Large planets may not form fractionally large moons

The study investigates why fractionally large moons like Earth’s Moon may be rare and under what planetary conditions impact-generated moons can form. Motivated by the lack of confirmed exomoons despite the expectation that giant impacts are common, the authors test the hypothesis that vapor-rich impact disks inhibit the growth of large moons because moonlet precursors suffer strong gas drag and rapidly spiral into the planet. They aim to constrain the initial disk conditions (particularly vapor mass fraction, VMF) and planetary mass–composition regimes that permit formation of large satellites, thereby informing lunar origin models and guiding exomoon searches.

Canonical lunar origin posits a giant impact between Earth and a Mars-sized body producing a partially vaporized disk (VMF ~0.1–0.3) from which the Moon accreted. Alternative higher-energy scenarios (e.g., two half-Earths, fast-spinning Earth impacts) generate higher VMF (0.7–1.0) but face challenges such as excess system angular momentum and mantle homogenization inconsistent with some geochemical observations. Multiple-impact models also exist with VMF ~0.1–0.5. Disk mixing and isotopic equilibration issues have been debated, including requirements that the impactor (Theia) share Earth-like isotopic signatures or that equilibration occurs during the disk phase. Prior work suggested vapor-rich disks may be dynamically unstable and lose mass rapidly, hindering large-moon formation. Exomoon detection efforts (e.g., HEK with Kepler data, HST follow-up) have not confirmed any exomoons; challenges include short lifetimes around close-in planets due to stellar tides and small Hill spheres leading to moon loss. Formation via circumplanetary disks typically yields total satellite masses ~10^-4 M⊕ due to dust-gas dynamics, and gravitational capture tends to produce fractionally small moons. Thus, impacts at relatively low velocity remain the natural route to fractionally large moons, but the role of disk vapor content has not been fully assessed for exoplanetary regimes.

The authors perform smoothed particle hydrodynamics (SPH) simulations of giant impacts to characterize moon-forming disks across planetary masses and compositions, and to evaluate the vapor mass fraction (VMF) and the gas pressure gradient parameter η that controls gas drag. They model two endmembers: rocky planets (70 wt% forsterite mantle, 30 wt% iron core) and icy planets (70 wt% water ice, 30 wt% forsterite core). Parameter ranges: total colliding mass MT up to 6 M⊕ for rocky bodies and 0.1–1 M⊕ for icy bodies; impactor-to-total mass ratio γ from 0.13 to 0.45; impact speed Vimp equal to mutual escape speed Vesc; impact angle θ ≈ 48.5°. SPH resolutions range from 50,000 to 100,000 particles. Equations of state: M-ANEOS for silicate and iron; a five-phase EOS for water (extended/interpolated with SESAME 7154) for icy cases. Initial mantle entropies correspond to ~2000 K (rocky) and ~300 K (icy) surfaces for Earth-sized planets (exception: one run with lower initial entropy). From SPH outputs they compute disk mass, angular momentum, entropy, and VMF assuming a hydrostatic disk with uniform entropy. They construct stable disk surface-density profiles (exponential and polynomial models) that conserve mass and angular momentum and satisfy the Rayleigh stability criterion. They evaluate η, typically ~0.02–0.06, about ten times higher than in protoplanetary disks. To quantify gas-drag-driven radial infall of solids, they derive stopping times and radial drift speeds using Newton drag with CD ≈ 0.44, and compute fall timescales tfall as a function of particle size, gas density, and local disk properties. Example values: at r ≈ 2–3 R⊕, for silicate vapor with ρg ~40 kg m^-3 and ρp ~3000 kg m^-3, τ ≈ 1 at Rp ≈ 2 km yielding tfall ≈ 1.2 days; for water vapor with ρg ~10 kg m^-3 and ρp ~1000 kg m^-3, τ ≈ 1 at Rp ≈ 1.3 km yielding tfall ~1 day. They assess evaporative losses during infall by comparing drag heating to latent heat, finding limited evaporation for ~km silicate bodies but complete evaporation for km-scale icy bodies under assumed conditions. They also implement a simple viscous evolution model for a fully vapor disk using an α-prescription (α = 5×10^-3) and sound speeds corresponding to T ~4000 K (silicate) and ~1000 K (water) to estimate disk spreading and mass loss over a disk lifetime comparable to condensation timescales (~100 years for rocky disks assuming photospheric Tph ~1410 K; longer for icy disks with Tph ~270 K).

• A high-VMF (vapor-rich) moon-forming disk strongly inhibits the growth of fractionally large moons because solids of ~100 m–100 km experience strong gas drag and rapidly lose angular momentum, spiraling into the planet (“km-barrier problem”). Estimated radial fall timescales are extremely short: ~1.2 days for a 2 km silicate moonlet (τ ≈ 1.18) and ~1 day for a 1.3 km icy moonlet; even 200 km bodies have tfall ~172 days, much less than disk lifetimes and accretion timescales.
• SPH simulations show VMF increases with total planetary mass and with larger impactor fraction γ. For rocky impacts, VMF ≥ 0.96 at MT ≥ 6 M⊕; for icy impacts, VMF ≈ 1.0 at MT ≥ 1 M⊕. Icy impacts yield higher VMF than rocky ones at the same mass due to lower latent heat of water (~2.3×10^6 J kg^-1) compared to silicate (~1.2×10^7 J kg^-1).
• The pressure gradient parameter η in impact disks is ~0.02–0.06, about an order of magnitude larger than typical protoplanetary disk values, enhancing radial drift.
• Vapor-disk viscous evolution further reduces available mass: a fully vapor rocky disk with initial disk mass fraction f=0.02 loses most mass over ~100 years, leaving Mfinal/MD,initial 0.2; icy vapor disks retain even less (<0.06) due to longer lifetimes and continued spreading.
• Consequently, initially vapor-rich disks (VMF close to 1) fail to produce fractionally large moons; large moon formation requires initially vapor-poor disks (VMF ~0.1–0.3), consistent with canonical Moon-forming impacts.
• Mass–radius thresholds: rocky planets larger than ~6 M⊕ (radii ~1.3–1.6 R⊕) and icy planets larger than ~1 M⊕ (~1.3 R⊕) produce entirely vapor disks and are unlikely to form fractionally large impact-induced moons. Planets smaller than these thresholds are better candidates.
• The results help explain the lack of confirmed exomoons to date and suggest focusing searches on exoplanets with radii <~1.6 R⊕ (particularly super-Earths rather than mini-Neptunes).

The findings directly address the research question by identifying vapor content as a controlling factor for moon formation efficiency in impact-generated disks. Strong gas drag in high-VMF disks removes growing moonlets before they can accrete into a large satellite, establishing a km-scale growth barrier analogous to the meter barrier in protoplanetary disks. This supports lunar origin scenarios that produce initially vapor-poor disks (canonical impacts) and disfavors highly energetic impacts that yield fully vaporized disks if a large moon is to form. The mass–composition thresholds imply that fractionally large moons should be rare around more massive rocky and icy planets and potentially around mini-Neptunes if H/He contributes to disk vapor. As vapor disks cool, small moons can still form, consistent with systems like Uranus with fractionally small satellites. Alternative formation pathways (circumplanetary accretion, capture) generally produce small total satellite masses, aligning with the inference that fractionally large moons predominantly arise from suitable impacts. The work provides actionable guidance for exomoon surveys to target smaller-radius exoplanets. Remaining complexities include the role of the Roche limit on fragmentation and coupling, potential for rapid clumping via streaming instability to bypass the km-barrier, and the influence of diverse impact parameters and mixed-composition collisions.

The study concludes that fractionally large impact-induced moons require initially vapor-poor moon-forming disks. High-VMF disks generated by impacts onto sufficiently massive rocky (≥6 M⊕) or icy (≥1 M⊕) planets prevent large-moon accretion due to rapid gas-drag-driven infall of moonlets. This supports canonical Moon-forming scenarios and predicts that exomoons large relative to their planets should preferentially orbit smaller planets (radii <~1.6 R⊕). The results offer an explanation for the lack of confirmed exomoons and refine target selection for future searches (e.g., Kepler archives, HST, CHEOPS, JWST). Future research should develop more detailed disk models including condensation, vapor–solid interactions, and Roche-limit physics; explore whether streaming instability can enable rapid formation of large moonlets in vapor-rich disks; broaden the parameter space of impact conditions; and examine mixed-composition impacts and the effects of residual H/He envelopes.

• Parameter space is limited: fixed impact angle (~48.5°) and impact velocity (Vimp = Vesc), with discrete values of γ and MT; other impact geometries and speeds may alter VMF and disk properties.
• Disk modeling simplifications: assumes uniform-entropy, hydrostatic disks; uses idealized surface-density fits; the fully vapor disk evolution uses an α-viscosity with a chosen α; the model neglects condensation kinetics, vapor–droplet coupling, turbulence details, and explicit treatment of the Roche-limit region.
• VMF threshold for inhibiting large-moon formation is not sharply defined; VMF ≈ 1 is treated as an upper limit, but the exact critical VMF is uncertain.
• Gas drag estimates depend on assumed gas densities, temperatures, and CD; local variations and time evolution could modify infall timescales.
• Compositional diversity is simplified to two endmembers; impacts between dissimilar bodies (icy–rocky) and contributions from H/He envelopes (mini-Neptunes) are not explicitly simulated.
• SPH resolution and EOS choices can influence thermodynamic outcomes (e.g., VMF); some EOS uncertainties remain for extreme conditions.