Analytical model for the evolution of giant extrasolar planets

For extrasolar planets with well determined radii and in thermal equilibrium, the planetary luminosity can be determined. A plot of the log of the luminosity against the log of the effective temperature of the planet was constructed. It was found that the gas giant planets lie on a narrow band that could be well fitted by a linear regression relation between log 10 L and log 10 T eff with a slope of 5.46. A model of contracting gas giants that is also receiving energy from the parent star is constructed and the contraction time calculated and the results compared to those by numerical integration. This time is far too long for giant planets due to the parent star, showing that they must initially contract further out before migrating inwards.