The Scaling of the RMS with Dwell Time in NANOGrav Pulsars

TL;DR

This study analyzes the noise scaling in pulsar timing residuals within NANOGrav data, confirming most pulsars follow the inverse square root law, which informs optimal observation strategies for gravitational wave detection.

Contribution

It provides empirical evidence that most NANOGrav pulsars' residuals scale with the inverse square root of dwell time, supporting improved observation planning for PTA-based GW detection.

Findings

15 of 17 pulsars follow the inverse square law

Most pulsars can be observed up to eight times longer without loss of noise scaling

Comparison with red noise pulsar highlights typical noise behavior

Abstract

Pulsar Timing Arrays (PTAs) are collections of well-timed millisecond pulsars that are being used as detectors of gravitational waves (GWs). Given current sensitivity, projected improvements in PTAs and the predicted strength of the GW signals, the detection of GWs with PTAs could occur within the next decade. One way we can improve a PTA is to reduce the measurement noise present in the pulsar timing residuals. If the pulsars included in the array display uncorrelated noise, the root mean square (RMS) of the timing residuals is predicted to scale as $\mathrm{T}^{-1/2}$, where T is the dwell time per observation. In this case, the sensitivity of the array can be increased by increasing T. We studied the 17 pulsars in the five year North American Nanohertz Observatory for Gravitational Waves (NANOGrav) data set to determine if the noise in the timing residuals of the pulsars observed was consistent with this property. For comparison, we performed the same analysis on PSR B1937+21, a pulsar that is known to display red noise. With this method, we find that 15 of the 17 NANOGrav pulsars have timing residuals consistent with the inverse square law. The data also suggest that these 15 pulsars can be observed for up to eight times as long while still exhibiting an RMS that scales as root T.