A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data

Propagation effects are one of the main sources of noise in high-precision pulsar timing. For pulsars below an ecliptic latitude of $5^\circ$, the ionised plasma in the solar wind can introduce dispersive delays of order 100 microseconds around solar conjunction at an observing frequency of 300 MHz. A common approach to mitigate this assumes a spherical solar wind with a time-constant amplitude. However, this has been shown to be insufficient to describe the solar wind. We present a linear, Gaussian-process piecewise Bayesian approach to fit a spherical solar wind of time-variable amplitude, which has been implemented in the pulsar software run_enterprise. Through simulations, we find that the current EPTA+InPTA data combination is not sensitive to such variations; however, solar wind variations will become important in the near future with the addition of new InPTA data and data collected with the low-frequency LOFAR telescope. We also compare our results for different high-precision timing datasets (EPTA+InPTA, PPTA, and LOFAR) of three millisecond pulsars (J0030$+$0451, J1022$+$1001, J2145$-$0450), and find that the solar-wind amplitudes are generally consistent for any individual pulsar, but they can vary from pulsar to pulsar. Finally, we compare our results with those of an independent method on the same LOFAR data of the three millisecond pulsars. We find that differences between the results of the two methods can be mainly attributed to the modelling of dispersion variations in the interstellar medium, rather than the solar wind modelling.