Simulations Of Neutron Star Mergers Research Articles

Effects of symmetry energy on the radius and tidal deformability of neutron stars in the relativistic mean-field model

Abstract The radii and tidal deformabilities of neutron stars are investigated in the framework of the relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, $\omega$ meson and $\rho$ meson coupling terms are included in a popular RMF Lagrangian, i.e., the TM1 parameter set, which is adopted for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector–isovector meson, $\rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii in the intermediate-mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number, which is related to the quadrupole deformation of the star in a static external tidal field and can be extracted from the observation of a gravitational wave generated by a binary star merger. We find that its value at $1.4 \mathrm{M}_\odot$ has a linear correlation to the slope of symmetry energy, unlike that previously studied. With the latest constraints of tidal deformabilities from the GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of a lower symmetry energy slope for the updated supernova EoS, which is applicable to simulations of neutron star mergers. Furthermore, an analogous analysis is also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 \mathrm{M}_\odot$ have very similar linear relations in these RMF models.

Magnetohydrodynamic simulations of binary neutron star mergers in general relativity: Effects of magnetic field orientation on jet launching.

Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as Γ = 2 polytropes with spin χ NS = 0.36 aligned along the direction of the total orbital angular momentum L. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment μ is either aligned or perpendicular to L and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where μ in both stars is aligned along L. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black hole + disk remnant, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [Δt ≳ 140(M NS/1.625 M ⊙) ms] and Poynting luminosities [L EM ≃ 1052 erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.

Effects of Symmetry Energy on the Equation of State for Simulations of Core-collapse Supernovae and Neutron-star Mergers

Abstract We construct a new equation of state (EOS) for numerical simulations of core-collapse supernovae and neutron-star mergers based on an extended relativistic mean-field model with a small symmetry energy slope L, which is compatible with both experimental nuclear data and recent observations of neutron stars. The new EOS table (EOS4) based on the extended TM1 (TM1e) model with L = 40 MeV is designed in the same tabular form and compared with the commonly used Shen EOS (EOS2) based on the original TM1 model with . This is convenient and useful for performing numerical simulations and examining the influences of symmetry energy and its density dependence on astrophysical phenomena. In comparison with the TM1 model used in EOS2, the TM1e model provides a similar maximum neutron-star mass but smaller radius and tidal deformability for a 1.4M ⊙ neutron star, which is more consistent with current constraints. By comparing the phase diagram and thermodynamic quantities between EOS4 and EOS2, it is found that the TM1e model predicts a relatively larger region of nonuniform matter and softer EOS for neutron-rich matter. Significant differences between EOS4 and EOS2 are observed in the case with low proton fraction, while the properties of symmetric matter remain unchanged.

Unequal mass binary neutron star simulations with neutrino transport: Ejecta and neutrino emission

We present twelve new simulations of unequal mass neutron star mergers. The simulations were preformed with the SpEC code, and utilize nuclear-theory based equations of state and a two-moment gray neutrino transport scheme with an improved energy estimate based on evolving the number density. We model the neutron stars with the SFHo, LS220 and DD2 equations of state (EOS) and we study the neutrino and matter emission of all twelve models to search for robust trends between binary parameters and emission characteristics. We find that the total mass of the dynamical ejecta exceeds $0.01M_\odot$ only for SFHo with weak dependence on the mass-ratio across all models. We find that the ejecta have a broad electron fraction ($Y_e$) distribution ($\approx 0.06-0.48$), with mean $0.2$. $Y_e$ increases with neutrino irradiation over time, but decreases with increasing binary asymmetry. We also find that the models have ejecta with a broad asymptotic velocity distribution ($\approx 0.05-0.7c$). The average velocity lies in the range $0.2c - 0.3c$ and decreases with binary asymmetry. Furthermore, we find that disk mass increases with binary asymmetry and stiffness of the EOS. The $Y_e$ of the disk increases with softness of the EOS. The strongest neutrino emission occurs for the models with soft EOS. For (anti) electron neutrinos we find no significant dependence of the magnitude or angular distribution or neutrino luminosity with mass-ratio. The heavier neutrino species have a luminosity dependence on mass-ratio but an angular distribution which does not change with mass-ratio.

Ab initio constraints on thermal effects of the nuclear equation of state

We exploit the many-body self-consistent Green's function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysical applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ${\it ab~initio}$ calculations. The inclusion of many-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our study questions the validity of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.

Resistive and Multi-fluid RMHD on Graphics Processing Units

Abstract In this work we present a proof of concept of CUDA-capable, resistive, multi-fluid models of relativistic magnetohydrodynamics (RMHD). Resistive and multi-fluid codes for simulating models of RMHD suffer from stiff source terms, so it is common to implement a set of semi-implicit time integrators to maintain numerical stability. We show, for the first time, that finite volume IMEX schemes for resistive and two-fluid models of RMHD can be accelerated by execution on graphics processing units, significantly reducing the demand set by these kinds of problems. We report parallel speed-ups of over 21× using double-precision floating-point accuracy, and highlight the optimization strategies required for these schemes, and how they differ from ideal RMHD models. The impact of these results is discussed in the context of the next-generation simulations of neutron star mergers.

Dense matter equation of state for neutron star mergers

In simulations of binary neutron star mergers, the dense matter equation of state (EOS) is required over wide ranges of density and temperature as well as under conditions in which neutrinos are trapped, and the effects of magnetic fields and rotation prevail. Here we assess the status of dense matter theory and point out the successes and limitations of approaches currently in use. A comparative study of the excluded volume (EV) and virial approaches for the $np\alpha$ system using the equation of state of Akmal, Pandharipande and Ravenhall for interacting nucleons is presented in the sub-nuclear density regime. Owing to the excluded volume of the $\alpha$-particles, their mass fraction vanishes in the EV approach below the baryon density 0.1 fm$^{-3}$, whereas it continues to rise due to the predominantly attractive interactions in the virial approach. The EV approach of Lattimer et al. is extended here to include clusters of light nuclei such as d, $^3$H and $^3$He in addition to $\alpha$-particles. Results of the relevant state variables from this development are presented and enable comparisons with related but slightly different approaches in the literature. We also comment on some of the sweet and sour aspects of the supra-nuclear EOS. The extent to which the neutron star gravitational and baryon masses vary due to thermal effects, neutrino trapping, magnetic fields and rotation are summarized from earlier studies in which the effects from each of these sources were considered separately. Increases of about $20\% (\gtrsim 50\%)$ occur for rigid (differential) rotation with comparable increases occurring in the presence of magnetic fields only for fields in excess of $10^{18}$ Gauss. Comparatively smaller changes occur due to thermal effects and neutrino trapping. Some future studies to gain further insight into the outcome of dynamical simulations are suggested.

Viscous-dynamical Ejecta from Binary Neutron Star Mergers

Abstract General-relativistic simulations of binary neutron star (NS) mergers with viscosity reveal a new outflow mechanism operating in unequal mass binaries on dynamical timescales and enabled by turbulent viscosity. These “viscous-dynamical” ejecta are launched during the merger due to the thermalization of mass exchange streams between the secondary and the primary NS. They are characterized by asymptotic velocities extending up to ∼0.8c, and have masses that depend on the efficiency of the viscous mechanism. Depending on the unknown strength of the effective viscosity arising from magnetohydrodynamic instabilities operating during the merger, the overall mass of the dynamical ejecta could be enhanced by a factor of a few and the mass of the fast tail of the ejecta, having asymptotic velocities ≥0.6c, by up to four orders of magnitude. The radioactive decay of the expanding viscous-dynamical ejecta could produce bright kilonova transients with signatures of free neutron decay in the first hour, and enhanced near-infrared flux on a timescale of a few days. The synchrotron remnant produced by the interaction between the ejecta and the interstellar medium could also be significantly enhanced by viscosity. Such a remnant could be detected in the case of GW170817 as a rebrightening of the radio signal in the next months to years.

Binary Neutron Star and Short Gamma-Ray Burst Simulations in Light of GW170817

In the dawn of the multi-messenger era of gravitational wave astronomy, which was marked by the first ever coincident detection of gravitational waves and electromagnetic radiation, it is important to take a step back and consider our current established knowledge. Numerical simulations of binary neutron star mergers and simulations of short GRB jets must combine efforts to understand such complicated and phenomenologically rich explosions. We review the status of numerical relativity simulations with respect to any jet or magnetized outflow produced after merger. We compare what is known from such simulations with what is used and obtained from short GRB jet simulations propagating through the BNS ejecta. We then review the established facts on this topic, as well as discuss things that need to be revised and further clarified.

Effects of chiral effective field theory equation of state on binary neutron star mergers

We present fully general relativistic simulations of binary neutron star mergers, employing a new zero- temperature chiral effective field theory equation of state, the BL EOS. We offer a comparison with respect to the older GM3 EOS, which is based on standard relativistic mean field theory, and separately determine the impact of the mass. We provide a detailed analysis of the dynamics, with focus on the post-merger phase. For all models, we extract the gravitational wave strain and the post-merger frequency spectrum. Further, we determine the amount, velocity, and polar distribution of ejected matter, and provide estimates for the resulting kilonova signals. We also study the evolution of the disk while it is interacting with the hypermassive remnant, and dis- cuss the merits of different disk mass definitions applicable before collapse, with regard to the mass remaining after BH formation. Finally, we investigate the radial mass distribution and rotation profile of the remnants, which validate previous results and also corroborate a recently proposed stability criterion.

Convective Excitation of Inertial Modes in Binary Neutron Star Mergers.

We present the first very long-term simulations (extending up to ∼140 ms after merger) of binary neutron star mergers with piecewise polytropic equations of state and in full general relativity. Our simulations reveal that, at a time of 30-50ms after merger, parts of the star become convectively unstable, which triggers the excitation of inertial modes. The excited inertial modes are sustained up to several tens of milliseconds and are potentially observable by the planned third-generation gravitational-wave detectors at frequencies of a few kilohertz. Since inertial modes depend on the rotation rate of the star and they are triggered by a convective instability in the postmerger remnant, their detection in gravitational waves will provide a unique opportunity to probe the rotational and thermal state of the merger remnant. In addition, our findings have implications for the long-term evolution and stability of binary neutron star remnants.

On the importance of resistivity and Hall effect in MHD simulations of binary neutron star mergers

We examine the range of rest-mass densities, temperatures and magnetic fields involved in simulations of binary neutron star mergers (BNSM) and identify the conditions under which the ideal magneto-hydrodynamics (MHD) breaks down using recently computed conductivities of warm, magnetized plasma created in such systems. While previous dissipative MHD studies of BNSM assumed that dissipation sets in due to low conduction at low rest-mass densities, we show that this paradigm must be shifted: the ideal MHD is applicable up to the regime where the hydrodynamic description of matter breaks down. We also find that the Hall effect can be important at low densities and low temperatures, where it can induce a non-dissipative rearrangement of the magnetic field. Finally, we mark the region in temperature-density plane where the hydrodynamic description breaks down.

Hyperons in hot dense matter: what do the constraints tell us for equation of state?

AbstractFor core-collapse and neutron star merger simulations, it is important to have adequate equations of state which describe dense and hot matter as realistically as possible. We present two newly constructed equations of state including the entire baryon octet, compatible with the main constraints coming from nuclear physics, both experimental and theoretical. One of the equations of state describes cold β-equilibrated neutron stars with a maximum mass of 2 Msun. Results obtained with the new equations of state are compared with the ones of DD2Y, the only existing equation of state containing the baryon octet and satisfying the above constraints. The main difference between our new equations of state and DD2Y is the harder symmetry energy of the latter. We show that the density dependence of the symmetry energy has a direct influence on the amount of strangeness inside hot and dense matter and, consequently, on thermodynamic quantities. We expect that these differences affect the evolution of a proto-neutron star or binary neutron star mergers. We propose also several parameterisations based on the DD2 and SFHo models calibrated to Lambda hypernuclei that satisfy the different constraints.

Python Open source Waveform ExtractoR (POWER): an open source, Python package to monitor and post-process numerical relativity simulations

Numerical simulations of Einstein’s field equations provide unique insights into the physics of compact objects moving at relativistic speeds, and which are driven by strong gravitational interactions. Numerical relativity has played a key role to firmly establish gravitational wave astrophysics as a new field of research, and it is now paving the way to establish whether gravitational wave radiation emitted from compact binary mergers is accompanied by electromagnetic and astro-particle counterparts. As numerical relativity continues to blend in with routine gravitational wave data analyses to validate the discovery of gravitational wave events, it is essential to develop open source tools to streamline these studies. Motivated by our own experience as users and developers of the open source, community software, the Einstein Toolkit, we present an open source, Python package that is ideally suited to monitor and post-process the data products of numerical relativity simulations, and compute the gravitational wave strain at future null infinity in high performance environments. We showcase the application of this new package to post-process a large numerical relativity catalog and extract higher-order waveform modes from numerical relativity simulations of eccentric binary black hole mergers and neutron star mergers. This new software fills a critical void in the arsenal of tools provided by the Einstein Toolkit consortium to the numerical relativity community.

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of core-collapse supernovae and neutron star mergers. The properties of matter near and above nuclear saturation density are uncertain, which translates into uncertainties in astrophysical simulations and their multi-messenger signatures. Therefore, a wide range of EOSs spanning the allowed range of nuclear interactions are necessary for determining the sensitivity of these astrophysical phenomena and their signatures to variations in input microphysics. We present a new set of finite temperature EOSs based on experimentally allowed Skyrme forces. We employ a liquid drop model of nuclei to capture the non-uniform phase of nuclear matter at sub-saturation density, which is blended into a nuclear statistical equilibrium EOS at lower densities. We also provide a new, open-source code for calculating EOSs for arbitrary Skyrme parametrizations. We then study the effects of different Skyrme parametrizations on thermodynamical properties of dense astrophysical matter, the neutron star mass-radius relationship, and the core collapse of 15 and 40 solar mass stars.

Modeling differential rotations of compact stars in equilibriums

Outcomes of numerical relativity simulations of massive core collapses or binary neutron star mergers with moderate masses suggest formations of rapidly and differentially rotating neutron stars. Subsequent fall back accretion may also amplify the degree of differential rotations. We propose new formulations for modeling differential rotations of those compact stars, and present selected solutions of differentially rotating, stationary, and axisymmetric compact stars in equilibriums. For the cases when rotating stars reach break-up velocities, the maximum masses of such rotating models are obtained.

Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy

Abstract We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter S 0. In addition, for assumed values of S 0 above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter L ,which describes the lowest-order density dependence of the symmetry energy. A lower bound on neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust–core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.

Structure of stable binary neutron star merger remnants: Role of initial spin

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.

Charged current neutrino interactions in hot and dense matter

We derive the charged current absorption rate of electron and anti-electron neutrinos in dense matter using a fully relativistic approach valid at arbitrary matter degeneracy. We include mean field energy shifts due to nuclear interactions and the corrections due to weak magnetism. The rates are derived both from the familiar Fermi's Golden Rule, and from the techniques of finite temperature field theory, and shown to be equivalent. In various limits, these results can also be used to calculate neutral current opacities. We find that some pieces of the response have been left out in previous derivations and their contribution at high density can be significant. Useful formulae and detailed derivations are presented and we provide a new open source implementation of these opacities for use in radiation hydrodynamic simulations of core-collapse supernovae and neutron star mergers.

General relativistic magnetohydrodynamic simulations of binary neutron star mergers forming a long-lived neutron star

Merging binary neutron stars (BNSs) represent the ultimate targets for multimessenger astronomy, being among the most promising sources of gravitational waves (GWs), and, at the same time, likely accompanied by a variety of electromagnetic counterparts across the entire spectrum, possibly including short gamma-ray bursts (SGRBs) and kilonova/macronova transients. Numerical relativity simulations play a central role in the study of these events. In particular, given the importance of magnetic fields, various aspects of this investigation require general relativistic magnetohydrodynamics (GRMHD). So far, most GRMHD simulations focused the attention on BNS mergers leading to the formation of a hypermassive NS, which, in turn, collapses within few tens of ms into a black hole surrounded by an accretion disk. However, recent observations suggest that a significant fraction of these systems could form a long-lived NS remnant, which will either collapse on much longer timescales or remain indefinitely stable. Despite the profound implications for the evolution and the emission properties of the system, a detailed investigation of this alternative evolution channel is still missing. Here, we follow this direction and present a first detailed GRMHD study of BNS mergers forming a long-lived NS. We consider magnetized binaries with different mass ratios and equations of state and analyze the structure of the NS remnants, the rotation profiles, the accretion disks, the evolution and amplification of magnetic fields, and the ejection of matter. Moreover, we discuss the connection with the central engine of SGRBs and provide order-of-magnitude estimates for the kilonova/macronova signal. Finally, we study the GW emission, with particular attention to the post-merger phase.