Simulations Of Neutron Star Mergers Research Articles

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.

General-relativistic Large-eddy Simulations of Binary Neutron Star Mergers

Abstract The flow inside remnants of binary neutron star (NS) mergers is expected to be turbulent, because of magnetohydrodynamics instability activated at scales too small to be resolved in simulations. To study the large-scale impact of these instabilities, we develop a new formalism, based on the large-eddy simulation technique, for the modeling of subgrid-scale turbulent transport in general relativity. We apply it, for the first time, to the simulation of the late-inspiral and merger of two NSs. We find that turbulence can significantly affect the structure and survival time of the merger remnant, as well as its gravitational-wave (GW) and neutrino emissions. The former will be relevant for GW observation of merging NSs. The latter will affect the composition of the outflow driven by the merger and might influence its nucleosynthetic yields. The accretion rate after black hole formation is also affected. Nevertheless, we find that, for the most likely values of the turbulence mixing efficiency, these effects are relatively small and the GW signal will be affected only weakly by the turbulence. Thus, our simulations provide a first validation of all existing post-merger GW models.

Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the stars’ rotation

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

Neutrino flavor evolution in binary neutron star merger remnants

We study the neutrino flavor evolution in the neutrino-driven wind from a binary neutron star merger remnant consisting of a massive neutron star surrounded by an accretion disk. With the neutrino emission characteristics and the hydrodynamical profile of the remnant consistently extracted from a three-dimensional simulation, we compute the flavor evolution by taking into account neutrino coherent forward scattering off ordinary matter and neutrinos themselves. We employ a "single-trajectory" approach to investigate the dependence of the flavor evolution on the neutrino emission location and angle. We also show that the flavor conversion in the merger remnant can affect the (anti-)neutrino absorption rates on free nucleons and may thus impact the $r$-process nucleosynthesis in the wind. We discuss the sensitivity of such results on the change of neutrino emission characteristics, also from different neutron star merger simulations.

Ther-process nucleosynthesis and related challenges

The rapid neutron-capture process, or r -process, is known to be of fundamental importance for explaining the origin of approximately half of the A > 60 stable nuclei observed in nature. Recently, special attention has been paid to neutron star (NS) mergers following the confirmation by hydrodynamic simulations that a non-negligible amount of matter can be ejected and by nucleosynthesis calculations combined with the predicted astrophysical event rate that such a site can account for the majority of r -material in our Galaxy. We show here that the combined contribution of both the dynamical (prompt) ejecta expelled during binary NS or NS-black hole (BH) mergers and the neutrino and viscously driven outflows generated during the post-merger remnant evolution of relic BH-torus systems can lead to the production of r -process elements from mass number A ≳ 90 up to actinides. The corresponding abundance distribution is found to reproduce the solar distribution extremely well. It can also account for the elemental distributions observed in low-metallicity stars. However, major uncertainties still affect our understanding of the composition of the ejected matter. These concern (i) the β -interactions of electron (anti)neutrinos with free neutrons and protons, as well as their inverse reactions, which may affect the neutron-richness of the matter at the early phase of the ejection, and (ii) the nuclear physics of exotic neutron-rich nuclei, including nuclear structure as well as nuclear interaction properties, which impact the calculated abundance distribution. Both aspects are discussed in the light of recent hydrodynamical simulations of NS mergers and microscopic calculations of nuclear decay and reaction probabilities.

Impact of an improved neutrino energy estimate on outflows in neutron star merger simulations

Binary neutron star mergers are promising sources of gravitational waves for ground-based detectors such as Advanced LIGO. Neutron-rich material ejected by these mergers may also be the main source of r-process elements in the Universe, while radioactive decays in the ejecta can power bright electromagnetic post-merger signals. Neutrino-matter interactions play a critical role in the evolution of the composition of the ejected material, which significantly impacts the outcome of nucleosynthesis and the properties of the associated electromagnetic signal. In this work, we present a simulation of a binary neutron star merger using an improved method for estimating the average neutrino energies in our energy-integrated neutrino transport scheme. These energy estimates are obtained by evolving the neutrino number density in addition to the neutrino energy and flux densities. We show that significant changes are observed in the composition of the polar ejecta when comparing our new results with earlier simulations in which the neutrino spectrum was assumed to be the same everywhere in optically thin regions. In particular, we find that material ejected in the polar regions is less neutron rich than previously estimated. Our new estimates of the composition of the polar ejecta make it more likely that the color and timescale of the electromagnetic signal depend on the orientation of the binary with respect to an observer's line-of-sight. These results also indicate that important observable properties of neutron star mergers are sensitive to the neutrino energy spectrum, and may need to be studied through simulations including a more accurate, energy-dependent neutrino transport scheme.

Gravitational waveforms from binary neutron star mergers with high-order weighted-essentially-nonoscillatory schemes in numerical relativity

The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in $(3+1)$-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We find that high-order WENO schemes can be robustly employed for simulating the inspiral-merger phase and they significantly improve the assessment of the waveform's error budget with respect to finite-volume methods. High-order WENO schemes can be thus efficiently used for high-quality waveforms production, also in future large-scale investigations of the binary parameter space.

M=1instability and gravitational wave signal in binary neutron star mergers

We examine the development and detectability of the $m=1$ instability in the remnant of binary neutron star mergers. The detection of the gravitational mode associated with the $m=1$ degree of freedom could potentially reveal details of the equation of state. We analyze the post-merger epoch of simulations of both equal and non-equal mass neutron star mergers using three realistic, microphysical equations of state and neutrino cooling. Our studies show such an instability develops generically and within a short dynamical time to strengths that are comparable or stronger than the $m=2$ mode which is the strongest during the early post-merger stage. We estimate the signal to noise ratio that might be obtained for the $m=1$ mode and discuss the prospects for observing this signal with available Earth-based detectors. Because the $m=1$ occurs at roughly half the frequency of the more powerful $m=2$ signal and because it can potentially be long-lived, targeted searches could be devised to observe it. We estimate that with constant amplitude direct detection of the mode could occur up to a distance of roughly $14\,\mathrm{Mpc}$ whereas a search triggered by the inspiral signal could extend this distance to roughly $100\,\mathrm{Mpc}$.

Binary neutron star merger simulations with different initial orbital frequency and equation of state

We present results from three-dimensional general relativistic simulations of binary neutron star coalescences and mergers using public codes. We considered equal mass models where the baryon mass of the two neutron stars is , described by four different equations of state (EOS) for the cold nuclear matter (APR4, SLy, H4, and MS1; all parametrized as piecewise polytropes). We started the simulations from four different initial interbinary distances (, and 60 km), including up to the last 16 orbits before merger. That allows us to show the effects on the gravitational wave (GW) phase evolution, radiated energy and angular momentum due to: the use of different EOS, the orbital eccentricity present in the initial data and the initial separation (in the simulation) between the two stars. Our results show that eccentricity has a major role in the discrepancy between numerical and analytical waveforms until the very last few orbits, where ‘tidal’ effects and missing high-order post-Newtonian coefficients also play a significant role. We test different methods for extrapolating the GW signal extracted at finite radii to null infinity. We show that an effective procedure for integrating the Newman–Penrose signal to obtain the GW strain h is to apply a simple high-pass digital filter to h after a time domain integration, where only the two physical motivated integration constants are introduced. That should be preferred to the more common procedures of introducing additional integration constants, integrating in the frequency domain or filtering before integration.

General relativistic magnetohydrodynamic simulations of binary neutron star mergers with the APR4 equation of state

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.

Dynamical mass ejection from binary neutron star mergers

We present fully general-relativistic simulations of binary neutron star mergers with a temperature and composition dependent nuclear equation of state. We study the dynamical mass ejection from both quasi-circular and dynamical-capture eccentric mergers. We systematically vary the level of our treatment of the microphysics to isolate the effects of neutrino cooling and heating and we compute the nucleosynthetic yields of the ejecta. We find that eccentric binaries can eject significantly more material than quasi-circular binaries and generate bright infrared and radio emission. In all our simulations the outflow is composed of a combination of tidally- and shock-driven ejecta, mostly distributed over a broad $\sim 60^\circ$ angle from the orbital plane, and, to a lesser extent, by thermally driven winds at high latitudes. Ejecta from eccentric mergers are typically more neutron rich than those of quasi-circular mergers. We find neutrino cooling and heating to affect, quantitatively and qualitatively, composition, morphology, and total mass of the outflows. This is also reflected in the infrared and radio signatures of the binary. The final nucleosynthetic yields of the ejecta are robust and insensitive to input physics or merger type in the regions of the second and third r-process peaks. The yields for elements on the first peak vary between our simulations, but none of our models is able to explain the Solar abundances of first-peak elements without invoking additional first-peak contributions from either neutrino and viscously-driven winds operating on longer timescales after the mergers, or from core-collapse supernovae.

Relativistic simulations of eccentric binary neutron star mergers: One-arm spiral instability and effects of neutron star spin

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.

THE ROLE OF FISSION IN NEUTRON STAR MERGERS AND ITS IMPACT ON THEr-PROCESS PEAKS

Comparing observational abundance features with nucleosynthesis predictions of stellar evolution or explosion simulations can scrutinize two aspects: (a) the conditions in the astrophysical production site and (b) the quality of the nuclear physics input utilized. We test the abundance features of r-process nucleosynthesis calculations for the dynamical ejecta of neutron star merger simulations based on three different nuclear mass models: The Finite Range Droplet Model (FRDM), the (quenched version of the) Extended Thomas Fermi Model with Strutinsky Integral (ETFSI-Q), and the Hartree-Fock-Bogoliubov (HFB) mass model. We make use of corresponding fission barrier heights and compare the impact of four different fission fragment distribution models on the final r-process abundance distribution. In particular, we explore the abundance distribution in the second r-process peak and the rare-earth sub-peak as a function of mass models and fission fragment distributions, as well as the origin of a shift in the third r-process peak position. The latter has been noticed in a number of merger nucleosynthesis predictions. We show that the shift occurs during the r-process freeze-out when neutron captures and {\beta}-decays compete and an (n,{\gamma})-({\gamma},n) equilibrium is not maintained anymore. During this phase neutrons originate mainly from fission of material above A = 240. We also investigate the role of {\beta}-decay half-lives from recent theoretical advances, which lead either to a smaller amount of fissioning nuclei during freeze-out or a faster (and thus earlier) release of fission neutrons, which can (partially) prevent this shift and has an impact on the second and rare-earth peak as well.

Dynamical mass ejection from binary neutron star mergers: Radiation-hydrodynamics study in general relativity

We perform radiation-hydrodynamics simulations of binary neutron star mergers in numerical relativity on the Japanese "K" supercomputer, taking into account neutrino cooling and heating by an updated leakage-plus-transfer scheme for the first time. Neutron stars are modeled by three modern finite-temperature equations of state (EOS) developed by Hempel and his collaborators. We find that the properties of the dynamical ejecta of the merger such as total mass, average electron fraction, and thermal energy depend strongly on the EOS. Only for a soft EOS (the so-called SFHo), the ejecta mass exceeds $0.01M_{\odot}$. In this case, the distribution of the electron fraction of the ejecta becomes broad due to the shock heating during the merger. These properties are well-suited for the production of the solar-like $r$-process abundance. For the other stiff EOS (DD2 and TM1), for which a long-lived massive neutron star is formed after the merger, the ejecta mass is smaller than $0.01M_{\odot}$, although broad electron-fraction distributions are achieved by the positron capture and the neutrino heating.

Properties of hypermassive neutron stars formed in mergers of spinning binaries

We present numerical simulations of binary neutron star mergers, comparing irrotational binaries to binaries of NSs rotating aligned to the orbital angular momentum. For the first time, we study spinning BNSs employing nuclear physics equations of state, namely the ones of Lattimer and Swesty as well as Shen, Horowitz, and Teige. We study mainly equal mass systems leading to a hypermassive neutron star (HMNS), and analyze in detail its structure and dynamics. In order to exclude gauge artifacts, we introduce a novel coordinate system used for post-processing. The results for our equal mass models show that the strong radial oscillations of the HMNS modulate the instantaneous frequency of the gravitational wave (GW) signal to an extend that leads to separate peaks in the corresponding Fourier spectrum. In particular, the high frequency peaks which are often attributed to combination frequencies can also be caused by the modulation of the $m=2$ mode frequency in the merger phase. As a consequence for GW data analysis, the offset of the high frequency peak does not necessarily carry information about the radial oscillation frequency. Further, the low frequency peak in our simulations is dominated by the contribution of the plunge and the first 1--2 bounces. The amplitude of the radial oscillations depends on the initial NS spin, which therefore has a complicated influence on the spectrum. Another important result is that HMNSs can consist of a slowly rotating core with an extended, massive envelope rotating close to Keplerian velocity, contrary to the common notion that a rapidly rotating core is necessary to prevent a prompt collapse. Finally, our estimates on the amount of unbound matter show a dependency on the initial NS spin, explained by the influence of the latter on the amplitude of radial oscillations, which in turn cause shock waves.

High resolution numerical relativity simulations for the merger of binary magnetized neutron stars

We perform high-resolution magnetohydrodynamics simulations of binary neutron star mergers in numerical relativity on the Japanese supercomputer K. The neutron stars and merger remnants are covered by a grid spacing of 70 m, which yields the highest-resolution results among those derived so far. By an in-depth resolution study, we clarify several amplification mechanisms of magnetic fields during the binary neutron star merger for the first time. First, the Kelvin-Helmholtz instability developed in the shear layer at the onset of the merger significantly amplifies the magnetic fields. A hypermassive neutron star (HMNS) formed after the merger is then subject to the nonaxisymmetric magnetorotational instability, which amplifies the magnetic field in the HMNS. These two amplification mechanisms cannot be found with insufficient-resolution runs. We also show that the HMNS eventually collapses to a black hole surrounded by an accretion torus which is strongly magnetized at birth.

MODA: a new algorithm to compute optical depths in multidimensional hydrodynamic simulations

We introduce a new algorithm for the calculation of multidimensional optical depths in approximate radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in three-dimensional simulations of core-collapse supernovae and neutron star mergers, our method makes no assumptions about the geometry of the matter distribution, apart from expecting optically transparent boundaries. Based on local information about opacities, the algorithm figures out an escape route that tends to minimize the optical depth without assuming any pre-defined paths for radiation. Its adaptivity makes it suitable for a variety of astrophysical settings with complicated geometry (e.g., core-collapse supernovae, compact binary mergers, tidal disruptions, star formation, etc.). We implement the MODA algorithm into both a Eulerian hydrodynamics code with a fixed, uniform grid and into an SPH code where we make use a tree structure that is otherwise used for searching neighbours and calculating gravity. In a series of numerical experiments, we compare the MODA results with analytically known solutions. We also use snapshots from actual 3D simulations and compare the results of MODA with those obtained with other methods such as the global and local ray-by-ray method. It turns out that MODA achieves excellent accuracy at a moderate computational cost. In an appendix we also discuss implementation details and parallelization strategies.

Thermal properties of supernova matter: The bulk homogeneous phase

We investigate the thermal properties of the potential model equation of state of Akmal, Pandharipande and Ravenhall. This equation of state approximates the microscopic model calculations of Akmal and Pandharipande, which feature a neutral pion condensate. We treat the bulk homogeneous phase for isospin asymmetries ranging from symmetric nuclear matter to pure neutron matter and for temperatures and densities relevant for simulations of core-collapse supernovae, proto-neutron stars, and neutron star mergers. Numerical results of the state variables are compared with those of a typical Skyrme energy density functional with similar properties at nuclear densities, but which differs substantially at supra-nuclear densities. Analytical formulas, which are applicable to non-relativistic potential models such as the equations of state we are considering, are derived for all state variables and their thermodynamic derivatives. A highlight of our work is its focus on thermal response functions in the degenerate and non-degenerate situations, which allow checks of the numerical calculations for arbitrary degeneracy. These functions are sensitive to the density dependent effective masses of neutrons and protons, which determine the thermal properties in all regimes of degeneracy. We develop the "thermal asymmetry free energy" and establish its relation to the more commonly used nuclear symmetry energy. We also explore the role of the pion condensate at supra-nuclear densities and temperatures. Tables of matter properties as functions of baryon density, composition (i.e., proton fraction) and temperature are being produced which are suitable for use in astrophysical simulations of supernovae and neutron stars.

Merging ``real'' neutron stars for gravitational waves and electromagnetic counterparts

Having more-or-less succeeded in learning to stably evolve Einstein’s equations, numerical relativity is taking the leap to including the physics of neutron stars, which will enable us to construct truly realistic pictures of neutron star-neutron star and black hole-neutron star binary mergers. The neutron star profile affects late inspirals and mergers, leaving its imprint on gravitational waveforms and electromagnetic counterpart signals. Furthermore, we expect neutrino radiation, magnetic field, and nuclear recombination effects to drive the post-merger evolution. In this talk, I will describe some recent neutron star merger simulations combining nuclear physics and general relativity. The goal is to connect assumptions about the nuclear equation of state and the premerger binary to resulting binary trajectories, matter outflows, accretion disk dynamics, and neutrino energy output. These can then hopefully be connected to observable signals in the form of gravitational waves, kilonovae, and gamma ray bursts. It is found that an interesting variety of disks, outflows, and neutrino bursts are possible. Connections to observables are being attempted by tracking nuclear reactions in tidal ejecta and estimating energy injection to gamma ray bursts from neutrino annihilation and other sources. Meanwhile, non-vacuum inspiral simulations are finally approaching the length and accuracy needed for interesting comparisons with binary black hole waveforms and post-Newtonian predictions, these being steps toward a reliable characterization of the imprint of the nuclear equation of state on the gravitational waves.