Engineering topics

Kidder, Lawrence E

Publications and source records attributed to Kidder, Lawrence E.

5 records

DOE OSTI2011

Reducing orbital eccentricity of precessing black-hole binaries

Building initial conditions for generic binary black-hole evolutions which are not affected by initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists of evolving the binary black hole for a couple of orbits, estimating the resulting eccentricity, and then restarting the simulation with corrected 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. For single-spin binary black holes these oscillations are a direct consequence of monopole-quadrupole interactions. However, spin-induced oscillations occur at approximately twice the orbital frequency, and therefore can be distinguished and disentangled from the initial spurious eccentricity which occurs at approximately the orbital frequency. Taking this into account, we develop a new eccentricity-removal procedure based on the derivative of the orbital frequency and find that it is rather successful in reducing the eccentricity measured in the orbital frequency to values less than 10{sup -4} 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 l=2, m=2 mode.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

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

The spin of black holes in black hole-neutron star binaries can have a strong influence on the merger dynamics and the post-merger 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 black hole-neutron star mergers with misaligned black hole spin. We vary the spin magnitude from a{sub BH}/M{sub BH}=0 to a{sub BH}/M{sub BH}=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 deg. for a{sub BH}/M{sub BH}=0.5. We restrict our study to 3 ratio 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 post-merger accretion disk, but only for angles greater than {approx_equal}40 deg. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes {approx_equal}100 ms. 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 time scale 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

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 pseudospectral 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 semidiscrete 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 multidomain 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonprecessing, 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, nonprecessing 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 radian and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin antialigned case, these differences can be reduced to 0.13 radian and 1% during inspiral and plunge, and to 0.4 radian 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 antialigned 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 30M{sub {center_dot}-}200M{sub {center_dot}}. 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 antialigned 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.

79 ASTRONOMY AND ASTROPHYSICS↗