Lava: Planetary Molten Silicate Dynamics

• Lava is molten silicate material erupted onto planetary surfaces, manifesting as thin flows, lakes, or vast magma oceans that drive crust formation and atmospheric exchanges.
• It plays a pivotal role in planetary differentiation and thermal evolution, as evidenced by laboratory rheology, thermochemical modeling, and direct geological observations.
• Modeling lava dynamics integrates experimental constraints, computational hazard mapping, and remote sensing, providing actionable insights for planetary science and exoplanet research.

Lava, in planetary science, designates the manifestation of molten silicates at or near the surfaces of planets and satellites. The scope of "lava" spans thin near-surface flows and lakes observed on contemporary volcanic terrains, through to hemispherical or global "magma oceans"—molten silicate layers hundreds to thousands of kilometers deep—which can dominate the early evolution or persistent states of terrestrial worlds and exoplanets. Lava plays a central role in planetary differentiation, crust formation, atmosphere–interior exchange, and surface–atmosphere observables. Investigations leverage laboratory rheology, thermochemical modeling, direct geological observation, computational hazard mapping, and exoplanetary emission spectroscopy to constrain the underlying physics and evolutionary pathways.

1. Definition, Physical Regimes, and Key Parameters

"Lava" refers to silicate melt erupted onto a planetary surface, while "magma ocean" denotes an interior layer where temperature exceeds the silicate liquidus, yielding a fully molten shell of depth $D \sim 10^2$–$10^3$ km. Terrestrial lava flows and lakes typically have thickness $<1$ km and surface temperatures $T_s \sim 1,400$–$1,700$ K. Key physical parameters are:

• Melting/liquidus temperature: $T_m \approx 1,300$ K at 1 bar (peridotite), rising to $\sim2,000$ K at $P \sim 10^2$ GPa.
• Latent heat of crystallization: $L \approx 2 \times 10^6$ J kg$^{-1}$.
• Melt fraction $10^3$0 denotes the liquid volume/mass fraction in partially crystallized rock.
• Viscosity $10^3$1 for silicate melts can span $10^3$2–$10^3$3 Pa$10^3$4s, depending on composition and temperature, with superliquidus Mercury analog lavas measured at $10^3$5–$10^3$6 Pa$10^3$7s in the $10^3$8–$10^3$9 K range (Vetere et al., 2017), and lower limits near $<1$0 Pa$<1$1s in silicate vaporization regimes (Chao et al., 2020).
• For magma oceans, the Rayleigh number $<1$2 ensures "hard-turbulent" convection.

2. Energetics, Dynamics, Crystallization, and Solidification

The thermal evolution of lava and magma-ocean systems is governed by the interplay of radiative cooling, convective transport, latent heat effects during crystallization, and, for planetary-scale melt layers, internal and external heat sources.

• The energy balance for a magma ocean per unit area is:

$<1$3

where $<1$4 is radiative loss ($<1$5), $<1$6 is convective flux, and the final term accounts for latent heat released as depth $<1$7 crystallizes (Chao et al., 2020, Herath et al., 2024).

Crystallization proceeds via either batch (equilibrium) or fractional (with segregated phases) processes. The solidus and liquidus are pressure- and composition-dependent:

$<1$8

where slopes $<1$9–$T_s \sim 1,400$0 K GPa$T_s \sim 1,400$1, $T_s \sim 1,400$2–$T_s \sim 1,400$3 K GPa$T_s \sim 1,400$4. Convection ceases ("lock-up") near melt fractions $T_s \sim 1,400$5–$T_s \sim 1,400$6.

For planetary lavas, high melt mobility is facilitated by low viscosity, rapid turbulent flow (Re $T_s \sim 1,400$7), and high effusion rates. For example, Mercury’s northern volcanic plains exhibit channel velocities $T_s \sim 1,400$8–$T_s \sim 1,400$9 m s$1,700$0 (depths $1,700$1–$1,700$2 m, $1,700$3 Pa$1,700$4s, slope $1,700$5), and require effusion rates $1,700$6 m$1,700$7 s$1,700$8 to traverse $1,700$9 km before quenching (Vetere et al., 2017).

3. Atmospheric Coupling, Evaporation, and Surface–Atmosphere Exchange

Lava/magma-ocean surfaces exchange mass and energy with their atmospheres via volatile outgassing and rock vaporization, especially on "lava planets"—rocky exoplanets with substellar temperatures $T_m \approx 1,300$0 K.

• Vapor pressures $T_m \approx 1,300$1 for surface constituents are well-described by:

$T_m \approx 1,300$2

where $T_m \approx 1,300$3 is latent heat of evaporation and $T_m \approx 1,300$4 the gas constant. Representative $T_m \approx 1,300$5 at $T_m \approx 1,300$6 K: $T_m \approx 1,300$7 Pa, $T_m \approx 1,300$8 Pa, $T_m \approx 1,300$9 Pa (Nguyen et al., 2020).

• The resultant silicate vapor atmospheres display significant compositional and scale-height variations: for K2-141b, scale heights $\sim2,000$0 km, $\sim2,000$1 km, $\sim2,000$2 km at the limb (Nguyen et al., 2020).
• Atmospheric mass-loading, driven by net evaporation, must be balanced by return melt flow in the magma ocean. Steady-state SiO/SiO$\sim2,000$3 atmospheres require day–night ocean currents $\sim2,000$4 m s$\sim2,000$5, while Na-rich atmospheres would require over $\sim2,000$6 m s$\sim2,000$7—not sustainable, implying long-term surface fractionation (Nguyen et al., 2020).

Thermal and compositional coupling between the melt layer and atmosphere sets observable properties and drives planetary evolution (Chao et al., 2020, Nguyen et al., 2024).

4. Observational Manifestations and Modeling

Lava and associated atmospheres express themselves via distinct observables on Solar System bodies and exoplanets.

• Infrared thermal emission is the primary signature; for lava worlds, secondary-eclipse depths and phase curves yield $\sim2,000$8, constrain day–night heat transport, and can reveal atmospheric bands (e.g., Si–O at 9–11 $\sim2,000$9m, CO$P \sim 10^2$0, Na features) (Chao et al., 2020, Nguyen et al., 2024).
• Clouds in silicate atmospheres (e.g., SiO condensation at lava-planet terminators) reduce surface temperatures by 100–200 K, though their effect on emergent infrared spectra is mainly to flatten the brightness temperature continuum rather than introduce strong lines (Nguyen et al., 2024).
• On terrestrial planets and satellites, lava lakes such as Erta Ale (Ethiopia) and Kīlauea Iki (Hawaii) exhibit convection, crust cycling, and measurable surface heat fluxes (e.g., $P \sim 10^2$1 W m$P \sim 10^2$2 for Erta Ale), serving as scaling analogs for deeper magma-ocean convection (Chao et al., 2020).
• On Io, persistent melting is sustained by tidal heating; Loki Patera's convecting magma sea is $P \sim 10^2$3 km wide with $P \sim 10^2$4–$P \sim 10^2$5 W m$P \sim 10^2$6 heat flux (Chao et al., 2020).

Modern computational tools model lava emplacement as stochastic or probabilistic processes. The Flowy code employs the MrLavaLoba method, simulating lava emplacement as stochastic sequences of elliptical "lobes," achieving computational speedups of $P \sim 10^2$7–$P \sim 10^2$8 over previous codes with high physical fidelity for hazard and thickness mapping (Sallermann et al., 2024).

5. Lava Emplacement: Experimental Constraints and Modeling

Rheological and emplacement experiments empirically constrain flow laws and landscape modification by lava.

• Mercury NVP analog lavas display moderate superliquidus viscosities ($P \sim 10^2$9–$L \approx 2 \times 10^6$0 Pa$L \approx 2 \times 10^6$1s for $L \approx 2 \times 10^6$2–$L \approx 2 \times 10^6$3 K), and crystal content–dependent, shear-thinning behavior subliquidus (e.g., a decrease in $L \approx 2 \times 10^6$4 by 1 log unit as shear rate increases from $L \approx 2 \times 10^6$5 to $L \approx 2 \times 10^6$6 s$L \approx 2 \times 10^6$7) (Vetere et al., 2017).
• Turbulent flow velocities and critical effusion rates required to avoid premature cooling and quenching are derived from numerical models coupling flow kinematics with thermal budget constraints (e.g., maintaining $L \approx 2 \times 10^6$8 above liquidus over 100 km requires $L \approx 2 \times 10^6$9 m$^{-1}$0 s$^{-1}$1 for channel widths $^{-1}$2 m).
• Probabilistic hazard mapping as in Flowy involves Monte Carlo–like ensembles of flows, tracking inundation and thickness fields over digital elevation models (DEMs), with volume-conserving rasterization and convergence metrics (e.g., coverage index $^{-1}$3 after 60 runs for $^{-1}$4) (Sallermann et al., 2024).

6. Lava Worlds and Exoplanets: Evolution, Feedbacks, and Detection

In ultra-short-period exoplanets, persistent magma oceans and their interactions with irradiation and tidal forces drive both observational signatures and thermal evolution.

• Tidally locked “lava planets” develop hemispherical dichotomy: dayside maintains a thick, hot magma ocean with fixed $^{-1}$5 (e.g., $^{-1}$6 K), while the nightside cools, crystallizes and solidifies over $^{-1}$7–$^{-1}$8 yr without net energy transfer or tidal heating (Herath et al., 2024).
• Sustaining a molten nightside requires either: (i) horizontal convection carrying $^{-1}$920% of intercepted stellar power (necessitating $10^3$00 Pa$10^3$01s), or (ii) tidal heating rates $10^3$02 W/kg in the mush, corresponding to orbital eccentricities $10^3$03 (Herath et al., 2024).
• If these criteria are not met, positive feedbacks—viscosity rise and mush mass loss—accelerate nightside freezing.
• Night–day phase curve observations of exoplanets (e.g., K2-141b) provide direct diagnostics of the efficiency of day–night heat transport and thus the physical state of lava and planetary interiors (Herath et al., 2024, Nguyen et al., 2020, Chao et al., 2020).
• Cloud radiative effects in partial atmospheres have been predicted to chill the dayside surface by up to 200 K without substantially altering banded spectral signatures, particularly in systems like HD 213885b and HD 20329b; detection requires absolute spectral precision of 10–20 ppm (Nguyen et al., 2024).

7. Knowledge Frontiers and Future Opportunities

Outstanding research needs and frontiers include:

• Rheological properties and phase diagrams of ultra-high-$10^3$04, volatile-poor, and silicate-vaporizing melts at $10^3$05 K and $10^3$06 GPa (Chao et al., 2020).
• Detailed evaporation kinetics, multi-phase convection modeling, and coupled atmosphere–interior chemistry under intense irradiation.
• Direct measurement and mapping of lava world