Uncertainty in hybrid gravitational waveforms: Optimizing initial orbital frequencies for binary black-hole simulations

TL;DR

This paper introduces a method to estimate the uncertainty in hybrid gravitational waveforms from binary black holes, optimizing initial orbital frequencies for simulations without prior data, aiding future waveform modeling.

Contribution

A novel, prior-data-independent method for estimating waveform uncertainty and optimizing initial conditions in binary black-hole simulations.

Findings

Optimal initial frequencies depend linearly on binary mass.

Longer simulations or better approximations are needed for accurate parameter estimation.

Current simulations are insufficient for high-spin, comparable-mass systems.

Abstract

A general method is presented for estimating the uncertainty in hybrid models of gravitational waveforms from binary black-hole systems with arbitrary physical parameters, and thence the highest allowable initial orbital frequency for a numerical-relativity simulation such that the combined analytical and numerical waveform meets some minimum desired accuracy. The key strength of this estimate is that no prior numerical simulation in the relevant region of parameter space is needed, which means that these techniques can be used to direct future work. The method is demonstrated for a selection of extreme physical parameters. It is shown that optimal initial orbital frequencies depend roughly linearly on the mass of the binary, and therefore useful accuracy criteria must depend explicitly on the mass. The results indicate that accurate estimation of the parameters of stellar-mass black-hole binaries in Advanced LIGO data or calibration of waveforms for detection will require much longer numerical simulations than are currently available or more accurate post-Newtonian approximations -- or both -- especially for comparable-mass systems with high spin.