Hot-Jupiter Core Mass from Roche-lobe Overflow

TL;DR

This paper analytically investigates how hot Jupiters lose mass and evolve as they approach the Roche limit, providing constraints on their core masses based on observed planetary remnants and tidal dissipation factors.

Contribution

It introduces an analytical model of Roche-lobe overflow for hot Jupiters, linking core mass to their fate and constraining the tidal dissipation factor Q.

Findings

Planets with cores less than ~6 Earth masses become Neptune-like after mass loss.

Heavier core planets are rapidly destroyed at the stellar surface.

Absence of stable gas-Neptune remnants suggests cores are likely above 6 Earth masses.

Abstract

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