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

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.