Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes

Abstract

We present new techniqes for evolving binary black hole systems which allow the accurate determination of gravitational waveforms directly from the wave zone region of the numerical simulations. Rather than excising the black hole interiors, our approach follows the "puncture" treatment of black holes, but utilzing a new gauge condition which allows the black holes to move successfully through the computational domain. We apply these techniques to an inspiraling binary, modeling the radiation generated during the final plunge and ringdown. We demonstrate convergence of the waveforms and good conservation of mass-energy, with just over 3% of the system's mass converted to gravitional radiation.PACS numbers: 04.25. Dm, 04.30.Db, 04.70.Bw, 95.30.Sf, 97.60.Lf Coalescing comparable mass black hole binaries are prodigious sources of gravitational waves. The final merger of these systems, in which the black holes leave their quasicircular orbits and plunge together to produce a highly distorted black hole that "rings down" to a quiescent Kerr state, will produce a strong burst of gravitational radiation. Such mergers are expected to be among the strongest sources for ground-based gravitational wave detectors, which will observe the mergers of stellar-mass and intermediate mass black hole binaries, and the spacebased LISA, which will detect mergers of massive black hole binaries. Observations of these systems will provide an unprecedented look into the strong-field dynamical regime of general relativity. With the first-generation of ground-based interferometers reaching maturity and LISA moving forward through the formulation phase, the need for accurate merger waveforms has become urgent.Such waveforms can only be obtained through 3-D numerical relativity simulations of the full Einstein equations. While this has proven to be a very challenging undertaking, new developments allow an optimistic outlook. Full 3-D evolutions of binary black holes, in which regions within the horizons have been excised from the computational grid, have recently been carried out. Using co-rotating coordinates, so that the holes remain fixed on the grid as the system evolves, a binary has been evolved through a little more than a full orbit [1] as well as through a plunge, merger, and ringdown [2], though without being able to extract gravitational waveforms. More recently, a simulation in which excised black holes move through the grid in a single plunge-orbit, merger, and ringdown has been accomplished, with the calculation of a waveform [3].In this Letter, we report the results of new simulations of inspiraling binary black holes through merger and ringdown. These have been carried out using new techniques which allow the black holes to move through the coordinate grid without the need for excision [17].Using fixed mesh refinement, we are able to resolve both the dynamical region where the black holes inspiral (with length scales ∼ M , where M is the total system mass) and the outer regions where the gravitational waves propagate (leng...

Numerical method for binary black hole/neutron star initial data: Code test

“…For physically motivated excision conditions, one imposes apparent horizon or isolated horizon boundary condition to the conformal factor at the excised sphere so as these spheres become automatically horizons [30,31]. Alternatively one can use the puncture method to produce accurate initial data as the ones used in binary black holes evolutions [4,5,6,7,8], and black hole/neutron star binary simulations [32]. …”

“…Initial data set for binary black holes with a variety of black hole parameters, such as binary mass ratio, and black hole spins, or the binary black hole-neutron star data will become more useful considering the remarkable progress made recently for the inspiraling binary black holes simulations up to a few orbits near the innermost stable circular orbits [1,2,3,4,5,6,7,8]. Several groups have been achieved to construct binary black hole initial data successfully [9,10,11,12,13,14,15,16,17,18], (for earlier works, see [19]).…”

Approximate initial data for binary black holes

“…The past year, however, has seen dramatic progress, and at this point independent codes using very different approaches and techniques can reliably model the coalescence, merger and ring-down of binary black holes [17][18][19][20][21]. Some of these calculations [18,19,21] treat the black hole singularity with the so-called puncture method [22] (see also [23,24]). Given that puncture initial data for binary black holes are most easily constructed in the transversetraceless formalism (see [4] and compare [25,26]), this development has renewed some interest in transversetraceless initial data.…”

A Practical Guide to the Massive Black Hole Cosmic History

“…Under this basic assumption, Hughes and Blandford [175] found that, in general, coalescences of MBHs with random spin directions result in a broad remnant spin distribution; in particular, highly spinning MBHs tend to spin down. With the advent of numerical relativity [176][177][178], it is now possible to construct accurate mappings of initial-to-final BH spins following purely GW-driven coalescences [179]. In general, unless the two initial MBH spins and the binary orbital angular momentum are aligned, coalescences are unlikely to result in highly spinning MBHs.…”