A fast joint analysis for stochastic signals and individual SMBHBs in PTA datasets via direct sampling of a Fourier basis

The analysis of pulsar timing array data has provided evidence for a stochastic gravitational wave background (SGWB). If the background is realized through a population of supermassive black hole binaries, then continuous wave (CW) signals should become resolvable as more data is collected. However, joint SGWB + CW models require many expensive likelihood evaluations to effectively explore the high-dimensional parameter space. Here we present a new approach which extends the pseudo-Fourier basis method, previously applied to the SGWB, to also include CW signals. Key elements of the method are that the likelihood evaluations are per-pulsar, avoiding expensive operations on large matrices, and the templates for individual binaries can be computed analytically or using fast Fourier methods on a sparsely sampled grid of time samples, resulting in a faster analysis.