Bayesian search for gravitational wave bursts in pulsar timing array data

The nanohertz frequency band explored by pulsar timing arrays provides a unique discovery space for gravitational wave signals. In addition to signals from anticipated sources, such as those from supermassive black hole binaries, some previously unimagined sources may emit transient gravitational waves (a.k.a. bursts) with unknown morphology. Unmodeled transients are not currently searched for in this frequency band, and they require different techniques from those currently employed. Possible sources of such gravitational wave bursts in the nanohertz regime are parabolic encounters of supermassive black holes, cosmic string cusps and kinks, or other, as-yet-unknown phenomena. In this paper we present BayesHopperBurst, a Bayesian search algorithm capable of identifying generic gravitational wave bursts by modeling both coherent and incoherent transients as a sum of Morlet-Gabor wavelets. A trans-dimensional Reversible Jump Markov Chain Monte Carlo sampler is used to select the number of wavelets best describing the data. We test BayesHopperBurst on various simulated datasets including different combinations of signals and noise transients. Its capability to run on real data is demonstrated by analyzing data of the pulsar B1855+09 from the NANOGrav 9-year dataset. Based on a simulated dataset resembling the NANOGrav 12.5-year data release, we predict that at our most sensitive time-frequency location we will be able to probe gravitational wave bursts with a root-sum-squared amplitude higher than $\sim 5 \times 10^{-11}$ Hz$^{-1/2}$, which corresponds to $\sim 40 M_{\odot} c^2$ emitted in GWs at a fiducial distance of 100 Mpc.