Hot-Jupiter core mass from Roche lobe overflow

摘要: The orbits of many observed hot Jupiters are decaying rapidly due to tidal interaction, eventually reaching the Roche limit. We analytically study ensuing coupled mass loss and orbital evolution during Roche-lobe overflow find two possible scenarios. Planets with light cores $M_c\lesssim 6M_\oplus$ (assuming a nominal dissipation factor $Q\sim 10^6$ for host star) transformed into Neptune-mass gas planets, orbiting at separation (relative stellar radius) $a/R_\star\approx 3.5$. heavier $M_c\gtrsim plunge until they destroyed surface. Remnant gas-Neptunes, which stable photo-evaporation, absent from observations, despite their unique transit radius ($5-10R_\oplus$). This result suggests that 6M_\oplus$, providing useful constraint on poorly-known core may distinguish between different formation theories giants. Alternatively, if one assumes prior $M_c\approx 6 M_\oplus$ core-accretion theory, our results suggest $Q$ does not lie in range $10^6\lesssim Q\lesssim 10^7$.