Exomoon Tidal Heating Detection

Exomoon Orbit

Orbital eccentricity e 0.030

Moon–planet distance 420,000 km

Tidal dissipation k₂/Q 0.0200

Planet–star distance 5.20 AU

Detection Readouts

Tidal heat power

— W

vs Io (1.5×10¹⁴ W)

—×

T (insolation only)

— K

T (with tidal heat)

— K

—

excess IR luminosity ÷ assumed noise floor (3σ)

Insolation-only baseline Combined system IR flux

How it works

A moon on an eccentric orbit is squeezed and stretched every revolution; internal friction converts that flexing into heat (Peale & Cassen 1979). The orbit-averaged power is:

H = (21/2) · (k₂/Q) · R⁵n⁵ · e² / G
n = √(GM_planet / a³)   (mean motion)

where R is the moon's radius, n its orbital mean motion, a the semi-major axis, e the eccentricity, G the gravitational constant, and k₂/Q the tidal Love number over dissipation quality factor — a material property lumping rigidity and internal friction into one number. This is exactly the mechanism heating Io to 1.5×10¹⁴ W today.

That heat is re-radiated as extra infrared light. Energy balance gives the moon's blackbody temperature with and without the tidal term:

4πR²σT_ins⁴ = F(1-A)·πR²         (insolation only)
4πR²σT_tot⁴ = F(1-A)·πR² + H     (insolation + tides)
F = L_star / (4πa_planet²)

The difference, ΔL = 4πR²σ(T_tot⁴ − T_ins⁴) = H, is an excess infrared luminosity that shows up as an anomaly in the star system's combined thermal light curve — brighter than a star+planet+moon model with insolation alone would predict. This is a real proposed method for finding "hidden" exomoons: photometry (e.g. JWST-class secondary-eclipse or phase-curve measurements) that reads systematically hotter than the insolation-only model implies a tidally active moon, even one too small or too faint to see directly. The chart compares that flat baseline against the modelled system flux (baseline plus a periapsis-weighted tidal pulse); the "Detection" indicator lights up green when the excess luminosity clears an assumed 3σ photometric noise floor.

Eccentricity / distance — set the orbit; heating grows as e² and falls off steeply with distance (n⁵ ∝ a⁻⁷·⁵).
k₂/Q — the moon's material response; icy or partially molten interiors dissipate far more than rigid rock.
Planet–star distance — sets stellar insolation, i.e. the "boring" baseline temperature the tidal excess must be measured against.

Star (light source) Planet Exomoon (glow ∝ heat)

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