Computationally efficient waveforms are of central importance for gravitational wave data analysis of inspiraling and coalescing compact binaries. We show that the postadiabatic (PA) approximation to the effective one-body (EOB) description of the binary dynamics, when pushed to high order, allows one to accurately and efficiently compute the waveform of coalescing binary neutron stars (BNSs) or black holes (BBHs) up to a few orbits before merger. This is accomplished bypassing the usual need of numerically solving the relative EOB dynamics described by a set of ordinary differential equations (ODEs). Under the assumption that radiation reaction is small, Hamilton's equations for the momenta can be solved analytically for given values of the relative separation. Time and orbital phase are then recovered by simple numerical quadratures. For the least adiabatic BBH case, equal-mass, quasiextremal spins antialigned with the orbital angular momentum, 6PA/8PA orders are able to generate waveforms that accumulate less than 10-3 rad of phase difference with respect to the complete EOB ones up to ∼3 orbits before merger. Analogous results hold for BNSs. The PA waveform generation is extremely efficient: for a standard BNS system from 10 Hz, a nonoptimized Matlab implementation of the TEOBResumS EOB model in the PA approximation is almost 100 times faster (∼0.09 s) than the corresponding C++ code based on a standard ODE solver. Once optimized further, our approach will allow us to (i) avoid the use of the fast, but often inaccurate, post-Newtonian inspiral waveforms, drastically reducing the impact of systematics due to inspiral waveform modeling, and (ii) alleviate the need of constructing EOB waveform surrogates to be used in parameter estimation codes.
Efficient effective one body time-domain gravitational waveforms
Rettegno P.Co-first
2019-01-01
Abstract
Computationally efficient waveforms are of central importance for gravitational wave data analysis of inspiraling and coalescing compact binaries. We show that the postadiabatic (PA) approximation to the effective one-body (EOB) description of the binary dynamics, when pushed to high order, allows one to accurately and efficiently compute the waveform of coalescing binary neutron stars (BNSs) or black holes (BBHs) up to a few orbits before merger. This is accomplished bypassing the usual need of numerically solving the relative EOB dynamics described by a set of ordinary differential equations (ODEs). Under the assumption that radiation reaction is small, Hamilton's equations for the momenta can be solved analytically for given values of the relative separation. Time and orbital phase are then recovered by simple numerical quadratures. For the least adiabatic BBH case, equal-mass, quasiextremal spins antialigned with the orbital angular momentum, 6PA/8PA orders are able to generate waveforms that accumulate less than 10-3 rad of phase difference with respect to the complete EOB ones up to ∼3 orbits before merger. Analogous results hold for BNSs. The PA waveform generation is extremely efficient: for a standard BNS system from 10 Hz, a nonoptimized Matlab implementation of the TEOBResumS EOB model in the PA approximation is almost 100 times faster (∼0.09 s) than the corresponding C++ code based on a standard ODE solver. Once optimized further, our approach will allow us to (i) avoid the use of the fast, but often inaccurate, post-Newtonian inspiral waveforms, drastically reducing the impact of systematics due to inspiral waveform modeling, and (ii) alleviate the need of constructing EOB waveform surrogates to be used in parameter estimation codes.
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