Simulations of Binary Black Hole Mergers Using Spectral Methods

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Abstract

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly ``generic'' systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4 M^2) pointing in various directions.

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Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case

Achamveedu Gopakumar, Mark Hannam, Bernd Brügmann … (2007)

We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches \(M\omega = 0.1\), the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal-mass case to 12% when the black holes' spins are \(S_i/M_i^2 = 0.85\). Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.