General relativistic simulations of magnetized binary neutron star mergers

Abstract

Binary neutron stars (NSNS) are expected to be among the leading sources of gravitational waves observable by ground-based laser interferometers and may be the progenitors of short-hard gamma ray bursts. We present a series of general relativistic NSNS coalescence simulations both for unmagnetized and magnetized stars. We adopt quasiequilibrium initial data for circular, irrotational binaries constructed in the conformal thin-sandwich (CTS) framework. We adopt the BSSN formulation for evolving the metric and a high-resolution shock-capturing scheme to handle the magnetohydrodynamics. Our simulations of unmagnetized binaries agree with the results of Shibata, Taniguchi and Uryū [1]. In cases in which the mergers result in a prompt collapse to a black hole, we are able to use puncture gauge conditions to extend the evolution and determine the mass of the material that forms a disk. We find that the disk mass is less than 2% of the total mass in all cases studied. We then add a small poloidal magnetic field to the initial configurations and study the subsequent evolution. For cases in which the remnant is a hypermassive neutron star, we see measurable differences in both the amplitude and phase of the gravitational waveforms following the merger. For cases in which the remnant is a black hole surrounded by a disk, the disk mass and the gravitational waveforms are about the same as the unmagnetized cases. Magnetic fields substantially affect the long-term, secular evolution of a hypermassive neutron star (driving 'delayed collapse') and an accretion disk around a nascent black hole.

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

“…Hence, we consider the growth time of the instability that has to compete with the dynamical time scale of the merger event (a few milliseconds), the saturation mechanism, the saturation field strength, and generic dynamical features of supersonic shear flows. Our results should also allow us to reassess the findings of global simulations extending the ones performed by Price & Rosswog (2006), e.g., the simulations by Anderson et al (2008) and Liu et al (2008).…”

“…The layer is prone to the Kelvin-Helmholtz instability, and thus, exponential growth of any weak seed field is possible, as observed by Price & Rosswog (2006) (see also Giacomazzo et al 2009;Anderson et al 2008;Liu et al 2008). The limitations of their simulations, mainly concerning grid resolution, did not allow these authors to determine the saturation level of the instability firmly and accurately.…”

“…Using it to simulate the entire merger event, however, is cumbersome due to the large computational costs required to cover the entire system with an appropriate computational grid. In spite of this fact, Giacomazzo et al (2009) (see also Liu et al 2008;Anderson et al 2008) have performed full general-relativistic MHD simulations using vertexcentered mesh refinement to assess the influence of magnetic fields on the merger dynamics and the resulting gravitational waveform. But, as we shall show below, even their (presently world-best) grid resolution (h ∼ 350 m) is still too crude to properly capture the disruptive dynamics after the KH amplification of the field.…”

Prospects for high frequency burst searches following binary neutron star coalescence with advanced gravitational wave detectors

“…ROpt is the effective range of an optimal matched-filter search, assuming a 3-σ statistical significance and O(100) BNS-inspiral triggers;Ṅ Opt det is the expected number of post-merger signal detections for a search with this effective range. The energy, EGW is the energy carried by the GW signal assuming elliptical polarization and computed according to equation 19. f peak is the frequency of the highest peak in the signal power spectrum.…”

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

“…However, as for the solenoidal condition for the magnetic field, non-evolutionary constraints must be preserved in the numerical evolution, and computational methods for modern codes are divided into two main classes: 1) free-evolution schemes, mainly based on hyperbolic equations alone, where this problem is alleviated by appropriate reformulations of the equations (BSSN: Shibata & Nakamura 1995;Baumgarte & Shapiro 1999), eventually with the addition of propagating modes and damping terms (Z4: Bona et al 2003;Bernuzzi & Hilditch 2010); 2) fully constrained schemes, where the constraints are enforced at each timestep through the solution of elliptic equations (Bonazzola et al 2004), a more robust but computationally demanding option, since elliptic solvers are notoriously difficult to parallelize. Most of the state-of-the-art 3D codes for GRMHD in dynamical spacetimes are based on freeevolution schemes in Cartesian coordinates (Duez et al 2005;Shibata & Sekiguchi 2005;Anderson et al 2006;Giacomazzo & Rezzolla 2007;Montero et al 2008;Farris et al 2008), and have been used for gravitational collapse in the presence of magnetized plasmas Shibata et al 2006a,b;Stephens et al 2007Stephens et al , 2008, evolution of NSs (Duez et al 2006b;Liebling et al 2010), binary NS mergers (Anderson et al 2008;Liu et al 2008;Giacomazzo et al 2009Giacomazzo et al , 2011, and accreting tori around Kerr BHs (Montero et al 2010).…”