Red Noise Suppression in Pulsar Timing Array Data Using Adaptive Splines

Noise in Pulsar Timing Array (PTA) data is commonly modeled as a mixture of white and red noise components. While the former is related to the receivers, and easily characterized by three parameters (EFAC, EQUAD and ECORR), the latter arises from a mix of hard to model sources and, potentially, a stochastic gravitational wave background (GWB). Since their frequency ranges overlap, GWB search methods must model the non-GWB red noise component in PTA data explicitly, typically as a set of mutually independent Gaussian stationary processes having power-law power spectral densities. However, in searches for continuous wave (CW) signals from resolvable sources, the red noise is simply a component that must be filtered out, either explicitly or implicitly (via the definition of the matched filtering inner product). Due to the technical difficulties associated with irregular sampling, CW searches have generally used implicit filtering with the same power law model as GWB searches. This creates the data analysis burden of fitting the power-law parameters, which increase in number with the size of the PTA and hamper the scaling up of CW searches to large PTAs. Here, we present an explicit filtering approach that overcomes the technical issues associated with irregular sampling. The method uses adaptive splines, where the spline knots are included in the fitted model. Besides illustrating its application on real data, the effectiveness of this approach is investigated on synthetic data that has the same red noise characteristics as the NANOGrav 15-year dataset and contains a single non-evolving CW signal.