Exoplanet Phase Curve

The big idea: a planet you cannot see, mapped anyway

We almost never resolve an exoplanet as anything more than a single unmeasurable point buried in the glare of its star — and usually not even that. A phase curve is the trick that turns this limitation into a map. The idea is borrowed straight from our own sky: the Moon brightens and dims through its phases because we see varying amounts of its sunlit face. A close-in, tidally locked planet does the same, except that it is so faint we only ever measure the total light of star plus planet. As the planet orbits, the fraction of its hot, illuminated dayside turned toward Earth changes, and the combined flux rises and falls by a sliver. Plot that sliver against orbital phase and you have a phase curve.

The payoff is enormous relative to the effort. Without ever separating the planet's light, the curve's amplitude tells you the day–night temperature contrast; the brightness at its trough tells you how warm the nightside is; the offset of the peak from secondary eclipse tells you which way the winds blow and how fast; and, with a spectrograph, the way all of this changes with wavelength tells you about clouds, molecules, and the vertical temperature structure. A phase curve is a longitudinal map of a world drawn from a single wiggling number.

The geometry: phases, transit, and secondary eclipse

Fix the geometry in your head with one orbit of a transiting hot Jupiter. At transit (orbital phase 0) the planet passes directly in front of the star; the side facing us is the cold nightside, so the planet contributes almost nothing and the system is faintest from the planet's perspective (the deep transit dip is a separate, much larger effect). A quarter orbit later we see the planet half-lit, like a first-quarter Moon. At secondary eclipse (phase 0.5) the fully lit dayside faces Earth — right before the planet slips behind the star and its light vanishes entirely, giving a clean measurement of the dayside flux alone. The phase curve is the smooth, sinusoid-like variation connecting these moments.

For a perfectly uniform, immediately-responding atmosphere, the brightness would peak exactly at secondary eclipse. It does not. On real hot Jupiters the peak arrives a little early, because the hottest patch of atmosphere is not at the point directly under the star.

The hot-spot offset: reading the wind

A tidally locked hot Jupiter has a permanent substellar point — the spot directly beneath the star, baked continuously. Naively the hottest place should be exactly there. But these atmospheres host powerful superrotating equatorial jets: a broad eastward wind, often supersonic, that drags heat downwind before the gas has time to radiate it away. The result is a hot spot offset to the east of the substellar point. Because the brightest region leads the geometric dayside, the phase-curve maximum occurs before secondary eclipse.

This is the single most beautiful inference in the field: a few-degree shift in the timing of a brightness peak, measured on a star you cannot resolve, becomes a wind-speed measurement on an alien atmosphere. Spitzer's landmark 8-micron phase curve of HD 189733b in 2007 (Knutson et al.) showed the peak leading eclipse by roughly 20–40 degrees of longitude, implying jet speeds of kilometers per second — in line with general-circulation models of these worlds.

Heat redistribution and day–night contrast

Two numbers from the curve quantify the climate. The first is the day–night contrast: how much brighter the system is at secondary eclipse than at transit (in thermal light). The second is the nightside flux, read directly from the curve's minimum. Together they measure heat redistribution — the efficiency with which winds carry energy around to the unlit hemisphere.

The pattern across the hot-Jupiter population is systematic and physically sensible: the very hottest planets redistribute heat poorly. On an ultra-hot Jupiter the dayside is so blistering that radiative cooling is faster than the winds can move heat, so the day–night contrast is extreme and the nightside is comparatively cold. Cooler hot Jupiters even out their temperatures more efficiently and show shallower phase curves. The trend was first laid out clearly by Komacek & Showman's circulation theory and confirmed by Spitzer phase-curve surveys.

How phase-curve features translate into physics

Observable	What it encodes	Typical hot-Jupiter value
Phase amplitude (thermal IR)	Day–night temperature contrast	~100–3000 ppm
Peak offset from eclipse	Eastward jet speed / wind direction	~10–40° east
Flux at curve minimum	Nightside brightness temperature	~700–1300 K
Secondary-eclipse depth	Dayside brightness temperature / albedo	~1000–3000 K (hot), up to 4000+ K (ultra-hot)
Optical peak after eclipse	Reflective clouds on western dayside	Seen on Kepler-7b, HAT-P-7b

Thermal emission vs reflected light

A phase curve is not always made of the same kind of light, and untangling the two is central to interpreting it. In the infrared, where Spitzer and JWST work, the planet's signal is dominated by its own thermal glow — thousands of kelvin of blackbody emission from the dayside. In the optical, where Kepler and TESS observe, the signal blends thermal emission with starlight reflected off the atmosphere and clouds, plus two subtle dynamical effects: Doppler beaming (the star appears brighter as it moves toward us in its tiny reflex orbit) and ellipsoidal variation (the star is slightly tidally distorted). For very hot planets thermal emission can leak into the optical; for cooler ones reflected light dominates.

Thermal vs reflected phase-curve components

Component	Wavelength regime	Peak location	What it reveals
Thermal emission	Infrared	Before eclipse (eastward hot spot)	Temperature map, jet speed, redistribution
Reflected light	Optical / blue	Often after eclipse (western clouds)	Albedo, cloud condensation, particle size
Doppler beaming	Broadband optical	Tracks radial velocity	Planet mass cross-check
Ellipsoidal variation	Broadband optical	Twice per orbit	Tidal distortion of the star

The cloud story is striking. Several Kepler hot Jupiters — most famously Kepler-7b — show optical phase curves that peak after secondary eclipse, the opposite of the thermal hot-spot offset. The natural reading is that the brightest part of the dayside is its cooler western half, where temperatures drop low enough for reflective silicate clouds to condense. That single phase offset produced the first crude cloud map of an exoplanet.

From Spitzer to JWST

Phase curves are demanding because the signal is buried in stellar noise and instrumental drift over many hours or days of continuous staring. Spitzer opened the field, observing full orbits of hot Jupiters in the mid-infrared and delivering the first hot-spot offsets and day–night maps. Kepler, with its photometric stability over four years, turned optical phase curves into precision tools, separating reflected light, thermal emission, and beaming. TESS brings the same to bright, nearby targets ideal for follow-up.

JWST changed the game again by making phase curves spectroscopic. Instead of one brightness number per orbit, it records a spectrum at every phase — a phase-resolved spectrum. The 2023 MIRI phase curve of WASP-43b mapped temperature with longitude, found a nightside far cooler than cloud-free models allow (implying thick nightside clouds), and detected the strong day–night water-abundance and temperature gradients predicted by circulation models. We are now reading weather, not just brightness.

Why hot Jupiters — and what is next

Hot Jupiters dominate phase-curve science for blunt reasons: they are big, blazing hot, and orbit in days, so their signal is as large as it gets and you can observe many full orbits quickly. A planet on a Mercury-like orbit blowtorched to 1500–3000 K radiates strongly in the infrared, and its short period makes a complete phase curve a feasible observation rather than a multi-year campaign.

The frontier is pushing down in temperature and size — warm Neptunes, sub-Neptunes, and eventually small rocky worlds — where amplitudes shrink to tens of ppm or less and systematics dominate. Phase curves of rocky planets like the TRAPPIST-1 worlds and lava planets such as 55 Cancri e probe whether they hold an atmosphere at all: a measurable hot-spot offset would betray winds, and therefore air, while a peak locked to the substellar point would point to a bare, heat-conducting rock. The same single wiggling number that mapped a hot Jupiter's jets may yet tell us which small worlds have skies.