To explain their observed radii , we present theoretical radius-age trajectories for the extrasolar giant planets ( EGPs ) TrES-4 , XO-3b , and HAT-P-1b .
We factor in variations in atmospheric opacity , the presence of an inner heavy-element core , and possible heating due to orbital tidal dissipation .
A small , yet non-zero , degree of core heating is needed to explain the observed radius of TrES-4 , unless its atmospheric opacity is significantly larger than a value equivalent to that at 10 \times solar metallicity with equilibrium molecular abundances .
This heating rate is reasonable , and corresponds for an energy dissipation parameter ( Q _ { p } ) of \sim 10 ^ { 3.8 } to an eccentricity of \sim 0.01 , assuming 3 \times solar atmospheric opacity and a heavy-element core of M _ { c } = 30 M _ { \oplus } .
For XO-3b , which has an observed orbital eccentricity of 0.26 , we show that tidal heating needs to be taken into account to explain its observed radius .
Furthermore , we reexamine the core mass needed for HAT-P-1b in light of new measurements and find that it now generally follows the correlation between stellar metallicity and core mass suggested recently .
Given various core heating rates , theoretical grids and fitting formulae for a giant planet ’ s equilibrium radius and equilibration timescale are provided for planet masses M _ { p } = 0.5 , 1.0 , and 1.5 M _ { J } with a = 0.02-0.06 AU , orbiting a G2V star .
When the equilibration timescale is much shorter than that of tidal heating variation , the “ effective age ” of the planet is shortened , resulting in evolutionary trajectories more like those of younger EGPs .
Motivated by the work of , we suggest that this effect could indeed be important in better explaining some observed transit radii .