QuickGWecc: Fast Bayesian pipeline for searching eccentric binaries in pulsar timing array data

Recent pulsar timing array (PTA) results have provided evidence for the presence of a nanohertz gravitational wave (GW) background, most likely originating from a population of supermassive black hole binaries (SMBHBs). The next major milestone is the detection of continuous GWs (CGWs) from an individual SMBHB and the identification of its electromagnetic counterpart. Typically, searches for CGWs in PTA data assume binaries in circular orbits. However, theoretical studies indicate that binaries emitting GWs in the PTA frequency band may retain significant eccentricity. In this paper, we present a fast and efficient Bayesian pipeline to search for CGWs from individual SMBHBs in relativistic eccentric orbits in PTA datasets. Our approach extends the QuickCW framework for circular binaries, in which model parameters are divided into projection and shape parameters. Computational efficiency is achieved by performing many updates of the projection parameters for a fixed set of shape parameters, an operation that is orders of magnitude faster than updating the shape parameters. We validate the pipeline through both detection and upper-limit analyses of simulated PTA datasets. This framework makes the search for eccentric SMBHBs computationally feasible, even in the next-generation PTA datasets with many more pulsars.