Calibration of moving puncture simulations

Abstract

We present single and binary black-hole simulations that follow the ''moving-puncture'' paradigm of simulating black-hole spacetimes without excision, and use ''moving boxes'' mesh refinement. Focusing on binary black-hole configurations where the simulations cover roughly two orbits, we address five major issues determining the quality of our results: numerical discretization error, finite extraction radius of the radiation signal, physical appropriateness of initial data, gauge choice, and computational performance. We also compare results we have obtained with the BAM code described here with the independent LEAN code.

Erratum: Template bank for gravitational waveforms from coalescing binary black holes: Nonspinning binaries [Phys. Rev. DPRVDAQ1550-799877, 104017 (2008)]

“…Numerical simulations were performed with the BAM [11] and CCATIE [23] codes. Both codes evolve blackhole binaries using the 'moving-puncture' approach [7,8].…”

“…For equal-mass evolutions performed with the CCATIE code, parameters for quasi-circular orbit were determined by minimizing an effective potential for the binary [23,67,68]. For the unequal-mass simulations performed with the BAM code [15], initial momenta were specified by the 3PN-accurate quasi-circular formula given in Section VII of [11]. For the longer unequal-mass simulations performed with higher-order spatial finite-difference methods [37] and used for verification, the initial momenta were taken from a PN prescription that takes radiation reaction into account to reduce the initial eccentricity to below e ≈ 10 −3 [38].…”

“…Although various resummation methods, such as Padé [4] and effective-onebody (EOB) approaches [5], have been developed to extend the validity of the PN approximation, unambiguous waveforms in the merger stage must be calculated numerically in full general relativity. Recent breakthroughs in numerical relativity [6,7,8] have allowed many groups [6,7,8,9,10,11,12,13] to evolve BH binaries fully numerically for the last several orbits through the plunge to single BH formation. The field is now rapidly developing the capability to routinely evolve generic black-hole binary configurations in the comparable-mass regime, and to accurately extract the gravitational-wave signal.…”

Model waveform accuracy standards for gravitational wave data analysis

“…Several gravitational wave detectors [1][2][3] have now achieved a high enough level of sensitivity that the first astrophysical observations are expected to occur within the next few years. The numerical relativity community has also matured to the point that several groups are now computing model gravitational waveforms for the inspiral and merger of black hole and neutron star binary systems [4][5][6][7][8][9][10][11][12][13]. Beyond the pioneering work of Mark Miller [14] and Stephen Fairhurst [15], however, little effort has gone into thinking about the question of how accurate these model waveforms need to be.…”

Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

“…The late stage of the inspiral, corresponding to the final few orbits and merger of the binary, is highly dynamical and involves strong gravitational fields, and it must be handled by numerical relativity. Breakthroughs in numerical relativity have allowed a system of two inspiraling black holes to be evolved through merger and the ringdown of the remnant black hole [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”