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Constraints on the tidal dissipation factor of a main sequence star: The case of OGLE-TR-56b

Institution:	1. Departamento de Ciencias de la Tierra y del Medio Ambiente, Universidad de Alicante, Campus San Vicente del Raspeig, 03690 San Vicente del Raspeig, Alicante, Spain;2. Instituto Geológico y Minero de España (IGME), Calle Ríos Rosas, 23. 28003 Madrid, Spain

Abstract:	The planet OGLE-TR-56b is the extrasolar giant planet closest to its host star. This planet and its star exchange extreme tidal forces. This leads to a reduction of the planetary orbit and a spin-up of the stellar rotation. The tidal migration rate depends crucially on the ratio of the tidal dissipation factor $Q_{}$ and the stellar love number $k_{2,^{}}$ of the star, which is only poorly known and estimates range within $5 \times 1 0^{5} < (Q_{} / k_{2^{}}) < 1 0^{10}$ . For values greater than $Q_{} / k_{2^{}} > 1.5 \times 1 0^{9}$ no observable influence by tidal forces on the planet's orbit within the lifetime for the star can be found. A lower limit for the possible values of the parameter $Q_{} / k_{2^{}}$ for the G-type star OGLE-TR-56 was found by studying the evolution of possible tidal interaction into the future and in the past. This study demonstrates that on the basis of conservative model assumptions, a considerable but unrealistic spin-up of the star can be expected if $Q_{} / k_{2^{}} < 2 \times 1 0^{7}$ , which is not in agreement with observed stellar rotation periods. From a statistical analysis based on a Monte-Carlo tidal evolution simulation, the $Q_{} / k_{2^{}}$ parameter can be constrained to the range $2 \times 1 0^{7} < Q_{} / k_{2^{}} < 1.5 \times 1 0^{9}$ if the system shall evolve significantly and realistically by tidal forces.

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