Variance in PTA Sensitivity Curves Due to Uncertainty in Gravitational Wave Background

Pulsar timing arrays (PTAs) use radio astronomy for gravitational wave (GW) detections in the nanohertz frequency band by precisely measuring the arrival times of millisecond pulsars. In June of 2023, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration and PTAs around the world reported evidence for the detection of the gravitational wave background (GWB). Further progress in GW detection is hindered by noise in the observational data. GW sensitivity curves provide a metric on the current sensitivity of PTA detectors as well as future sensitivity. through the implementation of noise models in both the time and Fourier domain. The parameters used in the noise models are generated through Bayesian inference, resulting in thousands of parameter samples leading to uncertainty in the resulting sensitivity curves. Standard methods for computing sensitivity circumvent this through the use of maximum posterior noise model parameters. However, sensitivity curves currently only use the maximum a posteriori noise. For constant noise this is sufficient but for time-dependent noise, this is an idealization. We use the Fourier Mode Formalism and the Fisher Information Matrix to analyze the variance in GW sensitivity curves due to model and forecast parameter uncertainty. These efforts will aid in our ability to tune PTAs for optimal science as we move into the detection era.