Convective Excitation of Inertial Modes in Binary Neutron Star Mergers.

Neutron stars are born when massive stars run out of their nuclear fuel and undergo gravitational collapse. Neutron stars belong to the most compact objects in the observable Universe. Macroscopic properties of neutron stars like their masses and radii are sensitive to the microscopic properties of the nuclear equation of state of dense matter. The equation of state is determined by the strong interaction among the constituents. The underlying theory is quantum chromodynamics that is, however, highly non-perturbative in the physics regime relevant for neutron stars. Moreover, neutron stars provide an interplay between nuclear physics and astrophysics. Astrophysical observations like the detection of 2 solar mass neutron stars have a major impact on the equation of state. Radii are, however, inherently difficult to measure due to systematic uncertainties. Other observables like the moment of inertia or the tidal deformability present promising alternatives. The double neutron star system PSR J0737-3039 constitutes an outstanding system as it provides the prospect of a moment of inertia measurement for the first time. A new era stated with the pioneering observation of gravitational waves from a binary neutron star merger. The analysis of the gravitational wave signal of GW170817 provides a range for the tidal deformability of typical neutron stars. Moreover, the current NICER mission will provide simultaneous mass-radius measurements. In this thesis, we use state-of-the-art chiral effective field theory interactions to describe the equation of state at nuclear densities. In the high-density regime beyond nuclear saturation density, we use different extrapolation approaches. First, we utilize the established ansatz of piecewise polytropic equations of state which provides a direct parametrization. However, piecewise polytropic equations of state possess unphysical behavior such as discontinuities in the speed of sound. Second, we use a physically motivated parametrization of the speed of sound inside the neutron star from which we derive the equation of state. Both methods allow us to probe the equation of state over a large range of densities. We further impose general constraints on the equation of state such as the requirement of causality at all densities and the support of at least 2 solar mass neutron stars. From the equations of state compatible with the constraints, we determine diverse neutron star observables. We begin with non-rotating neutron stars and focus on their masses and radii. We study correlations among properties of the equation of state at nuclear densities and observables of typical neutron stars. Moreover, we explore the impact of hypothetical, simultaneous measurements of masses and radii of neutron stars on the equation of state. Applying both simple compatibility cuts and the framework of Bayesian statistics, we investigate the sensitivity of the inference on the chosen parametrization of the equation of state. We extend then our considerations to slowly rotating neutron stars and study the moment of inertia. Assuming hypothetical moment of inertia measurements, we determine constraints for the radius of neutron stars and thus the equation of state. In addition, we extend our considerations of isolated neutron stars to binary neutron star systems. In particular, we treat the tidal field of the companion as a small perturbation. This allows us to determine the tidal deformability. By applying higher orders in the metric perturbation, we calculate the quadrupole moment of neutron stars. Although the structure of neutron stars is sensitive to the equation of state, relations between the moment of inertia, the tidal deformability, and the quadrupole moment are remarkably insensitive. We investigate the properties of neutron stars in binary systems and ultimately confront the results of our models with the gravitational wave constraints from a binary neutron star merger.

We analyze the properties of the gravitational wave signal emitted after the merger of a binary neutron star system when the remnant survives for more than a 80 ms (and up to 140ms). We employ four different piecewise polytropic equations of state supplemented by an ideal fluid thermal component. We find that the post-merger phase can be subdivided into three phases: an early post-merger phase (where the quadrupole mode and a few subdominant features are active), the intermediate post-merger phase (where only the quadrupole mode is active) and the late post-merger phase (where convective instabilities trigger inertial modes). The inertial modes have frequencies somewhat smaller than the quadrupole modes. In one model, we find an interesting association of a corotation of the quadrupole mode in parts of the star with a revival of its amplitude. The gravitational wave emission of inertial modes in the late post-merger phase is concentrated in a narrow frequency region and is potentially detectable by the planned third-generation detectors. This allows for the possibility of probing not only the cold part of the equation of state, but also its dependence on finite temperature. In view of these results, it will be important to investigate the impact of various type of viscosities on the potential excitation of inertial modes in binary neutron star merger remnants.

We perform general-relativistic hydrodynamical simulations of dynamical capture binary neutron star mergers, emphasizing the role played by the neutron star spin. Dynamical capture mergers may take place in globular clusters, as well as other dense stellar systems, where most neutron stars have large spins. We find significant variability in the merger outcome as a function of initial neutron star spin. For cases where the spin is aligned with the orbital angular momentum, the additional centrifugal support in the remnant hypermassive neutron star can prevent the prompt collapse to a black hole, while for antialigned cases the decreased total angular momentum can facilitate the collapse to a black hole. We show that even moderate spins can significantly increase the amount of ejected material, including the amount unbound with velocities greater than half the speed of light, leading to brighter electromagnetic signatures associated with kilonovae and interaction of the ejecta with the interstellar medium. Furthermore, we find that the initial neutron star spin can strongly affect the already rich phenomenology in the postmerger gravitational wave signatures that arise from the oscillation modes of the hypermassive neutron star. In several of our simulations, the resulting hypermassive neutron star develops the one-arm ($m=1$) spiral instability, the most pronounced cases being those with small but non-negligible neutron star spins. For long-lived hypermassive neutron stars, the presence of this instability leads to improved prospects for detecting these events through gravitational waves, and thus may give information about the neutron star equation of state.

We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.

We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A $\Gamma$-law equation of state $P=(\Gamma-1)\rho\epsilon$ is adopted, where $P$, $\rho$, $\varep$, and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take $\Gamma=2$ and the baryon rest-mass ratio $Q_M$ to be in the range 0.85--1. The typical grid size is $(633,633,317)$ for $(x,y,z)$ . We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest-mass of the system is more than $\sim 1.7$ times of the maximum allowed rest-mass of spherical neutron stars, a black hole is formed after the merger irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range $Q_M= 0.85$--1.

We perform binary neutron star (BNS) merger simulations in full dynamical general relativity with IllinoisGRMHD, on a Cartesian grid with adaptive-mesh refinement. After the remnant black hole has become nearly stationary, the evolution of the surrounding accretion disk on Cartesian grids over long timescales (1s) is suboptimal, as Cartesian coordinates over-resolve the angular coordinates at large distances, and the accreting plasma flows obliquely across coordinate lines dissipating angular momentum artificially from the disk. To address this, we present the Handoff, a set of computational tools that enables the transfer of general relativistic magnetohydrodynamic (GRMHD) and spacetime data from IllinoisGRMHD to HARM3D, a GRMHD code that specializes in modeling black hole accretion disks in static spacetimes over long timescales, making use of general coordinate systems with spherical topology. We demonstrate that the Handoff allows for a smooth and reliable transition of GRMHD fields and spacetime data, enabling us to efficiently and reliably evolve BNS dynamics well beyond merger. We also discuss future plans, which involve incorporating advanced equations of state and neutrino physics into BNS simulations using the \handoff approach.

We study the merger of black hole (BH)-neutron star (NS) binaries with a\nvariety of BH spins aligned or anti-aligned with the orbital angular momentum,\nand with the mass ratio in the range MBH/MNS = 2--5, where MBH and MNS are the\nmass of the BH and NS, respectively. We model NS matter by systematically\nparametrized piecewise polytropic equations of state. The initial condition is\ncomputed in the puncture framework adopting an isolated horizon framework to\nestimate the BH spin and assuming an irrotational velocity field for the fluid\ninside the NS. Dynamical simulations are performed in full general relativity\nby an adaptive mesh refinement code, SACRA. The treatment of hydrodynamic\nequations and estimation of the disk mass are improved. We find that the NS is\ntidally disrupted irrespective of the mass ratio when the BH has a moderately\nlarge prograde spin, whereas only binaries with low mass ratios, MBH/MNS <~ 3\nor small compactnesses of the NSs, bring the tidal disruption when the BH spin\nis zero or retrograde. The mass of the remnant disk is accordingly large as >~\n0.1 Msun, which is required by central engines of short gamma-ray bursts, if\nthe BH spin is prograde. Information of the tidal disruption is reflected in a\nclear relation between the compactness of the NS and an appropriately defined\n"cutoff frequency" in the gravitational-wave spectrum, above which the spectrum\ndamps exponentially. We find that the tidal disruption of the NS and excitation\nof the quasinormal mode of the remnant BH occur in a compatible manner in high\nmass-ratio binaries with the prograde BH spin. The correlation between the\ncompactness and the cutoff frequency still holds for such cases. It is also\nsuggested by extrapolation that the merger of an extremely spinning BH and an\nirrotational NS binary does not lead to formation of an overspinning BH.\n

Gravitational Wave (GW) signals from binary neutron star (BNS) mergers provide critical insights into the properties of matter under extreme conditions. Due to the scarcity of observational data, numerical relativity (NR) simulations are indispensable for exploring these phenomena, without replacing the need for observational confirmation. However, simulating BNS mergers is a formidable challenge, and ensuring the consistency, reliability or convergence, especially in the post-merger, remains a work in progress. In this paper we assess the performance of current BNS merger simulations by analyzing open-source GW waveforms from five leading NR codes – SACRA, BAM, THC, Whisky, and SpEC. We focus on the accuracy of these simulations and on the effect of the equation of state on waveform predictions. We first check if different codes give similar results for similar initial data, then apply two methods to calculate convergence and quantify discretization errors. Lastly, we perform a thorough investigation into the effect of tidal interactions on key frequencies in the GW spectrum. We introduce a novel quasi-universal relation for the transient post-merger time, enhancing our understanding of remnant dynamics in this region. This detailed analysis clarifies agreements and discrepancies between these leading NR codes, and highlights necessary improvements for the advanced accuracy requirements of future GW detectors.

We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large scale supercomputer. We take the typical grid size as (505,505,253) for (x,y,z) and the maximum grid size as (633,633,317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within $\sim 10%$ error) for the first time. To model neutron stars, we adopt a $\Gamma$-law equation of state in the form $P=(\Gamma-1)\rho\epsilon$, where P, $\rho$, $\varep$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain.

We present numerical results of three-dimensional simulations for the merger of binary neutron stars in full general relativity. Hybrid equations of state are adopted to mimic realistic nuclear equations of state. In this approach, we divide the equations of state into two parts as $P={P}_{\mathrm{cold}}+{P}_{\mathrm{th}}$. ${P}_{\mathrm{cold}}$ is the cold part for which we assign a fitting formula for realistic equations of state of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS equations of state for which the maximum allowed Arnowitt-Deser-Misner (ADM) mass of cold and spherical neutron stars is $\ensuremath{\approx}2.04{M}_{\ensuremath{\bigodot}}$ and $1.80{M}_{\ensuremath{\bigodot}}$, respectively. ${P}_{\mathrm{th}}$ denotes the thermal part which is written as ${P}_{\mathrm{th}}=({\ensuremath{\Gamma}}_{\mathrm{th}}\ensuremath{-}1)\ensuremath{\rho}(\ensuremath{\epsilon}\ensuremath{-}{\ensuremath{\epsilon}}_{\mathrm{cold}})$, where $\ensuremath{\rho}$, $\ensuremath{\epsilon}$, ${\ensuremath{\epsilon}}_{\mathrm{cold}}$, and ${\ensuremath{\Gamma}}_{\mathrm{th}}$ are the baryon rest-mass density, total specific internal energy, specific internal energy of the cold part, and the adiabatic constant, respectively. Simulations are performed for binary neutron stars of the total ADM mass in the range between $2.4{M}_{\ensuremath{\bigodot}}$ and $2.8{M}_{\ensuremath{\bigodot}}$ with the rest-mass ratio ${Q}_{M}$ to be in the range $0.9\ensuremath{\lesssim}{Q}_{M}\ensuremath{\le}1$. It is found that if the total ADM mass of the system is larger than a threshold ${M}_{\mathrm{thr}}$, a black hole is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive neutron star of a large ellipticity, which results from the large adiabatic index of the realistic equations of state adopted. The value of ${M}_{\mathrm{thr}}$ depends on the equation of state: ${M}_{\mathrm{thr}}\ensuremath{\sim}2.7{M}_{\ensuremath{\bigodot}}$ and $\ensuremath{\sim}2.5{M}_{\ensuremath{\bigodot}}$ for the SLy and FPS equations of state, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is $\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{ms}$, after which the hypermassive neutron star collapses to a black hole. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than $\ensuremath{\sim}100\text{ }\text{ }\mathrm{Mpc}$. Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

We present general relativistic numerical simulations of binary neutron star (BNS) mergers with different initial spin configurations. We focus on models with stars of mass 1.4 M_sol each, which employ the equation of state (EOS) by Shen, Horowitz, and Teige, and which result in stable NSs as merger remnants. For comparison, we consider two irrotational equal mass (M=1.35 M_sol) and unequal mass (M=1.29,1.42 M_sol) BNS models using the APR4 EOS, which result in a supramassive merger remnant. We present visualizations of the fluid flow and temperature distribution and find a strong impact of the spin on vortex structure and nonaxisymmetric deformation. We compute the radial mass distribution and the rotation profile in the equatorial plane using recently developed measures independent of spatial gauge, revealing slowly rotating cores that can be well approximated by the cores of spherical stars. We also study the influence of the spin on the inspiral phase and the gravitational wave (GW) signal. Using a newly developed analysis method, we further show that gravitational waveforms from BNS mergers can exhibit one or more phase jumps after merger, which occur together with minima of the strain amplitude. We provide a natural explanation in terms of the remnant's quadrupole moment, and show that cancellation effects due to phase jumps can have a strong impact on the GW power spectrum. Finally, we discuss the impact of the spin on the amount of ejected matter.

We present new (3+1) dimensional numerical relativity simulations of the\nbinary neutron star (BNS) mergers that take into account the NS spins. We\nconsider different spin configurations, aligned or antialigned to the orbital\nangular momentum, for equal and unequal mass BNS and for two equations of\nstate. All the simulations employ quasiequilibrium circular initial data in the\nconstant rotational velocity approach, i.e. they are consistent with Einstein\nequations and in hydrodynamical equilibrium. We study the NS rotation effect on\nthe energetics, the gravitational waves (GWs) and on the possible\nelectromagnetic (EM) emission associated to dynamical mass ejecta. For\ndimensionless spin magnitudes of $\\chi\\sim0.1$ we find that spin-orbit\ninteractions and also spin-induced-quadrupole deformations affect the\nlate-inspiral-merger dynamics. The latter is, however, dominated by finite-size\neffects. Spin (tidal) effects contribute to GW phase differences up to 5 (20)\nradians accumulated during the last eight orbits to merger. Similarly, after\nmerger the collapse time of the remnant and the GW spectrogram are affected by\nthe NSs rotation. Spin effects in dynamical ejecta are clearly observed in\nunequal mass systems in which mass ejection originates from the tidal tail of\nthe companion. Consequently kilonovae and other EM counterparts are affected by\nspins. We find that spin aligned to the orbital angular momentum leads to\nbrighter EM counterparts than antialigned spin with luminosities up to a factor\nof two higher.\n

The neutron star binary merger is one of the most energetic phenomena in our Universe. Based on the calculation of gravitational radiation (GR) with the separate consideration of revolution and stellar rotation, and electromagnetic radiation (ER) with unipolar induction DC circuit model and magnetic dipole model, the results are compared to analyse the extent to which the stellar rotation will affect the total gravitational radiation power. Besides, the relationships between radiation power and the related parameters (e.g., orbital radius and stellar mass) are investigated. Furthermore, the feasibility of different types of binary star merger as the progenitor of fast radio bursts and gamma-ray bursts were studied based on the two models of ER, obtaining that binary neutron star and neutron star-white dwarf systems are among the possible progenitors. Finally, the radiation power of both GR and ER are compared under the same conditions. According to the results, the energy dissipation of the system is dominated by gravitational radiation. These results shed lights on further studies on the radiation processes of binary neutron star mergers and binary star systems.

We study the detectability of postmerger QCD phase transitions in neutron star binaries with next-generation gravitational-wave detectors Cosmic Explorer and Einstein Telescope. We perform numerical relativity simulations of neutron star mergers with equations of state that include a quark deconfinement phase transition through either a Gibbs or Maxwell construction. These are followed by Bayesian parameter estimation of the associated gravitational-wave signals using the nrpmw waveform model, with priors inferred from the analysis of the inspiral signal. We assess the ability of the model to measure the postmerger peak frequency $f$$^{peak}_{2}$ and identify aspects that should be improved in the model. We show that, even at postmerger signal to noise ratios as low as 10, the model can distinguish (at the 90% level) $f$$^{peak}_{2}$ between binaries with and without a phase transition in most cases. Phase-transition induced deviations in the $f$$^{peak}_{2}$ from the predictions of equation-of-state insensitive relations can also be detected if they exceed 1.6⁢σ. Our results suggest that next-generation gravitational wave detectors can measure phase transition effects in binary neutron star mergers. Furthermore, unless the phase transition is “strong,” disentangling it from other hadronic physics uncertainties will require significant theory improvements.