Simulations of rotating neutron star collapse with the puncture gauge: end state and gravitational waveforms

We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the emission of radiation to the collapse dynamics using simplified spacetime diagrams, and discuss the similarity of the waveform structure with the one of black hole perturbation theory.Comment: 9 pages, 9 figure

Closed-form tidal approximants for binary neutron star gravitational waveforms constructed from high-resolution numerical relativity simulations

We construct closed-form gravitational waveforms (GWs) with tidal effects for the coalescence and merger of binary neutron stars. The method relies on a new set of eccentricity-reduced and high-resolution numerical relativity (NR) simulations and is composed of three steps. First, tidal contributions to the GW phase are extracted from the time-domain NR data. Second, those contributions are employed to fix high-order coefficients in an effective and resummed post-Newtonian expression. Third, frequency-domain tidal approximants are built using the stationary phase approximation. Our tidal approximants are valid from the low frequencies to the strong-field regime and up to merger. They can be analytically added to any binary black hole GW model to obtain a binary neutron star waveform, either in the time or in the frequency domain. This work provides simple, flexible, and accurate models ready to be used in both searches and parameter estimation of binary neutron star events

Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion

We improve the effective-one-body (EOB) description of nonspinning coalescing black hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios $q=(1,2,3,4,6)$. In particular, the comparison to NR data allows us to determine with high-accuracy ($\sim 10^{-4}$) the value of the main EOB radial potential: $A(u;\,\nu)$, where $u=GM/(R c^2)$ is the inter-body gravitational potential and $\nu=q/(q+1)^2$ is the symmetric mass ratio. We introduce a new technique for extracting from NR data an intrinsic measure of the phase evolution, ($Q_\omega(\omega)$ diagnostics). Aligning the NR-completed EOB quadrupolar waveform and the NR one at low frequencies, we find that they keep agreeing (in phase and amplitude) within the NR uncertainties throughout the evolution for all mass ratios considered. We also find good agreement for several subdominant multipoles without having to introduce and tune any extra parameters.Comment: 42 pages, 22 figures. Improved version, to appear in Phys. Rev. D. The EOB code will be freely available at eob.ihes.f

Binary black hole coalescence in the extreme-mass-ratio limit: Testing and improving the effective-one-body multipolar waveform

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses and M in the extreme-mass-ratio limit µ/M = v « 1. We focus on the transition from quasicircular inspiral to plunge, merger, and ringdown. We compare the EOB waveform to a Regge-Wheeler-Zerilli waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by a leading-order O(v) analytically resummed radiation reaction. The EOB and the Regge-Wheeler-Zerilli waveforms have an initial dephasing of about 5 X 10^(-4) rad and maintain then a remarkably accurate phase coherence during the long inspiral (~33 orbits), accumulating only about -2 X 10^(-3) rad until the last stable orbit, i.e. ΔØ/Ø~-5.95 X 10^(-6). We obtain such accuracy without calibrating the analytically resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for studies concerning the Laser Interferometer Space Antenna. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasicircular corrections in both the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasicircular parameters by requiring compatibility between EOB and Regge-Wheeler-Zerilli waveforms at the light ring. The resulting phase difference around the merger time is as small as ±0.015 rad, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasicircular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical-relativity waveforms

Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays

In this work we present a formulation of the Teukolsky equation for generic spin perturbations on the hyperboloidal and horizon penetrating foliation of Kerr recently proposed by Racz and Toth. An additional, spin-dependent rescaling of the field variable can be used to achieve stable, long-term, and accurate time-domain evolutions of generic spin perturbations. As an application (and a severe numerical test), we investigate the late-time decays of electromagnetic and gravitational perturbations at the horizon and future null infinity by means of 2+1 evolutions. As initial data we consider four combinations of (non-)stationary and (non-)compact-support initial data with a pure spin-weighted spherical harmonic profile. We present an extensive study of late time decays of axisymmetric perturbations. We verify the power-law decay rates predicted analytically, together with a certain "splitting" behaviour of the power-law exponent. We also present results for non-axisymmetric perturbations. In particular, our approach allows to study the behaviour of the late time decays of gravitational fields for nearly extremal and extremal black holes. For rapid rotation we observe a very prolonged, weakly damped, quasi-normal-mode phase. For extremal rotation the field at future null infinity shows an oscillatory behaviour decaying as the inverse power of time, while at the horizon it is amplified by several orders of magnitude over long time scales. This behaviour can be understood in terms of the superradiance cavity argument

Numerical relativity simulations of binary neutron stars

We present a new numerical relativity code designed for simulations of compact binaries involving matter. The code is an upgrade of the BAM code to include general relativistic hydrodynamics and implements state-of-the-art high-resolution-shock-capturing schemes on a hierarchy of mesh refined Cartesian grids with moving boxes. We test and validate the code in a series of standard experiments involving single neutron star spacetimes. We present test evolutions of quasi-equilibrium equal-mass irrotational binary neutron star configurations in quasi-circular orbits which describe the late inspiral to merger phases. Neutron star matter is modeled as a zero-temperature fluid; thermal effects can be included by means of a simple ideal-gas prescription. We analyze the impact that the use of different values of damping parameter in the Gamma-driver shift condition has on the dynamics of the system. The use of different reconstruction schemes and their impact in the post-merger dynamics is investigated. We compute and characterize the gravitational radiation emitted by the system. Self-convergence of the waves is tested, and we consistently estimate error-bars on the numerically generated waveforms in the inspiral phase

Constraint damping for the Z4c formulation of general relativity

One possibility for avoiding constraint violation in numerical relativity simulations adopting free-evolution schemes is to modify the continuum evolution equations so that constraint violations are damped away. Gundlach et. al. demonstrated that such a scheme damps low amplitude, high frequency constraint violating modes exponentially for the Z4 formulation of General Relativity. Here we analyze the effect of the damping scheme in numerical applications on a conformal decomposition of Z4. After reproducing the theoretically predicted damping rates of constraint violations in the linear regime, we explore numerical solutions not covered by the theoretical analysis. In particular we examine the effect of the damping scheme on low-frequency and on high-amplitude perturbations of flat spacetime as well and on the long-term dynamics of puncture and compact star initial data in the context of spherical symmetry. We find that the damping scheme is effective provided that the constraint violation is resolved on the numerical grid. On grid noise the combination of artificial dissipation and damping helps to suppress constraint violations. We find that care must be taken in choosing the damping parameter in simulations of puncture black holes. Otherwise the damping scheme can cause undesirable growth of the constraints, and even qualitatively incorrect evolutions. In the numerical evolution of a compact static star we find that the choice of the damping parameter is even more delicate, but may lead to a small decrease of constraint violation. For a large range of values it results in unphysical behavior.Comment: 13 pages, 24 figure

A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime

We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the code {\it Teukode} are presented. The code can efficiently deliver waveforms at future null infinity. As a first application of the method, we compute the gravitational waveforms from inspiraling and coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass black hole is modeled as a point particle whose dynamics is driven by an effective-one-body-resummed analytical radiation reaction force. We compare the analytical angular momentum loss to the gravitational wave angular momentum flux. We find that higher-order post-Newtonian corrections are needed to improve the consistency for rapidly spinning binaries. Close to merger, the subdominant multipolar amplitudes (notably the $m=0$ ones) are enhanced for retrograde orbits with respect to prograde ones. We argue that this effect mirrors nonnegligible deviations from circularity of the dynamics during the late-plunge and merger phase. We compute the gravitational wave energy flux flowing into the black hole during the inspiral using a time-domain formalism proposed by Poisson. Finally, a self-consistent, iterative method to compute the gravitational wave fluxes at leading-order in the mass of the particle is presented. For a specific case study with $\hat{a}$=0.9, a simulation that uses the consistent flux differs from one that uses the analytical flux by $\sim35$ gravitational wave cycles over a total of about $250$ cycles. In this case the horizon absorption accounts for about $+5$ gravitational wave cycles