Analytical model for the evolution of giant extrasolar planets

• We show that extrasolar planetary gas giants lie on a narrow band in the HR diagram.
• A model of contracting gas giants receiving stellar energy is developed.
• The results will be important when systems at distances over 1 AU are discovered.
• The timescales for planetary contraction are obtained and compared with numerical models.
• It was found that observed planets are a long way from reaching their final state.

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 log10Llog10L and log10Tefflog10Teff 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.