Null stream methods for resolvable pulsar timing array signals

Pulsar Timing Arrays (PTAs) are sensitive to nanohertz gravitational waves (GWs), which affect the pulse travel times between pulsars and the Earth. The most promising sources are super massive black hole binaries, some of which are expected to be detected as resolvable signals in the not-too-distant future. In this work, we develop a Bayesian method for localising these signals using null streams. Null streams are combinations of data from different detectors in which the GW signal from a particular direction is cancelled. Applying our method to idealised, simulated data, we assess the localisation capabilities of current PTAs and show the merit of combining data from different collaborations. For future multi-messenger astronomy with low frequency GWs and electromagnetic observations, it is crucial to identify the galaxy that hosts a detected binary. We develop a method that combines localisation information, a posterior on the signal's amplitude, and galaxy properties to significantly reduce the number of candidate hosts in a galaxy catalogue. We extend the null-stream method to data with arbitrary sampling times. Exploiting the null-stream property that separates dependencies on the source location and on the GW-model parameters, we construct a likelihood that is independent of the GW model