Mass$\unicode{x2013}$spin Re-Parameterization for Rapid Parameter Estimation of Inspiral Gravitational-Wave Signals

TL;DR

This paper introduces a new mass–spin re-parameterization for gravitational-wave parameter estimation that simplifies the posterior distribution, significantly improving the efficiency of MCMC sampling in binary neutron star analyses.

Contribution

The authors develop a novel mass–spin re-parameterization based on principal components of the Fisher matrix, enhancing MCMC efficiency in gravitational-wave source parameter estimation.

Findings

Re-parameterization improves MCMC efficiency by ~10 times for narrow-spin priors.

Re-parameterization improves MCMC efficiency by ~100 times for broad-spin priors.

Method assumes spins are aligned with orbital angular momentum.

Abstract

Estimating the source parameters of gravitational waves from compact binary coalescence(CBC) is a key analysis task in gravitational-wave astronomy. To deal with the increasing detection rate of CBC signals, optimizing the parameter estimation analysis is crucial. The analysis typically employs a stochastic sampling technique such as Markov Chain Monte Carlo(MCMC), where the source parameter space is explored and regions of high Bayesian posterior probability density are found. One of the bottlenecks slowing down the analysis is the non-trivial correlation between masses and spins of colliding objects, which makes the exploration of mass$\unicode{x2013}$spin space extremely inefficient. We introduce a new set of mass$\unicode{x2013}$spin sampling parameters which makes the posterior distribution to be simple in the new parameter space, regardless of the true values of the parameters. The new parameter combinations are obtained as the principal components of the Fisher matrix for the restricted 1.5 post-Newtonian waveform. Our re-parameterization improves the efficiency of MCMC by a factor of $\sim10$ for binary neutron star with narrow-spin prior ($|\vec{\chi}|<0.05$) and $\sim100$ with broad-spin prior ($|\vec{\chi}|<0.99$), under the assumption that the binary has spins aligned with its orbital angular momentum.