Dynamical damping terms for symmetry-seeking shift conditions

Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the shift and these have been successfully used both in vacuum and non-vacuum spacetimes when simulating binaries with comparable masses. At the same time, recent evidence has emerged that the standard "Gamma-driver" shift condition requires a careful and non-trivial tuning of its parameters to ensure long-term stable evolutions of unequal-mass binaries. We present a novel gauge condition in which the damping constant is promoted to be a dynamical variable and the solution of an evolution equation. We show that this choice removes the need for special tuning and provides a shift damping term which is free of instabilities in our simulations and dynamically adapts to the individual positions and masses of the binary black-hole system. Our gauge condition also reduces the variations in the coordinate size of the apparent horizon of the larger black hole and could therefore be useful when simulating binaries with very small mass ratios.Comment: 11 pages, 8 figure

A magnetar engine for short GRBs and kilonovae

We investigate the influence of magnetic fields on the evolution of binary neutron-star (BNS) merger remnants via three-dimensional (3D) dynamical-spacetime general-relativistic (GR) magnetohydrodynamic (MHD) simulations. We evolve a postmerger remnant with an initial poloidal magnetic field, resolve the magnetoturbulence driven by shear flows, and include a microphysical finite-temperature equation of state (EOS). A neutrino leakage scheme that captures the overall energetics and lepton number exchange is also included. We find that turbulence induced by the magnetorotational instability (MRI) in the hypermassive neutron star (HMNS) amplifies magnetic field to beyond magnetar-strength ($10^{15}\, \mathrm{G}$). The ultra-strong toroidal field is able to launch a relativistic jet from the HMNS. We also find a magnetized wind that ejects neutron-rich material with a rate of $\dot{M}_{\mathrm{ej}} \simeq 1 \times10^{-1}\, \mathrm{M_{\odot}\, s^{-1}}$. The total ejecta mass in our simulation is $5\times 10^{-3}\, \mathrm{M_{\odot}}$. This makes the ejecta from the HMNS an important component in BNS mergers and a promising source of $r$-process elements that can power a kilonova. The jet from the HMNS reaches a terminal Lorentz factor of $\sim 5$ in our highest-resolution simulation. The formation of this jet is aided by neutrino-cooling preventing the accretion disk from protruding into the polar region. As neutrino pair-annihilation and radiative processes in the jet (which were not included in the simulations) will boost the Lorentz factor in the jet further, our simulations demonstrate that magnetars formed in BNS mergers are a viable engine for short gamma-ray bursts (sGRBs).Comment: Resubmitted versio

Vacuum Electromagnetic Counterparts of Binary Black-Hole Mergers

As one step towards a systematic modeling of the electromagnetic (EM) emission from an inspiralling black hole binary we consider a simple scenario in which the binary moves in a uniform magnetic field anchored to a distant circumbinary disc. We study this system by solving the Einstein-Maxwell equations in which the EM fields are chosen with astrophysically consistent strengths. We consider binaries with spins aligned or anti-aligned with the orbital angular momentum and study the dependence of gravitational and EM signals with these spin configurations. Overall we find that the EM radiation in the lowest l=2, m=2 multipole accurately reflects the gravitational one, with identical phase evolutions and amplitudes that differ only by a scaling factor. We also compute the efficiency of the energy emission in EM waves and find that it is given by E^rad_EM/M ~ 10^-15 (M/10^8 M_Sun)^2 (B/10^4 G)^2, hence 13 orders of magnitude smaller than the gravitational energy for realistic magnetic fields. The corresponding luminosity is much smaller than the accretion luminosity if the system is accreting at near the Eddington rate. Most importantly, this EM emission is at frequencies of 10^-4 (10^8 M_Sun/M) Hz, well outside those accessible to astronomical radio observations. As a result, it is unlikely that the EM emission discussed here can be detected directly and simultaneously with the gravitational-wave one. However, indirect processes, driven by changes in the EM fields behavior could yield observable events. In particular if the accretion rate of the circumbinary disc is small and sufficiently stable over the timescale of the final inspiral, then the EM emission may be observable indirectly as it will alter the accretion rate through the magnetic torques exerted by the distorted magnetic field lines

Propagation of a realistic magnetar jet through binary neutron star merger medium and implications for short gamma-ray bursts

The origin of short gamma-ray bursts (sGRBs) is associated with outflows powered by the remnant of a binary neutron star merger. This remnant can be either a black hole or a highly magnetized, fastly spinning neutron star, also known as a magnetar. Here, we present the results of two relativistic magnetohydrodynamical (RMHD) simulations aimed at investigating the large-scale dynamics and propagation of magnetar collimated outflows through the medium surrounding the remnant. The first simulation evolves a realistic jet by injecting external simulation data, while the second evolves an analytical model jet with similar properties for comparison. We find that both outflows remain collimated and successfully emerge through the static medium surrounding the remnant. However, they fail to attain relativistic velocities and only reach a mean maximum speed of ~0.7c for the realistic jet, and ~0.6c for the analytical jet. We also find that the realistic jet has a much more complex structure. The lack of highly relativistic speeds, that makes these jets unsuitable as short GRB sources, is due to numerical limitations and not general to all possible magnetar outflows. A jet like the one we study, however, could give rise to or augment a blue kilonova component. In addition, it would make the propagation of a relativistic jet easier, should one be launched after the neutron star collapses into a black hole.Comment: 11 pages, 7 figures, accepted to Ap

R-process Nucleosynthesis from Three-Dimensional Magnetorotational Core-Collapse Supernovae

We investigate r-process nucleosynthesis in three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are a robust r-process source only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of order $10^{13}$G. Additionally, a comparison simulation that we restrict to axisymmetry, results in overly optimistic r-process production for lower magnetic field strengths.Comment: 10 pages, 9 figures, 2 tables. submitted to Ap

GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit

We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the toolkit builds upon previous releases and implements the evolution of relativistic magnetized fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both constrained transport and hyperbolic divergence cleaning schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfvén waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code's performance in curved spacetimes with spherical accretion onto a black hole on a fixed background spacetime and in fully dynamical spacetimes by evolutions of a magnetized polytropic neutron star and of the collapse of a magnetized stellar core. Our results agree well with exact solutions where these are available and we demonstrate convergence. All code and input files used to generate the results are available on http://einsteintoolkit.org. This makes our work fully reproducible and provides new users with an introduction to applications of the code