Stability of Multiplanet Systems Through Hot Jupiter Destruction

Recent observational and theoretical work suggests that the sub-Jovian desert (periods ${\lesssim}3$ days, masses ${\sim}10{-}100 \ M_{\oplus}$) hosts the remains of destroyed hot Jupiters (``desert dwellers"). In this work, we explore how differing hot Jupiter destruction mechanisms -- Roche lobe overflow (RLO) vs. tidal disruption during high eccentricity migration (HEM) -- may be discerned observationally based on the presence of companion planets to desert dwellers. We show that gas giant destruction via RLO clears out the desert of any companions inside orbital periods ${\lesssim}$4 days; desert dwellers should sit alone in the desert if they form through this mechanism. Numerically mapping the instability threshold in planet mass and orbital distance, we find that the majority of observed companions to desert dwellers are safely in the stability region. RLO therefore does not preclude the existence of nearby companions beyond the desert, in contrast to gas giant tidal disruption during HEM. Further characterization of desert dweller systems may therefore elucidate the fates of hot Jupiters.