Atmospheres and spectra
Planet atmospheres from grazing rays to molecular evidence
A planet’s atmosphere filters grazing starlight. Follow the gas and the missing photons into a spectrum, then ask which atmospheric and stellar explanations the data can separate.
Start
How several spectral bands reveal water around a planet
Water is identified through related absorption bands. Clouds and the star change their apparent strength, so several bands must agree.
L1
How temperature and gravity set an atmosphere’s height
Derive hydrostatic scale height, include changing gravity and calculate where a cloud sits above a specified pressure radius.
L2
Follow a grazing ray, then add the missing light
Derive slant optical depth, integrate an absorbing annulus and bin the transmitted area with stellar photon weights.
L3
What an atmospheric posterior can and cannot tell us
Build a proper posterior, expose radius–abundance–cloud degeneracies and use predictive residuals to recognize a failed atmospheric model.
Tutorial
Rerun a conditional retrieval of an actual NIRISS spectrum
Download measured WASP-39 b bins and a validated physical model; reproduce proper posteriors, prior sensitivity and failed residuals offline.
Paper guide
Read atmospheric asymmetry and resolved-line evidence from the original papers
Read fixed full-text WASP-39 b limb and high-resolution retrieval papers through their figures, likelihood assumptions and failure tests.
Three connected textbook chapters move from hydrostatic gas to slant absorption and a proper posterior. The public tutorial reruns an actual NIRISS spectrum and retains poor predictive fits. The paper guide adds the timing and resolved-line information that a mean depth spectrum cannot contain.
Sources and calculation scope
- Vehtari et al. (2021) · Rank-normalized split R-hat and effective sample size
Bayesian Analysis 16, 667–718; corrected rank-normalization denominator and author appendix https://avehtari.github.io/rhat_ess/rhat_ess.html. The independent NumPy implementation also follows the Stan 2.33 reference definition of autocorrelation and initial positive, monotone pair truncation. IID, AR(1) and deliberately separated-chain checks are included. These diagnostics concern sampling, not physical model adequacy.
- Feinstein et al. (2023) · Early Release Science of WASP-39 b with JWST NIRISS
Published Nature 614, 670–675. Read Figures 1–3 and the extraction, light-curve and atmospheric-model Methods. The tutorial uses a fixed author-released nirHiss spectrum, with 74 selected order-one bins; it does not repeat the paper’s full chemical and cloud retrieval.
- WASP-39 b NIRISS author data · Zenodo 7709712 and fixed repository commit
Archived data are CC BY 4.0. The exact CSV comes from author repository commit 0608071e1e70ec7ff12707774ea03ace4b52ea85, which also carries an MIT license. Original bytes, row selection, units and SHA256 are saved in the public provenance file. The complete archive was not downloaded.
- Heng and Kitzmann (2017) · Transmission spectra and the radius–pressure degeneracy
Fixed accepted version, arXiv 1702.02051v2; published MNRAS 470, 2972–2981, DOI 10.1093/mnras/stx1453. Section 2.2 derives the thin, constant-gravity limit; Sections 3.2–3.3 discuss the reference radius and pressure. The course derives its inverse-square-gravity extension separately.
- Chubb et al. (2021) · ExoMolOP cross sections and k-tables
A&A 646, A21, full text Sections 3.1–3.3 and Tables 1–3. The actual sampled cross-section product supplies pressure, temperature, wavenumber and square centimetres per molecule. Its approximate hydrogen–helium broadening and source resolution remain model assumptions.
- Polyansky et al. (2018) · The POKAZATEL water line list
Primary line-list description for the dominant water isotopologue. The delivered opacity is the derived ExoMolOP product, not a new computation of the full line list. ExoMol data and the extracted opacity derivatives retain CC BY-SA 4.0.
- Husser et al. (2013) · A PHOENIX library of stellar atmospheres and spectra
Primary model-library description. The frozen stellar input is the separately versioned medium-resolution derivative at Zenodo 17674612, version 1.0, CC BY 4.0. Actual ASCII units are nanometres and erg per square centimetre per second per nanometre; the spectra are unscaled surface fluxes.
- Stuitje · PHOENIX medium-resolution stellar spectra, version 1.0
Three exact 3500, 4500 and 5500 kelvin members at log gravity 4.5 in cgs units, solar metallicity and zero alpha enhancement. The public bundle preserves original members, ZIP offsets, CRC32, SHA256 and CC BY 4.0 attribution. Effective spectral resolution is 5000; oversampling does not increase that resolution.
- Rackham, Apai and Giampapa (2019) · The Transit Light Source Effect II
Fixed arXiv 1812.06184v1; published AJ 157, 96, DOI 10.3847/1538-3881/aaf892. Section III.1, Equations 3–6 define the unocculted-region correction and its uniform-intensity approximation. Section IV.3 explains why molecular contamination is generally weak at typical FGK activity levels.
- Espinoza et al. (2024) · Inhomogeneous terminators on WASP-39 b
Published Nature 632, 1017–1020; fixed preprint arXiv 2407.10294v1. Read Figures 1–3 and the orbital-parameter and limb-darkening robustness Methods. Its NIRSpec 2–5 micrometre limb spectra are a different product from the NIRISS tutorial spectrum. The guide performs figure-reading exercises, not a new limb retrieval.
- Brogi and Line (2019) · Retrieval with high-resolution cross-correlation spectroscopy
Fixed accepted arXiv 1811.01681v2; published AJ 157, 114, DOI 10.3847/1538-3881/aaffd3. Section II.2.2 derives the likelihood mapping; Figures 2, 5, 7 and 10 test processing, calibration, line-list choice and missing absorbers. The low-resolution teaching opacity cannot reproduce the paper’s resolved-line analysis.