The Exact Solution of the Riemann Problem in Relativistic MHD

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an important test for those numerical codes solving the MHD equations in relativistic regimes.Comment: 36 pages, 13 figures. Minor changes to match published versio

Prompt Electromagnetic Transients from Binary Black Hole Mergers

Binary black hole (BBH) mergers provide a prime source for current and future interferometric GW observatories. Massive BBH mergers may often take place in plasma-rich environments, leading to the exciting possibility of a concurrent electromagnetic (EM) signal observable by traditional astronomical facilities. However, many critical questions about the generation of such counterparts remain unanswered. We explore mechanisms that may drive EM counterparts with magnetohydrodynamic simulations treating a range of scenarios involving equal-mass black-hole binaries immersed in an initially homogeneous fluid with uniform, orbitally aligned magnetic fields. We find that the time development of Poynting luminosity, which may drive jet-like emissions, is relatively insensitive to aspects of the initial configuration. In particular, over a significant range of initial values, the central magnetic field strength is effectively regulated by the gas flow to yield a Poynting luminosity of $10^{45}-10^{46} \rho_{-13} M_8^2 \, {\rm erg}\,{\rm s}^{-1}$, with BBH mass scaled to $M_8 \equiv M/(10^8 M_{\odot})$ and ambient density $\rho_{-13} \equiv \rho/(10^{-13} \, {\rm g} \, {\rm cm}^{-3})$. We also calculate the direct plasma synchrotron emissions processed through geodesic ray-tracing. Despite lensing effects and dynamics, we find the observed synchrotron flux varies little leading up to merger.Comment: 22 pages, 21 figures; additional reference + clarifying text added to match published versio

Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles are $\Delta \phi\simeq \pm 0.24$ rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians

Magnetohydrodynamic Effects in Propagating Relativistic Ejecta: Reverse Shock and Magnetic Acceleration

We solve the Riemann problem for the deceleration of arbitrarily magnetized relativistic ejecta injected into a static unmagnetized medium. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization s (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when s exceeds a critical value, sc, defined by the balance between the magnetic pressure in the ejecta and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the ejecta

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

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

A multidimensional grid-adaptive relativistic magnetofluid code

A robust second order, shock-capturing numerical scheme for multi-dimensional special relativistic magnetohydrodynamics on computational domains with adaptive mesh refinement is presented. The base solver is a total variation diminishing Lax-Friedrichs scheme in a finite volume setting and is combined with a diffusive approach for controlling magnetic monopole errors. The consistency between the primitive and conservative variables is ensured at all limited reconstructions and the spatial part of the four velocity is used as a primitive variable. Demonstrative relativistic examples are shown to validate the implementation. We recover known exact solutions to relativistic MHD Riemann problems, and simulate the shock-dominated long term evolution of Lorentz factor 7 vortical flows distorting magnetic island chains.Comment: accepted for publication in Computer Physics Communication

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

Relativistic MHD and black hole excision: Formulation and initial tests

A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.Comment: 22 pages, 8 figure

Faranoff-Riley type I jet deceleration at density discontinuities "Relativistic hydrodynamics with realistic equation of state"

The deceleration mechanisms for relativistic jets in active galactic nuclei remain an open question, and in this paper we propose a model which could explain sudden jet deceleration, invoking density discontinuities. This is particularly motivated by recent indications from HYMORS. Exploiting high resolution, numerical simulations, we demonstrate that for both high and low energy jets, always at high Lorentz factor, a transition to a higher density environment can cause a significant fraction of the directed jet energy to be lost on reflection. This can explain how one-sided jet deceleration and a transition to FR I type can occur in HYMORS, which start as FR II (and remain so on the other side). For that purpose, we implemented in the relativistic hydrodynamic grid-adaptive AMRVAC code, the Synge-type equation of state introduced in the general polytropic case by Meliani et al. (2004). We present results for 10 model computations, varying the inlet Lorentz factor from 10 to 20, including uniform or decreasing density profiles, and allowing for cylindrical versus conical jet models. As long as the jet propagates through uniform media, we find that the density contrast sets most of the propagation characteristics, fully consistent with previous modeling efforts. When the jet runs into a denser medium, we find a clear distinction in the decelaration of high energy jets depending on the encountered density jump. For fairly high density contrast, the jet becomes destabilised and compressed, decelerates strongly (up to subrelativistic speeds) and can form knots. We point out differences that are found between cylindrical and conical jet models, together with dynamical details like the Richtmyer-Meshkov instabilities developing at the original contact interface.Comment: accepted in A&