Regularizing the Pulsar Timing Array likelihood: A path towards Fourier Space

The recent announcement of evidence for a stochastic background of gravitational waves (GWB) in pulsar timing array (PTA) data has piqued interest across the scientific community. A combined analysis of all currently available data holds the promise of confirming the announced evidence as a solid detection of a GWB. However, the complexity of individual pulsar noise models and the variety of modeling tools used for different types of pulsars present significant challenges for a truly unified analysis. In this work we propose a novel approach to the analysis of PTA data: first a posterior distribution over Fourier modes is produced for each pulsar individually. Then, in a global analysis of all pulsars these posterior distributions can be re-used for a GWB search, which retains all information regarding the signals of interest without the added complexity of the underlying noise models or implementation differences. This approach facilitates combining radio and gamma-ray pulsar data, while reducing the complexity of the model and of its implementations when carrying out a GWB search with PTA data.