Gravitational-wave astronomy with an uncertain noise power spectral density

TL;DR

This paper addresses the challenge of accounting for uncertainty in noise power spectral density estimation in gravitational-wave data analysis, deriving the correct likelihood for median average estimates and examining their impact on astrophysical inferences.

Contribution

It derives the proper likelihood function for median average noise PSD estimation and evaluates its effects on gravitational-wave parameter inference.

Findings

Simulated Gaussian noise matches predicted distributions.

Real GW data around GW151012 is consistent with stationary-Gaussian noise.

Different PSD estimation methods influence astrophysical inferences.

Abstract

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.