The primary goal of numerical relativity is to provide estimates of the wave strain, h, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically ...measure waves in terms of the Weyl curvature component, ? sub(4). Assuming Bondi gauge, transforming to the strain h reduces to integration of ? sub(4) twice in time. Integrations performed in either the time or frequency domain, however, lead to secular nonlinear drifts in the resulting strain h. These nonlinear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular nonlinear drifts in the resulting strain.
We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing nonprecessing spinning black hole binaries recently introduced by Damour and ...Nagar Phys. Rev. D 90, 044018 (2014). We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios 1< or =q< or =9.989 and dimensionless spin range -0.95< or = chi < or =+0.994. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy characteristic evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, E sub(b)j), for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one (ProQuest: Formulae and/or non-USASCII text omitted) entering the nonspinning sector, as a 5PN effective correction to the interaction potential, and one c sub(3)(a sub(1),a sub(2),nu) in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined together with a third functional parameter Delta t sub(NQC)( chi ) entering the waveform by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200 M sub(middot in circle) the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between 99.493% and 99.984% with a median value of 99.944%.
We present results from a controlled numerical experiment investigating the effect of stellar density gas on the coalescence of binary black holes (BBHs) and the resulting gravitational waves (GWs). ...This investigation is motivated by the proposed stellar core fragmentation scenario for BBH formation and the associated possibility of an electromagnetic counterpart to a BBH GW event. We employ full numerical relativity coupled with general-relativistic hydrodynamics and set up a 30+30 M_{⊙} BBH (motivated by GW150914) inside gas with realistic stellar densities. Our results show that at densities ρ≳10^{6}-10^{7} g cm^{-3} dynamical friction between the BHs and gas changes the coalescence dynamics and the GW signal in an unmistakable way. We show that for GW150914, LIGO observations appear to rule out BBH coalescence inside stellar gas of ρ≳10^{7} g cm^{-3}. Typical densities in the collapsing cores of massive stars are in excess of this density. This excludes the fragmentation scenario for the formation of GW150914.
ABSTRACT We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D ...general-relativistic hydrodynamic simulations of a 27 M progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), and (3) SASI-dominated evolution. This confirms previous 3D results of Hanke et al. and Couch & Connor. We carry out simulations with resolutions differing by up to a factor of ∼4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum E( ) develops in the heating layer. Like other 3D studies, we find E( ) ∝ −1 in the "inertial range," while theory and local simulations argue for E( ) ∝ −5/3. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy-containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.
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.
The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning ...binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.
Determining the final spin of a black hole (BH) binary is a question of key importance in astrophysics. Modeling this quantity in general is made difficult by the fact that it depends on the ...seven-dimensional space of parameters characterizing the two initial black holes. However, in special cases, when symmetries can be exploited, the description can become simpler. For BH binaries with unequal masses but with equal spins which are aligned with the orbital angular momentum, we show that the use of recent simulations and basic but exact constraints derived from the extreme mass-ratio limit allow us to model this quantity with a simple analytic expression. Despite the simple dependence, the expression models very accurately all of the available estimates, with errors of a couple of percent at most. We also discuss how to use the fit to predict when a Schwarzschild BH is produced by the merger of two spinning BHs, when the total angular momentum of the spacetime "flips" sign, or under what conditions the final BH is "spun up" by the merger. Finally, we suggest an extension of the fit to include unequal-spin binaries, thus potentially providing a complete description of the final spin from the coalescence of generic BH binaries with spins aligned to the orbital angular momentum.
In addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear 'memory' effect, sourced by the emitted ...gravitational radiation. The memory grows significantly during the late-inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes (BHs) to evaluate the nonlinear memory during late-inspiral, merger, and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the BH ringdown. Counterintuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning BHs anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise ratio (S/N) for interferometric detectors. The largest memory offset, however, occurs for highly spinning BHs, with an estimated value of h tot 20 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements.
Using accurate numerical-relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1, and 3:1, we compute the gauge-invariant relation between the (reduced) binding energy E ...and the (reduced) angular momentum j of the system. We show that the relation E(j) is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity E(NR)(j) curve with the predictions of several analytic approximation schemes, we find that, while the canonically defined, nonresummed post-Newtonian-expanded E(PN)(j) relation exhibits large and growing deviations from E(NR)(j), the prediction of the effective one body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.
We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their ...kind and 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. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipolar jet that develops in a simulation constrained to 2D is crippled by a spiral instability and fizzles in full 3D. While multiple (magneto-)hydrodynamic instabilities may be present, our analysis suggests that the jet is disrupted by an m = 1 kink instability of the ultra-strong toroidal field near the rotation axis. Instead of an axially symmetric jet, a completely new, previously unreported flow structure develops. Highly magnetized spiral plasma funnels expelled from the core push out the shock in polar regions, creating wide secularly expanding lobes. We observe no runaway explosion by the end of the full 3D simulation 185 ms after bounce. At this time, the lobes have reached maximum radii of ~900 km.
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