We introduce a highly-parallelizable architecture for estimating parameters of compact binary coalescence using gravitational-wave data and waveform models. Using a spherical harmonic mode decomposition, the waveform is expressed as a sum over modes
that depend on the intrinsic parameters (e.g. masses) with coefficients that depend on the observer dependent extrinsic parameters (e.g. distance, sky position). The data is then prefiltered against those modes, at fixed intrinsic parameters, enabling efficiently evaluation of the likelihood for generic source positions and orientations, independent of waveform length or generation time. We efficiently parallelize our intrinsic space calculation by integrating over all extrinsic parameters using a Monte Carlo integration strategy. Since the waveform generation and prefiltering happens only once, the cost of integration dominates the procedure. Also, we operate hierarchically, using information from existing gravitational-wave searches to identify the regions of parameter space to emphasize in our sampling. As proof of concept and verification of the result, we have implemented this algorithm using standard time-domain waveforms, processing each event in less than one hour on recent computing hardware. For most events we evaluate the marginalized likelihood (evidence) with statistical errors of less than about 5%, and even smaller in many cases. With a bounded runtime independent of the waveform model starting frequency, a nearly-unchanged strategy could estimate NS-NS parameters in the 2018 advanced LIGO era. Our algorithm is usable with any noise curve and existing time-domain model at any mass, including some waveforms which are computationally costly to evolve.
Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binarys nature and inspiral kinematics. Using the lalinference_mcmc Markov-chain Monte Carlo parameter estimation code, we use two fiducial exa
mples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Even for precessing binaries, we show the performance of detailed parameter estimation can be estimated by effective estimates: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. We use detailed and effective approaches to show higher harmonics provide nonzero but small local improvement when estimating the parameters of precessing BH-NS binaries. That said, we show higher harmonics can improve parameter estimation accuracy for precessing binaries ruling out approximately-degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as reliable component masses and the precise orientation of a precessing short gamma ray burst progenitor relative to the line of sight. Effective estimates may provide a simple way to estimate trends in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly-independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space.
Using the texttt{lalinference} Markov-chain Monte Carlo parameter estimation code, we examine two distinct nonprecessing black hole-neutron star (BH-NS) binaries with and without higher-order harmonics. Our simulations suggest that higher harmonics p
rovide a minimal amount of additional information, principally about source geometry. Higher harmonics do provide disproportionately more information than expected from the signal power. Our results compare favorably to the effective Fisher matrix approach. Extrapolating using analytic scalings, we expect higher harmonics will provide little new information about nonprecessing BH-NS binaries at the signal amplitudes expected for the first few detections. Any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here ($V/V_{rm prior}$ and $D_{KL}$) to assess whether new physics is accessible (e.g., modifications of gravity; spin-orbit misalignment) and if so precisely what information those new parameters provide. For astrophysicists, we provide a concrete illustration of how well parameters of a BH-NS binary can be measured, relevant to the astrophysical interpretation of coincident EM and GW events (e.g., short GRBs). For our fiducial initial-detector example, the individual masses can be determined to lie between $7.11-11.48 M_odot$ and $1.77-1.276M_odot$ at greater than 99% confidence, accounting for unknown BH spin. Assuming comparable control over waveform systematics, future measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions.
