Pulsar timing arrays and NANOGrav

Pulsar timing arrays use pulsars as galactic-scale detectors to observe nanoHertz gravitational waves. The target source for pulsar timing arrays is a stochastic background emitted by an ensemble of supermassive black hole binaries at the center of galaxies or early universe processes. Gravitational waves impart a spatially correlated offset on the arrival times of pulses, described by the Hellings and Downs curve. Using an array of dozens of pulsars and decade-long datasets, those correlations were recently observed. Our team works within the NANOGrav collaboration to analyze and interpret observational data as well as construct new data analysis methods and algorithms.

Analyzing decade-long data sets from dozens of pulsars is time- and resource-consuming. Caltech graduate student Sophie Hourihane led a study that proposed a faster but still accurate alternative. Rather than analyzing the data with a computationally expensive model that explicitly includes spatial correlations, we instead employ an approximate model and then reweight the posterior to the full, expensive model. Through extensive simulations, Hourihane validated the accuracy and computational gains of this approach. The plot exemplifies the method and its robustness, now routinely used on real data.

Unlike LIGO which observes individual compact binary mergers, NANOGrav observes a stochastic signal that is the combination of individual signals from numerous sources. Determining the source origin of this stochastic signal is challenging, since to date we can only measure its spectral shape, namely its amplitude and the slope of its spectrum. Led by Caltech postdoctoral scholar Pat Meyers, we proposed a method to assess whether our models for the signal spectrum and spatial correlations are robust. Based on posterior predictive checks, our method compares the observed data to predicted data.

Having validated posterior predictive checks on simulated data, we turned to the real NANOGrav data in which a stochastic signal has been detected. Meyers led a study as part of the NANOGrav collaboration using the most up-to-date dataset. We showed that our interpretation of the signal spectral shape (its amplitude and slope) is robust, as there is no evidence in the data for a deviation from a simple power-law. Moreover, we confirmed the presence of the crucial spatial correlations, the key signature of a gravitational-wave signal in pulsar timing array data.