General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes

Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this Letter, we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular we observe a total amplification of the magnetic field of ~2 orders of magnitude which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 10^4 larger than comparable calculations done in the force-free regime where such amplifications are not possible.Comment: 7 pages, 5 figures. Minor changes to match version accepted for publication on The Astrophysical Journal Letter

Accurate evolutions of inspiralling neutron-star binaries: assessment of the truncation error

We have recently presented an investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus (see arXiv:0804.0594). We here discuss in more detail the convergence properties of the results presented in arXiv:0804.0594 and, in particular, the deterioration of the convergence rate at the merger and during the survival of the merged object, when strong shocks are formed and turbulence develops. We also show that physically reasonable and numerically convergent results obtained at low-resolution suffer however from large truncation errors and hence are of little physical use. We summarize our findings in an "error budget", which includes the different sources of possible inaccuracies we have investigated and provides a first quantitative assessment of the precision in the modelling of compact fluid binaries.Comment: 13 pages, 5 figures. Minor changes to match published version. Added figure 5 right pane

WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics

The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of gamma-ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code and assess its accuracy. Such tests range from the solution of relativistic Riemann problems in flat spacetime, over to the stationary accretion onto a Schwarzschild black hole and up to the evolution of oscillating magnetized stars in equilibrium and constructed as consistent solutions of the coupled Einstein-Maxwell equations.Comment: minor changes to match the published versio

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

Context. Global MHD simulations show Kelvin-Helmholtz (KH) instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak fields in KH unstable shear flows, and the back-reaction of the field onto the flow. Methods. We use a high-resolution ideal MHD code to perform 2D and 3D local simulations of shear flows. Results. In 2D, the magnetic field is amplified in less than 0.01ms until it reaches locally equipartition with the kinetic energy. Subsequently, it saturates due to resistive instabilities that disrupt the KH vortex and decelerate the shear flow on a secular time scale. We determine scaling laws of the field amplification with the initial field strength and the grid resolution. In 3D, this hydromagnetic mechanism may be dominated by purely hydrodynamic instabilities limiting the amplification. We find maximum magnetic fields of 10^16 G locally, and r.m.s. maxima within the box of 10^15 G. However, such strong fields exist only for a short period. In the saturated state, the magnetic field is mainly oriented parallel to the shear flow for strong initial fields, while weaker initial fields tend to lead to a more balanced distribution of the field energy. In all models the flow shows small-scale features. The magnetic field is at most in equipartition with the decaying shear flow. (abridged)Comment: 26 pages, 22 figures (figure quality reduced); accepted for publication in Astronomy & Astrophysic

An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates

A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations at smaller computational costs and at considerably larger spatial resolutions. We here present a new flux-conservative formulation of the relativistic hydrodynamics equations in cylindrical coordinates. By rearranging those terms in the equations which are the sources of the largest numerical errors, the new formulation yields a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. We illustrate this through a series of numerical tests involving the evolution of oscillating spherical and rotating stars, as well as shock-tube tests.Comment: 19 pages, 9 figure

Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole

Binary neutron-star (BNS) systems represent primary sources for the gravitational-wave (GW) detectors. We present a systematic investigation in full GR of the dynamics and GW emission from BNS which inspiral and merge, producing a black hole (BH) surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use HRSC methods for the hydrodynamics equations and high-order finite-differencing techniques for the Einstein equations; (ii) We employ AMR techniques with "moving boxes"; (iii) We use as initial data BNSs in irrotational quasi-circular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the BHs produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the GWs. These techniques allow us to perform accurate evolutions on timescales never reported before (ie ~30 ms) and to provide the first complete description of the inspiral and merger of a BNS leading to the prompt or delayed formation of a BH and to its ringdown. We consider either a polytropic or an ideal fluid EOS and show that already with this idealized EOSs a very interesting phenomenology emerges. In particular, we show that while high-mass binaries lead to the prompt formation of a rapidly rotating BH surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating NS, which undergoes large oscillations and emits large amounts of GWs. Eventually, also the NS collapses to a rotating BH surrounded by a torus. Finally, we also show that the use of a non-isentropic EOS leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of GWs and to a geometrically thicker torus.Comment: 35 pages, 29 figures, corrected few typos to match the published version. High-resolution figures and animations can be found at http://numrel.aei.mpg.de/Visualisations/Archive/BinaryNeutronStars/Relativistic_Meudon/index.htm

On the Shear Instability in Relativistic Neutron Stars

We present new results on instabilities in rapidly and differentially rotating neutron stars. We model the stars in full general relativity and describe the stellar matter adopting a cold realistic equation of state based on the unified SLy prescription. We provide evidence that rapidly and differentially rotating stars that are below the expected threshold for the dynamical bar-mode instability, beta_c = T/|W| ~ 0.25, do nevertheless develop a shear instability on a dynamical timescale and for a wide range of values of beta. This class of instability, which has so far been found only for small values of beta and with very small growth rates, is therefore more generic than previously found and potentially more effective in producing strong sources of gravitational waves. Overall, our findings support the phenomenological predictions made by Watts, Andersson and Jones on the nature of the low-T/|W|.Comment: 20 pages; accepted to the Classical and Quantum Gravity special issue for MICRA200

Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].Comment: 15 pages, 9 figure

Radio precursors to neutron star binary mergings

We discuss a possible generation of radio bursts preceding final stages of binary neutron star mergings which can be accompanied by short gamma-ray bursts. Detection of such bursts appear to be advantageous in the low-frequency radio band due to a time delay of ten to several hundred seconds required for radio signal to propagate in the ionized intergalactic medium. This delay makes it possible to use short gamma-ray burst alerts to promptly monitor specific regions on the sky by low-frequency radio facilities, especially by LOFAR. To estimate the strength of the radio signal, we assume a power-law dependence of the radio luminosity on the total energy release in a magnetically dominated outflow, as found in millisecond pulsars. Based on the planned LOFAR sensitivity at 120 MHz, we estimate that the LOFAR detection rate of such radio transients could be about several events per month from redshifts up to $z\sim1.3$ in the most optimistic scenario. The LOFAR ability to detect such events would crucially depend on exact efficiency of low-frequency radio emission mechanism.Comment: 6 pages, 2 figures, Accepted for publication in Astrophysics & Space Science. Largely extended version of ArXiv:0912.521