Periodicity search in the timing of the 25 millisecond pulsars from the second data release of the European Pulsar Timing Array

In this work, we investigated the presence of strictly periodic, as well as quasi-periodic signals, in the timing of the 25 millisecond pulsars (MSPs) from the European Pulsar Timing Array Second Data Release data set. This is especially interesting in the context of the recent hints of a gravitational wave background in these data, and the necessary further study of red noise timing processes, which are known to behave quasi-periodically in some normal pulsars. We used Bayesian timing models developed through the RUN ENTERPRISE pipeline: a strict periodicity was modelled as the influence of a planetary companion on the pulsar, while a quasi-periodicity was represented as a Fourier-domain Gaussian process. We found that neither model would clearly improve the timing models of the 25 MSPs in this data set. This implies that noise and parameter estimates are unlikely to be biased by the presence of a (quasi-)periodicity in the timing data. Nevertheless, the results for PSRs J1744−1134 and J1012+5307 suggest that the standard noise models for these pulsars may not be sufficient. We also measure upper limits for the projected masses of planetary companions around each of the 25 pulsars. The data of PSR J1909−3744 yielded the best mass limits, such that we constrained the 95 percentile to ∼ 2 × 10⁻⁴ M (roughly the mass of the dwarf planet Ceres) for orbital periods between 5 d and 17 yr. These are the best pulsar planet-mass limits to date.