Inflated Eccentric Migration of Evolving Gas-Giants I: Accelerated Formation and Destruction of Hot and Warm Jupiters

Hot and warm Jupiters (HJs and WJs correspondingly) are gas-giants orbiting their host stars at very short orbital periods ($P_{HJ}<10$ days; $10<P_{WJ}<200$ days). HJs and a significant fraction of WJs are thought to have migrated from an initially farther-out birth locations. While such migration processes have been extensively studied, the thermal evolution of gas-giants and its coupling to the the migration processes are usually overlooked. In particular, gas-giants end their core-accretion phase with large radii and then contract slowly to their final radii. Moreover, intensive heating can slow the contraction at various evolutionary stages. The initial inflated large radii lead to faster tidal migration due to the strong dependence of tides on the radius. Here we explore this accelerated migration channel, which we term inflated eccentric migration, using a semi-analytical self-consistent modeling of the thermal-dynamical evolution of the migrating gas-giants, later validated by our numerical model (see a companion paper, paper II). We demonstrate our model for specific examples and carry a population synthesis study. Our results provide a general picture of the properties of the formed HJs\&WJs via inflated migration, and the dependence on the initial parameters/distributions. We show that tidal migration of gas-giants could occur far more rapidly then previously thought and lead to accelerated destruction and formation of HJs and enhanced formation rate of WJs. Accounting for the coupled thermal-dynamical evolution is therefore critical to the understanding of HJs/WJs formation, evolution and final properties of the population and play a key role in their migration process.