Explanation of the exceptionally strong timing noise of PSR J0337+1715 by a circum-ternary planet and consequences for gravity tests

Context. Timing of pulsar PSR J0337+1715 provides a unique opportunity to test the strong equivalence principle (SEP) with a strongly self-gravitating object. This is due to its unique situation in a triple stellar system with two white dwarfs. Aims. Our previous study suggested the presence of a strong low-frequency residual signal in the timing data, and we set out to model this signal on a longer dataset in order to determine its nature and improve accuracy. Methods. We considered three models: chromatic red noise, achromatic red noise, and a small planet in a hierarchical orbit with the triple stellar system. These models were implemented in our numerical timing model. We performed Bayesian inference of posterior distributions. Best fits were compared using information-theoretic criteria. Results. We rule out chromatic red noise from dispersion-measure variations. Achromatic red noise or a planet in Keplerian orbit provide the best fits. If the residual signal is red noise, then it appears exceptionally strong. When assuming the presence of a planet, we obtained a marginal detection of mutual interactions that allowed us to constrain its mass to ∼0.5 M_Moon as well as its inclination. The latter is intriguingly coincident with a Kozai resonance. We show that a longer observation span will ultimately lead to a clear signature of the planet model due to its mutual interactions with the triple system. We produce new limits on SEP violation: |Δ|< 1.5 · 10^-6 or |Δ|< 2.3 · 10^-6 at a 95% confidence level under the planet or red-noise hypothesis, respectively. This model dependence emphasises the need for additional data and model selection. As a by-product, we estimated a rather low supernova kick velocity of ∼110-125 km/s, strengthening the idea that it is a necessary condition for the formation of pulsar triple systems.