Impact of quasi-periodic and steep-spectrum timing noise on the measurement of pulsar timing parameters

Timing noise in pulsars is often modelled with a Fourier-basis Gaussian process that follows a power law with periodic boundary conditions on the observation time, Tspan. However, the actual noise processes can extend well below 1/Tspan, and many pulsars are known to exhibit quasi-periodic timing noise. In this paper, we investigate several adaptions that try to account for these differences between the observed behaviour and the simple power-law model. First, we propose to include an additional term that models the quasi-periodic spin-down variations known to be present in many pulsars. Secondly, we show that a Fourier basis of 1/2Tspan can be more suited for estimating long-term timing parameters such as the spin frequency second derivative (F2), and is required when the exponent of the power spectrum is greater than ∼4. We also implement a Bayesian version of the generalized least-squares ‘Cholesky’ method which has different limitations at low frequency, but find that there is little advantage over Fourier-basis methods. We apply our quasi-periodic spin-down model to a sample of pulsars with known spin-down variations and show that this improves parameter estimation of F2 and proper motion for the most pathological cases, but in general the results are consistent with a power-law model. The models are all made available through the run_enterprise software package.