The distribution of eccentricities e of extra-solar planets with semi-major axes a > 0.2 AU is very uniform , and values for e are generally large .
For a < 0.2 AU , eccentricities are much smaller ( most e < 0.2 ) , a characteristic widely attributed to damping by tides after the planets formed and the protoplanetary gas disk dissipated .
We have integrated the classical coupled tidal evolution equations for e and a backward in time over the estimated age of each planet , and confirmed that the distribution of initial e values of close-in planets matches that of the general population for reasonable tidal dissipation values Q , with the best fits for stellar and planetary Q being \sim 10 ^ { 5.5 } and \sim 10 ^ { 6.5 } , respectively .
The current small values of a were only reached gradually due to tides over the lifetimes of the planets , i.e . , the earlier gas disk migration did not bring all planets to their current orbits .
As the orbits tidally evolved , there was substantial tidal heating within the planets .
The past tidal heating of each planet may have contributed significantly to the thermal budget that governed the planet ’ s physical properties , including its radius , which in many cases may be measured by observing transit events .
Here we also compute the plausible heating histories for a few planets with anomalously large measured radii , including HD 209458 b .
We show that they may have undergone substantial tidal heating during the past billion years , perhaps enough to explain their large radii .
Theoretical models of exoplanet interiors and the corresponding radii should include the role of large and time-variable tidal heating .
Our results may have important implications for planet formation models , physical models of “ hot Jupiters ” , and the success of transit surveys .