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

¹ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université de Paris, CNRS, F-92190 Meudon, France
² Laboratoire de Physique et Chimie de l’Environnement et de l’Espace, Université d’Orléans/CNRS, 45071 Orléans Cedex 02, France
³ Observatoire Radioastronomique de Nançay, Observatoire de Paris, Université PSL, Université d’Orléans, CNRS, 18330 Nançay, France
⁴ IMCCE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Lille, 75014 Paris, France
⁵ Dept. of Materials and Production, Aalborg University, DK-9220 Aalborg Øst, Denmark
⁶ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany

^⋆ Corresponding author; guillaume.voisin@obspm.fr

Received: 3 September 2024
Accepted: 12 November 2024

Abstract

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.