The Impact of Tidal Migration of Hot Jupiters on the Rotation of Sun-like Main-sequence Stars

TL;DR

This study models how tidal interactions and magnetic braking influence the rotation of Sun-like stars hosting hot Jupiters, revealing how planetary migration and engulfment affect stellar spin over time.

Contribution

It introduces a comprehensive grid of stellar models incorporating tidal effects, magnetic braking, and initial conditions to analyze star-planet interactions across various parameters.

Findings

Stars with inward migrating planets spin faster before engulfment.

Post-engulfment, stars with thick convective envelopes return to normal rotation faster.

Stars with thinner envelopes remain faster rotators for longer periods.

Abstract

The tidal interactions of planets affect the stellar evolutionary status and the constraint of their physical parameters by gyrochronology. In this work, we incorporate the tidal interaction and magnetic braking of the stellar wind into MESA and calculate a large grid of 25000 models, covering planets with masses of 0.1-13.0$\,$$M_{\mathrm{J}}$ with different orbital distances that orbit late-type stars of different metallicities. We also explore the effect of different stellar initial rotations on the tidal interactions. Our results show that in the case of tidal inward migration, the stellar rotation periods are always lower than that of the star without planet before the planet is engulfed and the difference in the rotation period of its host star always increases with time. After the planet is engulfed, the stellar rotation periods are still lower than that of star without planet, but the difference of periods can be quickly eliminated if the star has a thick convective envelope(smaller mass and larger metallicity), regardless of the mass of the planet and the initial rotation period of the star. In the case of stars with thinner convective envelopes(larger mass and smaller metallicity), the stars will be spined up and remain the faster rotation in a long time. Meanwhile, the planet is easily swallowed and the period differences are large if the initial rotation period of its host star is higher. Final, we also study the evolution of WASP-19 and estimate the range of tidal quality parameter $Q'_{*} = (4.6 \pm 0.9) \times 10^{6}$ and initial semi-major axis as $(0.035 \pm 0.004)$$\,$au.