Stability of Multiplanet Systems Through Hot Jupiter Destruction

Abstract: 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.

• The paper demonstrates that lossy Roche lobe overflow destabilizes companions with periapses inside about 0.05 au through mean-motion resonance crossing and eccentricity pumping, largely independent of core mass or entropy.
• Numerical simulations show that companions beyond the instability boundary can survive while mutual inclinations remain near their pre-overflow values, allowing cotransiting systems to persist after hot Jupiter destruction.
• Applying the stability maps to eight observed desert-dweller systems finds six clearly compatible and two marginally compatible with Roche lobe overflow, supporting companion statistics as a test of hot Jupiter origins.

Motivation and context

The sub-Jovian desert — the near-dearth of planets with masses $\sim$10–100 $M_{\oplus}$ at orbital periods ${\lesssim}3$ days — was long thought to be empty, but $TESS$ has now revealed a population of "desert dwellers" occupying this regime. One proposed origin, developed by Hallatt & Millholland (2026), holds that desert dwellers are the exposed cores of hot Jupiters (HJs) destroyed by tidal inspiral followed by runaway Roche lobe overflow (RLO). The chief alternative is tidal disruption during high-eccentricity migration (HEM). These two channels make different predictions for companions: HEM disintegrates inner planetary systems and should leave desert dwellers strictly alone, whereas RLO preserves outer planets if the system remains dynamically stable through the mass-transfer event. This Letter by Liveoak, Hallatt & Millholland (2604.19918) addresses precisely that question: do companion planets survive the reconfiguration of a hot Jupiter undergoing lossy RLO?

The observational stakes are concrete. At least ${\sim}$10% of hot Jupiters harbor nearby planets, and one survey finds that ${\sim}$26% of desert planets reside in multiplanet systems. If companions can survive RLO, then the presence or absence of neighbors becomes a discriminating observable between formation theories.

Numerical implementation

The authors couple $N$-body dynamics to prescribed hot Jupiter mass loss using REBOUND augmented with REBOUNDx. The key physical ingredient is that RLO must be "lossy": most of the donor's orbital angular momentum is removed along with its mass, so only the mass-losing planet experiences an outward torque. Mass and semi-major axis evolution follow precomputed tracks from Hallatt & Millholland (2026), implemented via time-dependent exponential timescales on planet mass and orbit. Stellar spin-up during mass transfer is modeled self-consistently through a time-dependent quadrupole moment $J_2(t) = (k_2/3)(\Omega/\Omega_B)^2$ with $k_2 = 0.028$, reaching values as large as $J_2 \sim 10^{-5}$ — comparable to a zero-age main-sequence star.

Two methodological caveats are acknowledged. First, enforcing the mass-loss track ignores possible feedback of companion perturbations on the RLO itself; the authors argue this is acceptable because lossy RLO is a runaway process completing in $M_{\oplus}$0 yr. Second, all simulations fix $M_{\oplus}$1 and $M_{\oplus}$2, which limits direct applicability to observed systems with stellar masses $M_{\oplus}$3.

The stability threshold

Simulating 1600 systems per core-mass choice ($M_{\oplus}$4, 20, 30 $M_{\oplus}$5), sampling companion masses from 10–300 $M_{\oplus}$6 at 0.035–0.2 au with eccentricities up to 0.2, the authors map the instability boundary in companion periapse distance and mass. The central result is robust: regardless of core mass or pre-RLO entropy, no companion survives interior to a periapse distance of $M_{\oplus}$70.05 au, corresponding to an orbital period of roughly 4 days. Since the sub-Jovian desert is conventionally defined inside $M_{\oplus}$83 days, the implication is stark: desert dwellers formed via RLO must be alone in the desert.

Crucially, this threshold is not set by ordinary two-planet Hill stability. A pair of 20 $M_{\oplus}$9 planets at 0.025 and 0.05 au is separated by ${\lesssim}3$0 mutual Hill radii, and the chaos criterion of Hadden & Lithwick (2018) confirms such pairs remain stable for eccentricities well above those typically observed. RLO itself therefore clears the desert of companions: the instability is caused by the migration event, not by marginal packing.

Mechanism: resonant eccentricity pumping

The authors identify mean motion resonance (MMR) crossing during the hot Jupiter's outward expansion as the instability driver. Near-instability systems pile up at low-order period ratios, particularly 2:1; in tracked examples, the resonant angle transitions from circulation to libration, eccentricities are pumped to ${\lesssim}3$10.1–0.8, and the pair crosses the eccentricity-corrected Hill stability boundary. Consistently, the numerically measured instability boundary spans the 3:2 to 3:1 period-ratio range. Companions beyond the threshold simply never encounter low-order commensurability.

Stellar oblateness, despite reaching substantial ${\lesssim}3$2, plays no significant role. Because nodal regression scales as ${\lesssim}3$3, the orbital expansion drives the quadrupolar regression rate down, so for giant-planet companions planet–planet forcing dominates and no secular frequency crossing occurs. For low-mass companions (${\lesssim}3$4) crossings can occur, but they are too brief relative to the secular oscillation period for adiabatic inclination resonance — explaining why the behavior differs from the in-situ hot Jupiter scenario of Batygin et al. (2016).

A secondary dynamical result follows directly: mutual inclination oscillations damp in amplitude after RLO while increasing in frequency, fixing the mutual inclination near its pre-RLO value. Cotransiting systems therefore remain cotransiting through RLO, provided they avoid instability.

Application to observed systems

Applying the numerical thresholds to eight known desert dwellers with exterior companions yields a consistent picture:

System	Desert dweller mass (${\lesssim}3$5)	Companion mass (${\lesssim}3$6)	Companion ${\lesssim}3$7 (au)	RLO stable?
Kepler-094 b	10.8	3126	1.04	Yes
Kepler-411 b	25.6	26.4	0.065	Yes
TOI-1288 b	44.1	85.7	1.07	Yes
TOI-1347 b	11.1	<9.0	0.055	Marginal
TOI-2000 b	11.0	81.7	0.082	Yes
TOI-4010 b	11.0	20.3	0.056	Yes
WASP-084 c	15.2	220	0.078	Marginal
TOI-1410 b	12.5	27	0.239	Yes

Six of eight systems lie unambiguously within the stable region; TOI-1347 b and WASP-084 c sit on the cusp. None fall in the clearly unstable region, so the data are consistent with the RLO channel. Pre-RLO initial conditions — the observed architectures with a hot Jupiter inserted at 0.017 au — were verified stable via IAS15 integration (>10${\lesssim}3$8 inner orbits), the SPOCK classifier, and mutual Hill separations ${\lesssim}3$9. The two higher-multiplicity systems (TOI-4010, Kepler-411) also survive RLO in dedicated integrations. The authors note these verdicts are indicative rather than definitive, given the solar-mass assumption underlying the stability maps.

Additional discriminants and limitations

Beyond companion occurrence, the paper highlights two further tests. First, the RLO theory predicts the desert remains empty around stars hotter than the Kraft break, where weak tidal dissipation precludes inspiral, whereas HEM disruption should occur indiscriminately across spectral type. No desert planets are currently known above the Kraft break, but bias-corrected statistics are needed to confirm this is real. Second, HEM should excite stellar obliquities while tidally driven RLO aligns them, making obliquity measurements an independent discriminator.

Several limitations bear on the interpretation. The instability classification uses an ad hoc but empirically reliable threshold on deviation from the prescribed orbital track; post-instability outcomes are estimated rather than simulated (no collision handling), though Safronov number arguments indicate mergers rather than ejections. The analysis assumes coplanar configurations misaligned from the stellar spin by only 5°, fixed solar stellar parameters, and a single representative pre-RLO entropy. Whether any specific observed system truly descends from RLO additionally requires constraints the study does not address, including pre-inspiral stability, density, stellar age, and tidal quality factor.

Conclusion

This work establishes that lossy Roche lobe overflow destabilizes companions interior to $TESS$00.05 au (periods $TESS$14 days) through resonant eccentricity excitation, while leaving more distant companions intact. Consequently, RLO-formed desert dwellers may retain companions beyond the desert but must be solitary within it — a prediction intermediate between strict isolation (HEM) and unconstrained multiplicity. With 6/8 observed multiplanet desert dweller systems compatible with survival through RLO, companion statistics in the growing desert dweller sample offer a direct empirical route to distinguishing hot Jupiter fates.