based gravitational-wave interferometers. Mock Einstein Telescope observations of fiducial events indicate that Bayesian inferences can constrain the maximum density to ∼15% (90% credibility level) for a single signal at the minimum sensitivity threshold for a detection. If the postmerger signal is included in a full-spectrum (inspiral-merger-postmerger) analysis of such a signal, the pressure-density function can be tightly constrained up to the maximum density, and the maximum neutron star mass can be measured with an accuracy better than 12% (90% credibility level).

Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We treat hadronic matter using a Brueckner-Hartree-Fock quantum many-body approach and modern two-body and three-body nuclear interactions derived within chiral effective field theory. Quark matter is modeled using an extended version of the bag model. We combine these approaches to construct a new finite-temperature composition-dependent equation of state (EOS) with a first-order phase transition between hadrons and deconfined quarks. We perform numerical relativity simulations of BNS mergers with this new EOS and compare results obtained with or without the deconfinment phase transition. We find that deconfined quark production in a neutron star merger results from matter crossing the phase boundary over a wide range of temperatures and densities. The softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasiuniversal relations for the postmerger GW peak frequency. Consequently, the postmerger GW peak frequency alone is not sufficient to conclusively exclude or confirm the presence of a phase transition in a BNS merger. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, $r$-process nucleosynthetic yields and associated electromagnetic counterparts. While there are differences in the electromagnetic counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two, so they are degenerate with other effects. An exception is the nonthermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

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.

Constraining the onset density of the hadron-quark phase transition with gravitational-wave observations

We study the possible occurrence of the hadron-quark phase transition (PT) during the merging of neutron star binaries by hydrodynamical simulations employing a set of temperature-dependent hybrid equations of state (EOSs). Following previous work, we describe an unambiguous and measurable signature of deconfined quark matter in the gravitational-wave (GW) signal of neutron star binary mergers including equal-mass and unequal-mass systems of different total binary mass. The softening of the EOS by the PT at higher densities, i.e., after merging, leads to a characteristic increase of the dominant postmerger GW frequency ${f}_{\mathrm{peak}}$ relative to the tidal deformability $\mathrm{\ensuremath{\Lambda}}$ inferred during the premerger inspiral phase. Hence, measuring such an increase of the postmerger frequency provides evidence for the presence of a strong PT. If the postmerger frequency and the tidal deformability are compatible with results from purely baryonic EOS models yielding very tight relations between ${f}_{\mathrm{peak}}$ and $\mathrm{\ensuremath{\Lambda}}$, a strong PT can be excluded up to a certain density. We find tight correlations of ${f}_{\mathrm{peak}}$ and $\mathrm{\ensuremath{\Lambda}}$ with the maximum density during the early postmerger remnant evolution. These GW observables thus inform about the density regime which is probed by the remnant and its GW emission. Exploiting such relations, we devise a directly applicable, concrete procedure to constrain the onset density of the QCD PT from future GW measurements. We point out two interesting scenarios: if no indications for a PT are inferred from a GW detection, our procedure yields a lower limit on the onset density of the hadron-quark PT. On the contrary, if a merger event reveals evidence for the occurrence of deconfined quark matter, the inferred GW parameters set an upper limit on the PT onset density. Both scenarios would thus have strong implications for high-density matter physics, e.g., determining the range of validity of nuclear physics and constraining the properties for quark deconfinement. These prospects demonstrate the importance of simultaneously measuring pre- and postmerger GW signals to exploit the complementarity of the information encoded in both phases. Hence, our work stresses the value added by dedicated high-frequency GW instruments.

Strong Post-merger Gravitational Radiation of GW170817-like Events

Abstract The post-merger gravitational-wave (GW) radiation of the remnant formed in the binary neutron star (BNS) coalescence has not been directly measured yet. We show in this work that the properties of the BNS involved in GW170817, additionally constrained by PSR J0030+0451, the lower limit on the maximum gravitational mass of nonrotating neutron star (NS), and some nuclear data, are in favor of strong post-merger GW radiation. This conclusion applies to the mergers of Galactic BNS systems as well. Significant post-merger GW radiation is also preferred to improve the consistency between the maximum gravitational mass of the nonrotating NS inferred from GW170817/GRB170817A/AT2017gfo and the latest mass measurements of pulsars. The prominent post-merger gravitational radiation of GW170817-like events are expected to be detectable by advanced LIGO/Virgo detectors in the next decade and then shed valuable light on the properties of the matter in the extremely high density.

Post-merger chirps from binary black holes as probes of the final black-hole horizon

The merger of a binary black hole gives birth to a highly distorted final black hole. The gravitational radiation emitted as this black hole relaxes presents us with the unique opportunity to probe extreme gravity and its connection with the dynamics of the black hole horizon. Using numerical relativity simulations, we demonstrate a connection between a concrete observable feature in the gravitational waves and geometrical features on the dynamical apparent horizon of the final black hole. Specifically, we show how the line-of-sight passage of a “cusp”-like defect on the horizon of the final black hole correlates with “chirp”-like frequency peaks in the post-merger gravitational-waves. These post-merger chirps should be observed and analyzed as the sensitivity of LIGO and Virgo increase and as future generation detectors, such as LISA and the Einstein Telescope, become operational.