Empirically Constraining the Spectra of Stellar Surface Features Using Time-resolved Spectroscopy

Transmission spectroscopy is currently the technique best suited to study a wide range of planetary atmospheres, leveraging the filtering of a star's light by a planet's atmosphere rather than its own emission. However, as both a planet and its star contribute to the information encoded in a transmission spectrum, an accurate accounting of the stellar contribution is pivotal to enabling robust atmospheric studies. As current stellar models lack the required fidelity for such accounting, we investigate here the capability of time-resolved spectroscopy to yield high-fidelity, empirical constraints on the emission spectra of stellar surface heterogeneities (i.e., spots and faculae). Using TRAPPIST-1 as a test case, we simulate time-resolved JWST/NIRISS spectra and demonstrate that with a blind approach incorporating no physical priors, it is possible to constrain the photospheric spectrum to ≤0.5% and the spectra of stellar heterogeneities to within ≲10%, a precision that enables photon-limited (rather than model-limited) science. Now confident that time-resolved spectroscopy can propel the field in an era of robust high-precision transmission spectroscopy, we introduce a list of areas for future exploration to harness its full potential, including wavelength dependency of limb darkening and hybrid priors from stellar models as a means to further break the degeneracy between the position, size, and spectra of heterogeneities.