Session H10: Numerical Simulations of Neutron Stars

Magnetized Neutron Stars

Magnetized neutron stars, whether considered individually or within compact binary systems, demonstrate a number of interesting dynamical effects. Using a distributed adaptive mesh refinement (AMR) code, we evolve such stars and study their dynamics.   

Collapse of magnetized hypermassive neutron stars in general relativity: Disk evolution and outflows

We simulate the evolution in axisymmetry of accretion disks formed self-consistently through collapse of magnetized hypermassive neutron stars (HMNSs) to black holes (BHs). Such stars can arise following the merger of binary neutron stars (NSs) and are secularly unstable to collapse due to MHD-driven angular momentum transport. The rotating BH which forms in this process is surrounded by a hot, massive, magnetized torus. Our code integrates the coupled Einstein-Maxwell-MHD equations and is used to follow the collapse of magnetized HMNSs in full GR until the spacetime settles down to a quasi-stationary state. We then employ the Cowling approximation, in which the spacetime is frozen, to track the subsequent evolution of the disk. This approximation allows us to greatly extend the disk evolutions and study the resulting outflows, which may be relevant to the generation of a gamma-ray burst. We find that outflows are suppressed when a stiff equation of state is assumed for low density disk material and are sensitive to the initial magnetic field configuration.   

A different way to evolve black hole-neutron star binaries

We give a status report on our simulations of comparable mass black hole-neutron star binaries. We evolve the full Einstein equations for the spacetime metric using multidomain pseudospectral methods, and we evolve the hydrodynamic variables using finite volume methods on a separate grid. Our two-grid approach allows us to model the inspiral with particular accuracy.   

Evolution of Excised BHBH and BHNS Initial Data: Numerical Methods and Tests

We are now able to perform fully general relativistic simulations of black hole-black hole (BHBH) and black hole-neutron star (BHNS) binaries using conformal thin-sandwich (CTS) initial data and the BSSN-based moving puncture evolution technique. We fill the excised BH regions in the CTS initial data with smooth, constraint-violating ``junk'' data. To test this technique, we apply the junk-filling procedure to excised irrotational CTS BHBH initial data and evolve it. We compare the resulting waveform to that found using {\it puncture} initial data with the same initial orbital frequency and find good agreement. In our most recent work, this junk-filling technique is employed to stably evolve excised CTS BHNS binary initial data through inspiral, merger, and ringdown ($t > 200M$). We present results from our BHNS simulations that validate our numerical technique and briefly outline future plans.   

Fully General Relativistic Simulations of black hole-neutron star Mergers

Black hole-neutron star (BHNS) binaries are expected to be among the leading sources of gravitational waves observable by ground-based detectors, and may be the progenitors of short-hard gamma ray bursts as well. We present our new fully general relativistic calculations of merging BHNS binaries, which use our recent conformal thin-sandwich (CTS) quasi-circular configurations as initial data. Our evolutions are performed using a BSSN-based moving puncture method and a fully relativistic, high-resolution shock-capturing hydrodynamics scheme. We investigate the inspiral, merger, and disk formation in the systems. We find that the vast majority of material is promptly accreted and no more than 3\% of the NS's rest mass is ejected into a tenuous, gravitationally bound disk. We compute gravitational radiation, finding measurable differences between our waveforms and those produced by binary black hole mergers within the advanced LIGO band. These differences appear at frequencies corresponding to the onset of NS tidal disruption. The resulting information about the NS radius may be used to constrain the NS equation of state.   

Neutron Star Binary Coalescences: How realistic is the initial data?

Quasi-equilibrium approximations are often used as initial data for numerical simulations of binary neutron star inspiral coalescence. The standard is to begin the simulations at a separation close to that of the inner-most-stable-circular orbit. We examine how realistic it is to use quasi-equilibrium approximations at such close separations. Several measures of the validity are developed to determine what initial separation one must have for the quasi-equilibrium approximations to yield astrophysically realistic initial data.   

Critical Collapse of Non-Rotating and Rotating Neutron Star Systems with Axisymmetry

GRAstro-2D is the package for simulation of system with axisymmetry. The convergence of this code is ensured. With this code we study the threshold of gravitational collapses of neutron stars. We find type I critical collapses in both non-rotating and rotating neutron star systems. Further, we show that a critical collapse may happen in a cooling process.   

Neutron Star Binary Coalescences: Angular Momentum Threshold Against a Prompt Collapse

We performed fully general relativistic simulations of neutron star binary coalescences to investigate how much angular momentum is needed to support the merged system against a prompt gravitational collapse. For a polytropic equation equation of state with the polytropic index in the range of $\Gamma = 2$ to $1.8$, we find that the angular momentum threshold for an equal mass system can be described quite accurately by a simple formula $L/M2=M_{ADM}/M_{ADM}^{max}$, where $L$ is the total angular momentum of the binary neutron star system, $M$ is the total ADM mass of the system, $M_{ADM}$ is the ADM mass of the neutron star in isolation, $M_{ADM}^{max}$ is the maximum ADM mass of a single neutron star with the same equation of state.   

Differentially rotating neutron stars: A perturbative study

We present a study of non-axisymmetric oscillations of differentially rotating neutron stars in the perturbative framework of General Relativity. Differential rotation plays an important role in nascent neutron stars, and recent numerical studies have shown that it can be responsible for an instability at low values of the ratio $T/W$. We study the oscillation spectrum of those stars and we investigate the possible effect of the existence of the corrotation band on the low $T/W$ instability.