Ensemble noise properties of the European Pulsar Timing Array

ABSTRACT The null hypothesis in Pulsar Timing Array (PTA) analyses includes assumptions about ensemble properties of pulsar time-correlated noise. These properties are encoded in prior probabilities for the amplitude and the spectral index of the power-law power spectral density of temporal correlations of the noise. Because multiple realizations of time-correlated noise processes are found in pulsars, these ensemble noise properties could and should be modelled in the full-PTA observations by parametrizing the respective prior distributions using the so-called hyperparameters. This approach is known as the hierarchical Bayesian inference. In this work, we introduce a new procedure for numerical marginalization over hyperparameters. The procedure may be used in searches for nanohertz gravitational waves and other PTA analyses to resolve prior misspecification at negligible computational cost. Furthermore, we infer the distribution of amplitudes and spectral indices of the power spectral density of spin noise and dispersion measure variation noise based on the observation of 25 millisecond pulsars by the European Pulsar Timing Array. Our results may be used for the simulation of realistic noise in PTAs.