Rush the inspiral: efficient Effective One Body time-domain gravitational waveforms

Computationally efficient waveforms are of central importance for gravitational wave data analysis of inspiralling and coalescing compact binaries. We show that the post-adiabatic (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, the Hamilton's equations for the momenta can be solved {\it 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, quasi-extremal spins anti-aligned 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 $\sim 3$ orbits before merger. Analogous results hold for BNSs. The PA waveform generation is extremely efficient: for a standard BNS system from 10Hz, a nonoptimized Matlab implementation of the TEOBResumS EOB model in the PA approximation is more than 100 times faster ($\sim 0.09$ sec) than the corresponding $C^{++}$ code based on a standard ODE solver. Once optimized further, our approach will allow 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 modelling; (ii) alleviate the need of constructing EOB waveform surrogates to be used in parameter estimation codes.