arXiv subjects

Lawrence E. Kidder

Publications and source records attributed to Lawrence E. Kidder.

At least 163 records · Page 9Linked to original sources

arXiv2013

First direct comparison of non-disrupting neutron star-black hole and binary black hole merger simulations

We present the first direct comparison of numerical simulations of neutron star-black hole and black hole-black hole mergers in full general relativity. We focus on a configuration with non spinning objects and within the most likely range of mass ratio for neutron star-black hole systems (q=6). In this region of the parameter space, the neutron star is not tidally disrupted prior to merger, and we show that the two types of mergers appear remarkably similar. The effect of the presence of a neutron star on the gravitational wave signal is not only undetectable by the next generation of gravitational wave detectors, but also too small to be measured in the numerical simulations: even the plunge, merger and ringdown signals appear in perfect agreement for both types of binaries. The characteristics of the post-merger remnants are equally similar, with the masses of the final black holes agreeing within dM< 5 10^{-4}M_BH and their spins within da< 10^{-3}M_BH. The rate of periastron advance in the mixed binary agrees with previously published binary black hole results, and we use the inspiral waveforms to place constraints on the accuracy of our numerical simulations independent of algorithmic choices made for each type of binary. Overall, our results indicate that non-disrupting neutron star-black hole mergers are exceptionally well modeled by black hole-black hole mergers, and that given the absence of mass ejection, accretion disk formation, or differences in the gravitational wave signals, only electromagnetic precursors could prove the presence of a neutron star in low-spin systems of total mass ~10Msun, at least until the advent of gravitational wave detectors with a sensitivity comparable to that of the proposed Einstein Telescope.

gr-qc↗

arXiv2013

Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism

We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree with the EOB waveforms recently calibrated to numerical-relativity waveforms. Without recalibrating the EOB model, we then compare EOB and post-Newtonian precessing waveforms to two numerical-relativity waveforms produced by the Caltech-Cornell-CITA collaboration. The numerical waveforms are strongly precessing and have 35 and 65 gravitational-wave cycles. We find a remarkable agreement between EOB and numerical-relativity precessing waveforms and spins' evolutions. The phase difference is ~ 0.2 rad at merger, while the mismatches, computed using the advanced-LIGO noise spectral density, are below 2% when maximizing only on the time and phase at coalescence and on the polarization angle.

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arXiv2013

Massive disk formation in the tidal disruption of a neutron star by a nearly extremal black hole

Black hole-neutron star (BHNS) binaries are important sources of gravitational waves for second-generation interferometers, and BHNS mergers are also a proposed engine for short, hard gamma-ray bursts. The behavior of both the spacetime (and thus the emitted gravitational waves) and the neutron star matter in a BHNS merger depend strongly and nonlinearly on the black hole's spin. While there is a significant possibility that astrophysical black holes could have spins that are nearly extremal (i.e. near the theoretical maximum), to date fully relativistic simulations of BHNS binaries have included black-hole spins only up to $S/M^2$=0.9, which corresponds to the black hole having approximately half as much rotational energy as possible, given the black hole's mass. In this paper, we present a new simulation of a BHNS binary with a mass ratio $q=3$ and black-hole spin $S/M^2$=0.97, the highest simulated to date. We find that the black hole's large spin leads to the most massive accretion disk and the largest tidal tail outflow of any fully relativistic BHNS simulations to date, even exceeding the results implied by extrapolating results from simulations with lower black-hole spin. The disk appears to be remarkably stable. We also find that the high black-hole spin persists until shortly before the time of merger; afterwards, both merger and accretion spin down the black hole.

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arXiv2013

Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes

Simulations of binary black hole systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions inside the black holes. It is imperative that the excision boundaries are outflow boundaries with respect to the hyperbolic evolution equations used in the simulation. We employ a time-dependent mapping between the fixed computational frame and the inertial frame through which the black holes move. The time-dependent parameters of the mapping are adjusted throughout the simulation by a feedback control system in order to follow the motion of the black holes, to adjust the shape and size of the excision surfaces so that they remain outflow boundaries, and to prevent large distortions of the grid. We describe in detail the mappings and control systems that we use. We show how these techniques have been essential in the evolution of binary black hole systems with extreme configurations, such as large spin magnitudes and high mass ratios, especially during the merger, when apparent horizons are highly distorted and the computational domain becomes compressed. The techniques introduced here may be useful in other applications of partial differential equations that involve time-dependent mappings.

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arXiv2013

Suitability of hybrid gravitational waveforms for unequal-mass binaries

This article studies sufficient accuracy criteria of hybrid post-Newtonian (PN) and numerical relativity (NR) waveforms for parameter estimation of strong binary black-hole sources in second- generation ground-based gravitational-wave detectors. We investigate equal-mass non-spinning binaries with a new 33-orbit NR waveform, as well as unequal-mass binaries with mass ratios 2, 3, 4 and 6. For equal masses, the 33-orbit NR waveform allows us to recover previous results and to extend the analysis toward matching at lower frequencies. For unequal masses, the errors between different PN approximants increase with mass ratio. Thus, at 3.5PN, hybrids for higher-mass-ratio systems would require NR waveforms with many more gravitational-wave (GW) cycles to guarantee no adverse impact on parameter estimation. Furthermore, we investigate the potential improvement in hybrid waveforms that can be expected from 4th order post-Newtonian waveforms, and find that knowledge of this 4th post-Newtonian order would significantly improve the accuracy of hybrid waveforms.

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arXiv2013

Black hole-neutron star mergers at realistic mass ratios: Equation of state and spin orientation effects

Black hole-neutron star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the post-merger remnant are very sensitive to the parameters of the binary. In this paper, we study the impact of the radius of the neutron star and the alignment of the black hole spin for systems within the range of mass ratio currently deemed most likely for field binaries (M_BH ~ 7 M_NS) and for black hole spins large enough for the neutron star to disrupt (J/M^2=0.9). We find that: (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0.3M_NS to 0.1M_NS for changes of only 2 km in the NS radius; (ii) 0.01-0.05M_sun of unbound material can be ejected with kinetic energy >10^51 ergs, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable optical and radio afterglows. (iii) Only a small fraction (<3%) of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star. (iv) A misaligned black hole spin works against disk formation, with less neutron star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks (v>300 km/s) can be given to the final black hole as a result of a precessing BHNS merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

gr-qc↗

arXiv2013

Precession-tracking coordinates for simulations of compact-object-binaries

Binary black hole simulations with black hole excision using spectral methods require a coordinate transformation into a co-rotating coordinate system where the black holes are essentially at rest. This paper presents and discusses two coordinate transformations that are applicable to precessing binary systems, one based on Euler angles, the other on quaternions. Both approaches are found to work well for binaries with moderate precession, i.e. for cases where the orientation of the orbital plane changes by much less than 90 degrees. For strong precession, performance of the Euler-angle parameterization deteriorates, eventually failing for a 90 degree change in orientation because of singularities in the parameterization ("gimbal lock"). In contrast, the quaternion representation is invariant under an overall rotation, and handles any orientation of the orbital plane as well as the Euler-angle technique handles non-precessing binaries.

gr-qc↗

arXiv2012

Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?

Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is \emph{not} explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within $δϕ\lesssim 10^{-2}$ radians and the amplitudes agree to within $δA/A \lesssim 5 \times 10^{-3}$, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in $10^{5}

gr-qc↗

arXiv2012

Black hole-neutron star mergers for 10 solar mass black holes

General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes (less than 7 solar mass), even though population synthesis models indicate that a majority of mergers might involve more massive black holes (10 solar mass or more). We present the first general relativistic simulations of black hole-neutron star mergers with 10 solar mass black holes. For massive black holes, the tidal forces acting on the neutron star are usually too weak to disrupt the star before it reaches the innermost stable circular orbit of the black hole. Varying the spin of the black hole in the range a/M = 0.5-0.9, we find that mergers result in the disruption of the star and the formation of a massive accretion disk only for large spins a/M>0.7-0.9. From these results, we obtain updated constraints on the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as a function of the mass and spin of the black hole. We also discuss the dependence of the gravitational wave signal on the black hole parameters, and provide waveforms and spectra from simulations beginning 7-8 orbits before merger.

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arXiv2012

Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism

We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2,2) mode and of the subleading modes (2,1), (3,3), (4,4) and (5,5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2,2) mode between model and numerical simulation remains below 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2,2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch, between the EOB and numerical-relativity polarizations which include only the (2,2) mode is smaller than 0.2% for binaries with total mass 20-200 Msun and mass ratios 1, 2, 3, 4, and 6. When numerical-relativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than 50Msun are considered, the mismatch for mass ratio 6 (1) can be as high as 5% (0.2%) when only the EOB (2,2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than 50Msun the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.

gr-qc↗

arXiv2012

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.

gr-qc↗

arXiv2011

Reducing orbital eccentricity of precessing black-hole binaries

Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists in evolving the binary for a couple of orbits, estimating the eccentricity, and then correcting the initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. However, spin-induced oscillations occur at approximately twice the orbital frequency, therefore they can be distinguished from the initial spurious eccentricity, which occurs at approximately the orbital frequency. We develop a new removal procedure based on the derivative of the orbital frequency and find that it is successful in reducing the eccentricity measured in the orbital frequency to less than 0.0001 when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5 and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant mode.

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arXiv2011

Black hole-neutron star mergers: effects of the orientation of the black hole spin

The spin of black holes in black hole-neutron star (BHNS) binaries can have a strong influence on the merger dynamics and the postmerger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of BHNS mergers with misaligned black hole spin. We vary the spin magnitude from a/m=0 to a/m=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 degrees for a/m=0.5. We restrict our study to 3:1 mass ratio systems and use a simple Gamma-law equation of state. We find that the misalignment angle has a strong effect on the mass of the postmerger accretion disk, but only for angles greater than ~ 40 degrees. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes ~ 100ms. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole's spin axis. This will cause the disk to precess, but on a timescale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole.

astro-ph.HE↗

arXiv2010

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.

gr-qc↗

arXiv2010

Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations

We compare different methods of computing the orbital eccentricity of quasi-circular binary black hole systems using the orbital variables and gravitational wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of non-spinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.

gr-qc↗

arXiv2010

Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.

gr-qc↗

arXiv2010

Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200Ms. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

gr-qc↗

arXiv2009

Equation of state effects in black hole-neutron star mergers

The merger dynamics of a black hole-neutron star (BHNS) binary is influenced by the neutron star equation of state (EoS) through the latter's effect on the neutron star's radius and on the character of the mass transfer onto the black hole. We study these effects by simulating a number of BHNS binaries in full general relativity using a mixed pseudospectral/finite difference code. We consider several models of the neutron star matter EoS, including Gamma=2 and Gamma=2.75 polytropes and the nuclear-theory based Shen EoS. For models using the Shen EoS, we consider two limits for the evolution of the composition: source-free advection and instantaneous beta-equilibrium. To focus on EoS effects, we fix the mass ratio to 3:1 and the initial aligned black hole spin to a/m=0.5 for all models. We confirm earlier studies which found that more compact stars create a stronger gravitational wave signal but a smaller postmerger accretion disk. We also vary the EoS while holding the compaction fixed. All mergers are qualitatively similar, but we find signatures of the EoS in the waveform and in the tail and disk structures.

astro-ph.HE↗