{
  "abstract": "Transmission spectroscopy of rocky exoplanets orbiting late M dwarfs is limited by stellar contamination rather than photon noise. We present a framework for this contamination-dominated regime, fitting all transit epochs jointly with a Gaussian process per epoch for the time-varying stellar contamination and a single atmospheric model shared across epochs. We use pure CO$_2$, H$_2$O, and CH$_4$ models scaled by their peak-to-trough amplitude, allowing us to measure how large a signal must be to be recovered. We calibrate this framework using injection-recovery tests and 17 archival JWST/PRISM transits of the airless sibling TRAPPIST-1 b to quantify the spurious signals that stellar contamination alone produces. Applied to four JWST/NIRSpec PRISM transits of TRAPPIST-1 c, our framework recovers injected CO$_2$ signals without bias and reaches detection thresholds of 146 (171) ppm for moderate (strong) evidence, compared with 96 ppm if there were no stellar contamination. CO$_2$ and CH$_4$ produce no spurious signals on the airless control planet, whereas H$_2$O shows a persistent stellar floor of $+55 \\pm 34$ ppm. TRAPPIST-1 c is consistent with a featureless, airless baseline for all three molecules. Our 95 per cent upper limit of 90 ppm for CO$_2$-shaped signals effectively rules out clear, isothermal pure-CO$_2$ atmospheres ($\\geq$0.1 bar) and N$_2$-dominated atmospheres with 1 per cent CO$_2$ ($\\geq$1 bar) at the equilibrium temperature. An empirical scaling study using 2 to 10 transits of TRAPPIST-1 b shows the CO$_2$ detection threshold decreasing with the number of transits $k$ as $k^{-0.6}$, reaching 80 ppm at ten transits, while water searches become limited by the stellar floor beyond about six transits. CO$_2$ atmospheres, by contrast, are detectable when we utilize our framework to account for stellar activity at the cost of roughly 1.5 to 2 times as many transits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37722",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander D. Rathcke"
    },
    {
      "name": "Lars A. Buchhave"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a840bydct9nz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37722",
  "fulltext_url": null,
  "id": "a840bydct9nz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37722",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.EP"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "openalex",
      "3103|Stellar, planetary, and galactic studies"
    ]
  ],
  "openalex": "W7214996869",
  "pdf_url": "https://arxiv.org/pdf/2609.37722",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a840bydct9nz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37722",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37722"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.EP",
      "subfield": "planetary"
    }
  ],
  "title": "Detecting atmospheres in the presence of stellar contamination: an empirically calibrated framework applied to four JWST/NIRSpec PRISM transits of TRAPPIST-1c",
  "title_text": "Detecting atmospheres in the presence of stellar contamination: an empirically calibrated framework applied to four JWST/NIRSpec PRISM transits of TRAPPIST-1c",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/a840bydct9nz1",
  "venue": "arXiv",
  "versions": []
}