---
title: "Exoplanet Thermal Phase Curves Interactive Lab | Sandbox Physics"
description: "How does a wind change the brightness of an unresolved planet? Wind carries absorbed heat onto the nightside before the gas cools."
canonical_url: "https://sandboxphysics.com/labs/exoplanet-thermal-phase-curve/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/exoplanet-thermal-phase-curve/"
last_modified: "2026-11-03"
---

AC21 · Carry daylight into the night

# Exoplanet Thermal Phase Curves

**How does a wind change the brightness of an unresolved planet?** Wind carries absorbed heat onto the nightside before the gas cools. As a planet orbits, different longitudes face us, changing its total brightness. The curve measures projected emission; separating wind speed, thermal inertia and cloud effects needs additional assumptions or observations.

Drag the wind and spin of a radiating planet. Follow transported heat, the same temperature field’s phase curve, and secondary eclipse.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Synthetic single-layer thermal model with constant configured areal capacity, prescribed zonal angular flow, periodic longitude and independent latitude bands. The orbit is circular and aligned. Unit thermal emissivity and a separate bolometric Lambert reflector approximate distinct incoming and outgoing bands. No momentum, meridional transport, clouds, vertical transfer or chemistry is solved. False color shows the computed layer temperature. Presets start new steady records; other configuration changes retain temperature and record any capacity-related energy jump. An implicit conservative upwind step evolves the field. Eclipse affects observer visibility only. The real MIRI tutorial uses separately labeled reduced measurements and conditional uncertainties.

The globe is false-color layer temperature, not a resolved photograph. Cyan tracers show gas moving relative to the star, amber meridians follow the body, and the blue arrow shows wind relative to the body.

Freeze this field and observe a full orbit

Equatorial temperatures in this same field

Orange is thermal emission; green is the separately computed ideal Lambert reflection. Both are bolometric planet-to-star ratios. Phase zero is primary transit and secondary conjunction is halfway around; the vertical line marks the physical clock, while the frozen-field forecast is distinct from the evolving saved history.

Numerical resolution and what the night fraction means

The layer has 128 periodic longitude cells and 24 equal-area latitude bands. Its temperatures are piecewise constant; the observer integrates that field across a projected disk. Implicit upwind transport has numerical diffusion. At the default parameters, the nightside fraction changes by about 0.83 percent between 128 and 512 longitude cells. The night fraction subtracts the prescribed internal heat; during a transient it is not yet a steady redistribution efficiency.

Physics tutorial

## A warm parcel crosses the evening edge

**Background** A close planet absorbs starlight on one hemisphere. Moving gas carries thermal energy before radiation removes it.

**Why it matters** An unresolved infrared curve changes as different longitudes face us. Its maximum can occur before the star hides the planet.

Start with the essentials

- **Focus question**: Can the same phase curve determine heat capacity and wind speed separately?
- **One-sentence intuition**: The steady circular temperature field depends on the product of capacity and relative angular flow. Its light is then a projected hemisphere sum.

### Core mathematical model

#### Relative flow

$$
\omega_{\rm eff}=\Omega_{\rm core}+u_{\rm eq}/R_p-n
$$

A synchronized body can have a moving atmosphere. Positive angular flow is eastward from the substellar point.

#### The radiating layer

$$
C(\partial_tT+\omega_{\rm eff}\partial_\lambda T)=(1-A_B)F_\star\mu_s^++F_{\rm int}-\sigma T^4
$$

The illuminating cosine is clipped at zero on the dark side. Every term is a power per area.

#### Projected emission

$$
F_p=\frac{R_p^2}{D^2}\int_{\rm visible,unocculted}\frac{\sigma T^4}{\pi}\mu_o\,d\Omega
$$

The observing cosine weights projected area. Secondary eclipse changes this visible region while the thermal equation continues.

### Common difficulties

#### A maximum is a hemisphere sum

**Typical misconception** Peak timing directly locates the hottest parcel.

**Better mental model** Many longitudes contribute together, weighted by projected area. Compare the temperature profile with the timing of the phase-curve peak.

#### Fast flow averages longitudes

**Typical misconception** Rapid zonal flow makes every latitude equally hot.

**Better mental model** Each latitude has its own mean stellar heating. This model has no exchange between latitude bands.

### Run the experiment

1. 01

   #### Reverse the wind

   Compare Eastward heat with Heat flows west. Predict the shift before changing presets.

   **What to observe:** The temperature map mirrors, and the unobscured curve maximum changes sides of secondary conjunction.

2. 02

   #### Keep the steady product

   Pause Eastward heat, double capacity and halve wind, then continue the clock.

   **What to observe:** The retained field remains a steady solution because its capacity-flow product is unchanged. The capacity storage jump is saved as configuration energy.

3. 03

   #### Change the view

   Switch to Observer view through eclipse, then inspect the same field in Flow view.

   **What to observe:** The star hides planetary light on its path to the observer. Stellar illumination continues during secondary eclipse.

Physical conclusion

Follow heating, material motion and observer visibility separately, then connect them through the same temperature field.

## Related experiments and articles

Heat carried into an unseen night · Reading path

### Heat carried into an unseen night

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Seeing day and night on an unresolved planet**](https://sandboxphysics.com/stories/planet-phase-curves/dayside-in-starlight/)
2. [Article **The areas that set a planet's temperature**](https://sandboxphysics.com/stories/planet-phase-curves/areas-and-temperatures/)
3. [Article **Follow a gas parcel into the night**](https://sandboxphysics.com/stories/planet-phase-curves/a-parcel-crosses-night/)
4. [Article **Add a globe's light to make a phase curve**](https://sandboxphysics.com/stories/planet-phase-curves/from-a-globe-to-a-curve/)
5. [Article **Replay the WASP-43b MIRI phase curve**](https://sandboxphysics.com/stories/planet-phase-curves/replay-wasp43-miri/)
6. [Article **Read the chemistry, clouds and maps behind a phase curve**](https://sandboxphysics.com/stories/planet-phase-curves/clouds-chemistry-and-maps/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)