State-space algorithm for detecting the nanohertz gravitational wave background

TL;DR

This paper introduces a computationally efficient state-space algorithm utilizing a non-linear Kalman filter and nested sampling to detect the nanohertz gravitational wave background in pulsar timing array data, demonstrating high accuracy and speed on synthetic datasets.

Contribution

The paper presents a novel state-space framework with a non-linear Kalman filter for SGWB detection, extending previous methods and enabling rapid, accurate analysis of PTA data.

Findings

Distinguishes SGWB from noise for $A_{gw} \\geq 3 \\times 10^{-14}$

Recovers full posterior distributions accurately

Evaluates likelihood in under 0.1 seconds on standard CPU

Abstract

The stochastic gravitational wave background (SGWB) can be observed in the nanohertz band using a pulsar timing array (PTA). Here a computationally efficient state-space framework is developed for analysing SGWB data, in which the stochastic gravitational wave strain at Earth is tracked with a non-linear Kalman filter and separated simultaneously from intrinsic, achromatic pulsar spin wandering. The filter is combined with a nested sampler to estimate the parameters of the model, and to calculate a Bayes factor for selecting between models with and without a SGWB. The procedure extends previous state-space formulations of PTA data analysis applied to individually resolvable binary black hole sources. The performance of the new algorithm is tested on synthetic data from the first International PTA Mock Data Challenge. It is shown that the algorithm distinguishes a SGWB from pure noise for $A_{\rm gw} \geq 3 \times 10^{-14}$, where $A_{\rm gw}$ denotes the standard normalization factor for a power spectral density with power-law exponent $-13/3$. Additional, systematic validation tests are also performed with synthetic data generated independently by adjusting the injected parameters to cover astrophysically plausible ranges. Full posterior distributions are recovered and tested for accuracy. The state-space procedure is memory-light and evaluates the likelihood for a standard-sized PTA dataset in $\lesssim 10^{-1}$ s without optimization on a standard central processing unit.