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

Abstract

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. 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. 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. 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 $ 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: $| $ or $| $ at a 95<!PCT!> 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 $ km/s$, strengthening the idea that it is a necessary condition for the formation of pulsar triple systems.