Chaotic Tides in Migrating Gas Giants: Forming Hot and Transient Warm Jupiters via High-Eccentricity Migration

High-eccentricity migration is an important channel for the formation of hot Jupiters (HJs). In particular, Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant planetary or stellar companion, combined with tidal friction, have been shown to produce HJs on Gyr timescales, provided that efficient tidal dissipation operates in the planet. We re-examine this scenario with the inclusion of dynamical tides. When the planet's orbit is in a high-eccentricity phase, the tidal force from the star excites oscillatory f-modes and r-modes in the planet. For sufficiently large eccentricity and small pericentre distance, the mode can grow chaotically over multiple pericentre passages and eventually dissipate non-linearly, drawing energy from the orbit and rapidly shrinking the semi-major axis. We study the effect of such chaotic tides on the planet's orbital evolution. We find that this pathway produces very eccentric ($e\gtrsim 0.9$) warm Jupiters (WJs) on short timescales (a few to 100 Myrs). These WJs efficiently circularize to become HJs due to their persistently small pericentre distances. Chaotic tides can also save some planets from tidal disruption by truncating the LK eccentricity oscillations, significantly increasing the HJ formation fraction for a range of planet masses and radii. Using a population synthesis calculation, we determine the characteristics of WJs and HJs produced in this scenario, including the final period distribution, orbital inclinations and stellar obliquities. Chaotic tides endow LK migration with several favorable features to explain observations of HJs. We expect that chaotic tides are also important in other flavours of high-$e$ migration.