Exomoon

The missing population

Inside our Solar System, moons outnumber planets by roughly 20 to 1 — Jupiter alone has 95 confirmed natural satellites, Saturn 146 at last count, with new icy bodies announced almost annually. By straightforward extrapolation, exomoons should be the most abundant class of solid body in the Galaxy. The Milky Way has perhaps a trillion planets; if each averages a couple of moons, exomoons number in the trillions. And yet, more than thirty years into the exoplanet revolution and with nearly 5,800 exoplanets confirmed in NASA's Exoplanet Archive as of 2024, the confirmed exomoon count stands at zero.

The mismatch is not because exomoons fail to exist — they almost certainly do — but because the methods that find exoplanets so prolifically degrade badly at finding their moons. A planet transit of a Sun-like star produces a dip of order (R_p / R_*)² ≈ 1% for a Jupiter analogue. Add a Mars-sized moon and the moon's own dip is (R_m / R_*)² ≈ 10⁻⁵, a tenth of a part per million. Even the moon's gravitational tug on the planet — the cleanest second-order signal — shifts the host's mid-transit time by tens of seconds at most. Both are at the edge of what space photometry can resolve. The bottleneck is not concept; it is signal-to-noise.

Five ways to catch a moon

Several detection strategies have been proposed since the late 1990s, each exploiting a different observable. They are not mutually exclusive — a confirmation will almost certainly combine two or more of them.

1. Transit-timing variation (TTV). Sartoretti and Schneider (1999) noted that a planet with a moon orbits not the star alone but the planet-moon barycentre. The planet therefore wanders around its mean ephemeris by a displacement of order (M_m / M_p) × a_moon, which translates into mid-transit timing offsets of seconds to minutes. The amplitude grows with the moon's mass.
2. Transit-duration variation (TDV). A companion to TTV. As the moon orbits the planet, it adds or subtracts from the planet's projected velocity at transit. A faster crossing means a shorter transit duration, and vice versa. TTV and TDV are exactly 90° out of phase for an inclined moon orbit, which gives a powerful joint signature.
3. Hill-sphere transit signature. Within the Hill radius r_H ≈ a (M_p / 3 M_*)^(1/3) of the planet, any orbiting moon spends much of its time inside the planet's transit window. A moon may transit the star before, during, or after the planet — producing a small extra dip in the light curve adjacent to the main one. Kipping's HEK survey explicitly searches for this.
4. Rossiter-McLaughlin (RM) anomaly. When a body transits a rotating star, it preferentially blocks the redshifted or blueshifted limb depending on its sky-projected motion. The resulting line-profile distortion is the RM effect. A moon's RM signature appears as a small wobble on top of the planet's RM curve and could in principle reveal its orbit geometry directly.
5. Doppler reflex of the planet. If the planet is itself detected by radial velocity, the planet-moon barycentre's motion around the star is what the star tracks. The planet's own oscillation around that barycentre is in principle observable as a small periodic residual at the planet's transit. Direct radio detection — picking up auroral or magnetic emissions from an Io-analogue moon — has been suggested but is so far speculative.

Kepler-1625b-i — the candidate that broke into the headlines

In 2018 Alex Teachey and David Kipping at Columbia, the principal investigators of HEK, announced a candidate exomoon orbiting Kepler-1625b, a Jupiter-sized planet 8,000 light-years away around a Sun-like star. Their analysis combined three Kepler transits with a dedicated 40-hour Hubble Space Telescope campaign. Two independent statistical signals supported the claim:

• A roughly 4σ extra dip in the Hubble light curve at a separation consistent with an orbit half a Hill radius from the planet, with depth and duration matching a Neptune-sized companion.
• A 77-minute advance of the planet's transit relative to the predicted ephemeris from the previous Kepler epochs — exactly the TTV expected if the planet were being pulled forward by a trailing moon.

The result was striking but uncomfortable: a Neptune-mass moon around a Jupiter-mass planet implies a moon-to-planet mass ratio of about 3%, far above anything in the Solar System. The discovery team explicitly cast Kepler-1625b-i as a "candidate" pending follow-up. Two independent re-analyses (Kreidberg, Luger & Bedell 2019; Heller, Rodenbeck & Bruno 2019) applied different detrending pipelines to the Hubble data and reduced the significance to ~2σ or less, with the exact value depending on detrending choices. The candidate was neither confirmed nor refuted; it was relegated to "disputed." Subsequent JWST cycles have observed the system, but no public confirmation has been published as of 2025.

A follow-up HEK paper (Kipping et al. 2022) flagged a second candidate, Kepler-1708 b-i, around a Jupiter-sized planet with similar Neptune-class moon parameters. It too remains in the candidate-not-confirmed category.

Why exomoon detection is genuinely hard

The combination of three problems pushes confirmation below the noise floor of present instruments:

Problem	Effect	Magnitude (Jupiter analogue + Earth moon)
Small mass ratio	TTV amplitude	~25 seconds
Small radius ratio	Extra-dip depth	~80 ppm
Orbital phase aliasing	Dip in different place each transit	Smears under naive folding
Stellar noise & spots	Photometric scatter	50–500 ppm/transit
Detrending degeneracy	Pipeline-dependent residuals	1σ shifts between methods

The phase-aliasing point is subtle and deserves emphasis. The transit shape of a planet folded over many epochs averages cleanly to one curve. The moon, by contrast, is at a different orbital phase on each transit, so its extra dip lands at a different lateral offset each time. Folding the light curve washes the dip out into a broad bath rather than a sharp feature — exactly the opposite of what conventional planet-search algorithms are built for. You need a parameter-space scan over moon phase, not a fold-and-search.

Hill-sphere stability and the moon-to-planet ratio

For a moon to remain bound to a planet over Gyr timescales, its orbit must lie inside the Hill sphere by a comfortable margin. Numerical integrations of three-body systems show prograde moons are stable out to roughly 0.5 r_H; retrograde moons (rare, captured) are stable to ~0.7 r_H. The Hill radius itself is

r_H ≈ a × (M_p / 3 M_*)^(1/3)

For Earth at 1 AU around the Sun, r_H ≈ 0.01 AU = 1.5 million km — and the Moon orbits at 384,000 km, about a quarter r_H. For Kepler-1625b at a ≈ 0.87 AU around a 1.1 M☉ star, r_H ≈ 1/30 AU ≈ 5 × 10⁶ km, and the candidate moon orbits at ~2 × 10⁶ km — about 0.4 r_H. Inside the stable zone, comfortably so.

The moon-to-planet mass ratio sets the prior on what we expect to find. Solar System ratios cluster in two clumps: small (Galilean moons, Jupiter at 10⁻⁴; Titan at Saturn 2 × 10⁻⁴; Triton at Neptune 2 × 10⁻⁴) and one outlier (the Earth-Moon at 10⁻²). Pluto-Charon, technically a dwarf planet, sits at ~12% — produced by a major impact. A Kepler-1625b-i-style 3% ratio is plausible only via a giant impact or capture from a binary protoplanet system. If real, it would imply that planet-scale moon-formation channels exist and we have simply not seen them in our own Solar System.

Could an exomoon be habitable?

Habitability for moons is, in some respects, easier than for planets. A large moon in the stellar habitable zone of a giant planet receives:

• Stellar insolation at the standard level set by the host star and orbital distance.
• Tidal heating from the planet's gravity, which on Io reaches ~3 W/m² — comparable to the geothermal flux of Earth — and on Europa keeps a global subsurface ocean liquid despite a surface at −170 °C.
• Planetshine — reflected starlight from the giant planet, modest in absolute terms but non-negligible during eclipses by the planet.

Heller and Barnes (2013) showed that a moon needs a mass above roughly 0.25 Earth masses to hold onto an atmosphere over Gyr against atmospheric escape. That sets the floor; the ceiling is set by Hill-sphere stability and impact-driven formation. The implied "Pandora" — borrowing the Avatar terminology — is a 0.3 to 5 M_Earth moon around a Jupiter-class planet in the habitable zone of a K or G dwarf. Many such systems should exist; finding one and confirming surface conditions is the long-term prize.

The HEK survey and the wait for PLATO

David Kipping's Hunt for Exomoons with Kepler (HEK) survey, launched in 2012, has been the systematic effort behind both Kepler-1625b-i and Kepler-1708 b-i. HEK takes the Kepler photometry, looks for planet candidates with high signal-to-noise, then runs joint Bayesian fits over planet + moon parameter space — including the moon's mass, radius, semi-major axis, inclination, and phase at each transit. The Bayes-factor threshold for "candidate" is intentionally conservative.

The instrumental story since Kepler has been one of slow improvement:

• K2 (2014–2018). Kepler's reaction-wheel-failure follow-on. Lower precision per target but new fields. Some exomoon-friendly long transits.
• TESS (2018–). Wide-field two-minute cadence, mostly short-period planets. Transit baselines are usually too short for exomoon TTV detection, but bright-target precision is excellent.
• CHEOPS (2019–). Targeted high-precision photometry of known planet hosts. Has been used for exomoon follow-up.
• JWST (2022–). NIRCam and NIRSpec reach 10–30 ppm photometry on bright transit hosts. Single-transit detection of a Mars-sized moon around a hot Jupiter is in principle within reach.
• PLATO (2026 launch). ESA's wide-field 50-ppm-precision long-baseline mission, deliberately designed for Earth-twin transit detection around bright stars. Multi-year stares on the same fields make it the natural exomoon machine.

Kipping has publicly forecast a confirmed exomoon in the 2025–2030 window, with the strongest hopes pinned on PLATO's first multi-year stare. The community's working assumption is that the first confirmation will be a large moon — Neptune to super-Earth scale — around a giant planet, because that combination maximises detectability and is the only class of moon currently above the noise floor.

How exomoons might form

By analogy with the Solar System, three formation channels are expected to dominate:

• Circumplanetary-disk formation. The Galilean moons and Titan formed in disks of gas and dust around the young Jupiter and Saturn — small-scale versions of the protoplanetary disk that built the planets. This channel naturally yields moon-to-planet mass ratios of 10⁻⁴, regular prograde orbits, and ice-rich compositions. A Kepler-1625b-i style 3% ratio is hard to make this way.
• Giant impact. The Earth-Moon system formed from a Mars-sized impactor (Theia) striking the proto-Earth ~4.5 Gyr ago. Impact moons have prograde orbits, masses comparable to but smaller than the planet, and compositions enriched in the planet's mantle. A 3% mass ratio is plausible if the impactor is comparably massive to the proto-planet.
• Capture. Triton, retrograde at Neptune, was almost certainly captured from a binary trans-Neptunian object. Capture is geometrically rare but allows for very large moons — including up to the binary-planet limit (Pluto-Charon at 12%).

An exomoon population that includes a non-trivial fraction of Neptune-scale or super-Earth-scale satellites would indicate that one of the rarer channels — giant impact or capture — operates more frequently than Solar-System statistics suggest. This is, in fact, what Kepler-1625b-i would imply, which is one reason the claim is so consequential.

Common pitfalls and misconceptions

• "No detection" is not "no exomoons." The absence of confirmed exomoons reflects detection limits, not absence of moons. Estimated occurrence rates from HEK suggest at most ~50% of giant planets host Neptune-mass moons; that is consistent with the data even if none are confirmed yet.
• TTV is not unique to moons. A second non-transiting planet in the system also induces TTV via gravitational interaction. The TTV-TDV phase relation and amplitude scaling are different for planet-planet vs planet-moon, but disentangling them requires multiple high-S/N transits.
• The "moon transit" is not just the moon eclipsing the star. A naive picture imagines a planet plus a small extra dip from the moon transiting in sequence. In reality the moon may transit before, during, or after the planet, or not at all (its inclination may carry it above or below the stellar disk). Sky-projected geometry varies transit to transit.
• Hill-sphere edge is not a hard boundary. Numerical integrations show the outer Hill sphere is unstable on Myr timescales for prograde moons. Sustainable orbits sit at less than ~0.5 r_H.
• Tidal heating cuts both ways. A moon close enough for strong tidal heating is also close enough for tidal locking and orbit-altering dissipation. Long-term thermal habitability requires being on the right side of the runaway-greenhouse boundary, which depends on the moon's mass, eccentricity, and the planet's gravitational coupling.