We investigate the possibility of substantial inflation of short-period Jupiter-mass planets , as a result of their internal tidal dissipation associated with the synchronization and circularization of their orbits .
We employ the simplest prescription based on an equilibrium model with a constant lag angle for all components of the tide .
We show that 1 ) in the low-eccentricity limit , the synchronization of the planets ’ spin with their mean motion is established before tidal dissipation can significantly modify their internal structure .
2 ) But , above a critical eccentricity , which is a function of the planets ’ semimajor axis , tidal dissipation of energy during the circularization process can induce planets to inflate in size before their eccentricity is damped .
3 ) For moderate eccentricities , the planets adjust to stable thermal equilibria in which the rate of their internal tidal dissipation is balanced by the enhanced radiative flux associated with their enlarged radii .
4 ) For sufficiently large eccentricities , the planets swell beyond two Jupiter radii and their internal degeneracy is partially lifted .
Thereafter , their thermal equilibria become unstable and they undergo runaway inflation until their radii exceed the Roche radius .
5 ) We determine the necessary and sufficient condition for this tidal inflation instability .
6 ) These results are applied to study short-period planets .
We show that for young Jupiter-mass planets , with a period less than 3 days , an initial radius about 2 Jupiter radii , and an orbital eccentricity greater than 0.2 , the energy dissipated during the circularization of their orbits is sufficiently intense and protracted to inflate their sizes up to their Roche radii .
7 ) We estimate the mass loss rate , the asymptotic planetary masses , and the semi-major axes for various planetary initial orbital parameters .
The possibility of gas overflow through both inner ( L1 ) and outer ( L2 ) Lagrangian points for the planets with short periods or large eccentricities is discussed .
8 ) Planets with more modest eccentricity ( < 0.3 ) and semi-major axis ( > 0.03 - 0.04 AU ) lose mass via Roche-lobe overflow mostly through the inner Lagrangian ( L1 ) point .
Due to the conservation of total angular momentum , these mass-losing planets migrate outwards , such that their semi-major axes and Roche radii increase while their mass , eccentricity , and tidal dissipation rate decrease until the mass loss is quenched .
9 ) Based on these results , we suggest that the combined effects of self-regulated mass loss and tidally driven orbital evolution may be responsible for the apparent lack of giant planets with ultra-short periods \lesssim 3 days .
10 ) Mass loss during their orbital circularization may also have caused the planets with periods in the range \sim 3 - 7 days to be less massive than long-period planets which are not affected by the star-planet tidal interaction .
11 ) The accretion of the short-period planets ’ tidal debris can also lead to the surface-layer contamination and metallicity enhancement of their host stars .
12 ) Among the planets with periods of 1-3 weeks today , some may have migrated outwards and attained circular orbits while others may have preserved their initial eccentricity and semimajor axis .
Therefore , planets with circular orbits are expected to coexist with those with eccentric orbits in this period range .
13 ) Gross tidal inflation of planets occurs on the time scale \sim 10 ^ { 6 } yrs after their formation for a brief interval of \sim 10 ^ { 5 } yrs .
The relatively large sizes of their classical and weak-line T Tauri host stars increases the planets ’ transit probability .
The inflated sizes of the tidally heated planets also increases the eclipse depth of such transit events .
Thus , the tidal inflation and disruption of planets may be directly observable around classical and weak-line T Tauri stars .