JWST Transit Stacking: Detecting an Exoplanet Atmosphere from Noise

Observation

Transits stacked (N) 1

Instrument photon noise 120 ppm

Cloud / haze cover 0%

Planet radius 1.10 R⊕

Atmosphere composition

Detection

SNR — H₂O (1.4 μm)

0.0σ

SNR — CO₂ (4.3 μm)

0.0σ

Transit depth

0 ppm

Noise / transit set

0 ppm

How it works

During a transit the planet blocks a fraction of the star's light. At a wavelength where its atmosphere is opaque (an absorption line), the planet looks slightly bigger, so the transit is slightly deeper. The baseline transit depth and the size of that extra dip are:

δ(λ) = (Rp(λ) / Rs)²
Δδ_feature ≈ 2 · Rp · H / Rs²     (H = atmospheric scale height)

Each single transit is buried in photon noise σ₁ set by how many photons JWST collects. Stacking N independent transits averages the noise down while the real spectral shape stays fixed, so the signal-to-noise ratio of a feature grows as:

σ_N = σ₁ / √N
SNR = Δδ_feature / σ_N = Δδ_feature · √N / σ₁

This √N law is exactly why JWST needed several stacked transits of TRAPPIST-1 b/e — not one — before the CO₂ and H₂O features could be told apart from noise at high confidence (SNR ≳ 5σ, marked "detected" below).

Transits stacked (N) — more transits observed and co-added → noise shrinks by √N.
Instrument photon noise — a fainter host star or smaller aperture raises σ₁ per transit.
Cloud / haze cover — high-altitude aerosols flatten the spectrum (Rayleigh/Mie scattering masks molecular lines), directly muting Δδ_feature — the real degeneracy that makes some exoplanet spectra ambiguous.
H₂O / CO₂ toggles — turn each molecule's absorption band on or off in the true (noiseless) spectrum being sampled.

TRAPPIST-1 (star) Planet + atmosphere

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