Detecting super-Nyquist-frequency gravitational waves using a pulsar timing array

TL;DR

This paper proposes a novel method to detect gravitational waves with frequencies higher than the Nyquist limit of pulsar timing arrays by analyzing the white noise variance in timing residuals, demonstrated with simulated and real data.

Contribution

It introduces a new approach to identify super-Nyquist-frequency gravitational waves through their unique white noise signature in pulsar timing data, expanding detection capabilities beyond traditional limits.

Findings

No significant detection of super-Nyquist-frequency GWs in the datasets analyzed.

An all-sky sensitivity map for super-Nyquist GW sources was produced.

The minimum detectable GW strain at 10^-5 Hz is approximately 6.31×10^-11.

Abstract

The maximum frequency of gravitational waves (GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency ($f_{\rm{Ny}}$) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency $>$ $f_{\rm{Ny}}$ (super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data. Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5\% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is $\lambda_{\rm{s}}=-0.82$, $\beta_{\rm{s}}=-1.03$ (rad); the corresponding minimum GW strain is $h=6.31\times10^{-11}$ at $f=1\times10^{-5}$ Hz.