---
title: "Exoplanet Transmission Spectra Interactive Lab | Sandbox Physics"
description: "Does a spectral bump prove that a planet has water? Water leaves several absorption bands at related wavelengths."
canonical_url: "https://sandboxphysics.com/labs/exoplanet-transmission-spectrum/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/exoplanet-transmission-spectrum/"
last_modified: "2026-11-03"
---

Starlight through an atmosphere

# Exoplanet Transmission Spectra, Clouds and Starspots

**Does a spectral bump prove that a planet has water?** Water leaves several absorption bands at related wavelengths. Their joint shape and strength can identify it more reliably than one bump. Cloud height, atmospheric temperature and cool regions on the star change the same spectrum, so the interpretation must compare those possibilities together.

Drag the cloud top or warm the atmospheric ring. Follow grazing starlight into a water absorption spectrum, then change the unocculted stellar surface.

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

Model assumptions

Synthetic, spherical, isothermal hydrostatic atmosphere with inverse-square gravity and a finite top. A prescribed hydrogen–helium mixture contains a constant water number fraction; the molecular mass changes with that fraction. Actual ExoMolOP POKAZATEL cross sections retain the dominant water isotopologue and their stated sampled resolution, temperature and pressure grid. Below the minimum source pressure the cross section is frozen; sensitivity to that choice is reported separately from numerical accuracy. The opaque reference radius is defined at ten bar and a gray cloud supplies a second opaque boundary. CIA, other gases, wavelength-dependent aerosol scattering, refraction, thermal emission, escape and three-dimensional terminator structure are omitted. Native wavelength-dependent blocked areas are solved before photon and stellar weighting in the reported observation bins. PHOENIX photosphere and cool-region spectra describe a uniform-intensity stellar disk with an immaculate transit chord; active regions are unocculted. The measured NIRISS points are an independently fitted radius-ratio spectrum with an upstream limb-darkening treatment. This experiment does not refit those original light curves. The planet and gas retain their radial proportions; the star, separation and photon-marker speed are schematic. The public tutorial compares restricted proper posteriors and retains their systematic residuals.

## From grazing rays to a transit spectrum

Gold: planetary prediction. Coral: the same atmosphere behind the chosen stellar surface. White points: frozen WASP-39 b NIRISS measurements with reported errors.

### Photon-weighted depth in the observed bins

Water opacity is evaluated before the nonlinear transmitted fraction and annular area. The supplied bin halfwidths define an approximate top-hat response. This is a fitted-radius spectrum comparison, with the original light-curve limb-darkening treatment upstream.

### How each grazing ray becomes transparent

Four actual native wavelengths from the same gas column. Height starts at the ten-bar radius. The gold marker locates the opaque cloud; paths below it are hidden by the cloud.

Real-data conditional inference and source files

The public exercise fits all 74 frozen bins with normalized priors, compares gray-cloud and stellar-contamination models, and saves posterior predictions and residuals. The interactive controls are synthetic physical conditions, not an automatic retrieval.

[Rerun the frozen NIRISS analysis](https://sandboxphysics.com/stories/planet-atmospheres/retrieve-a-frozen-niriss-spectrum/)

Physics tutorial

## Why an atmosphere changes a planet’s apparent size

**Background** During transit, most blocked light hits the opaque body. A small extra fraction skims through the surrounding gas. The gas absorbs different wavelengths by different amounts.

**Why it matters** The same water molecule leaves several bands. Their relative heights also depend on how much gas the ray crosses and where an opaque cloud interrupts the path.

Start with the essentials

- **Focus question**: Can a higher cloud hide water without removing the water?
- **One-sentence intuition**: A cloud hides the deepest grazing paths. Molecular bands that already become opaque higher up can remain visible after weaker features have flattened.

### Core mathematical model

#### Scale height near the reference radius

$$
H_0=\frac{k_B T}{\bar m g_0}
$$

Temperature raises the vertical distance over which pressure changes appreciably; heavier molecules and stronger gravity reduce it. The complete calculation lets gravity decrease with radius.

#### A grazing ray loses photons along its whole path

$$
\tau_\lambda(b)=\int_{\mathrm{ray}}n(r)x_{\mathrm{H_2O}}\sigma_\lambda[T,P(r)]\,ds
$$

The dimensionless optical depth adds number density times molecular fraction times cross section over path length. The same value sets the light markers and the absorbed annulus.

#### Partially transparent rings add an effective area

$$
A_\lambda=\pi R_c^2+2\pi\int_{R_c}^{r_{\mathrm{top}}}(1-e^{-\tau_\lambda})b\,db
$$

The opaque cloud contributes a disk. Each surrounding annulus contributes its area multiplied by the fraction of light it removes.

### Common difficulties

#### An absorption band can raise a transit spectrum

**Typical misconception** Absorption should always point downward.

**Better mental model** This plot measures blocked light, not transmitted intensity. A stronger molecular absorption makes the planet appear larger and raises the depth.

#### A cold patch changes the reference starlight

**Typical misconception** Anything outside the transit chord cancels from a normalized spectrum.

**Better mental model** The occulted light comes from the normal photosphere, but the out-of-transit denominator includes the cooler spectrum. Their wavelength-dependent ratio changes the measured depth.

### Run the experiment

1. 01

   #### Lift the cloud

   Start with Clear water bands. Predict which bands will survive, then drag the gold cloud ring outward and compare the band shapes.

   **What to observe:** The weak windows fill in first. The strongest water bands stay above the opaque boundary longer.

2. 02

   #### Change temperature at the same composition

   Reset, then raise Atmospheric temperature. Wait for the native gas calculation to finish and compare the complete spectrum and ray profile together.

   **What to observe:** The atmospheric scale and the real temperature-dependent molecular opacity both change.

3. 03

   #### Move the stellar denominator

   Load Spotted star, then reduce Unocculted cool-region fraction to zero. Keep the planetary spectrum fixed and compare the coral and gold curves.

   **What to observe:** The stellar correction disappears without changing the gas column. The 3500-kelvin stress preset is a synthetic active surface.

Physical conclusion

Compare several bands and a stellar-contamination model before interpreting one feature. Radius, temperature, cloud pressure and abundance can compensate for one another.

## Related experiments and articles

Starlight through a planet’s atmosphere · Reading path

### Starlight through a planet’s atmosphere

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

1. [Article **How several spectral bands reveal water around a planet**](https://sandboxphysics.com/stories/planet-atmospheres/why-water-needs-more-than-one-spectral-bump/)
2. [Article **How temperature and gravity set an atmosphere’s height**](https://sandboxphysics.com/stories/planet-atmospheres/scale-height-and-an-absorbing-annulus/)
3. [Article **Follow a grazing ray, then add the missing light**](https://sandboxphysics.com/stories/planet-atmospheres/derive-a-pressure-dependent-transmission-spectrum/)
4. [Article **What an atmospheric posterior can and cannot tell us**](https://sandboxphysics.com/stories/planet-atmospheres/probability-radius-and-atmospheric-degeneracy/)
5. [Article **Rerun a conditional retrieval of an actual NIRISS spectrum**](https://sandboxphysics.com/stories/planet-atmospheres/retrieve-a-frozen-niriss-spectrum/)
6. [Article **Read atmospheric asymmetry and resolved-line evidence from the original papers**](https://sandboxphysics.com/stories/planet-atmospheres/read-limb-asymmetry-and-high-resolution-evidence/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

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