SVEEEETIES: Singular vector expansion to estimate Earth-like exoplanet temperatures from infrared emission spectra

Abstract

Context. Detailed characterizations of exoplanets are moving to the forefront of planetary science. Temperature is a key marker for understanding atmospheric physics and chemistry. Aims. We aim to retrieve temperatures of N2-O2 dominated atmospheres from secondary eclipse spectroscopic observations of the thermal emission of Earth-like exoplanets orbiting G-, K-, and M-stars using large future space telescopes. Methods. Line-by-line radiative transfer was used to generate synthetic thermal infrared (TIR) observations. Atmospheric temperature is approximated by an expansion with base vectors defined by a singular value decomposition of a matrix comprising representative profiles. Nonlinear least squares fitting is used to estimate the expansion coefficients. Results. Analysis of the $4.3 \rm\,\mu m$ and $15 \rm\,\mu m$ CO2 bands in the TIR permits inference of temperatures even for low signal-to-noise (S/N) ~5 at medium resolution. Deviations from the true temperature in the upper troposphere and stratosphere are usually a few Kelvin, with larger deviations in the upper atmosphere and, less often, in the lower troposphere. Although the performance of the two bands is equivalent in most cases, the longwave TIR is more favorable than the shortwave due to increased star-planet contrast. A high spectral resolution, as provided by JWST instruments, is important for retaining sensitivity to the upper atmosphere. Furthermore, the selection of an appropriate set of base functions is also key. Conclusions. Temperature in the mid-atmosphere can be suitably characterized by IR spectroscopy with a resolution of at least 1000 (ideally ~2500). Obtaining the necessary S/N could be feasible with future missions, such as the Origins Space Telescope or the Large Interferometer for Exoplanets. Meanwhile a least squares fitting with appropriate base functions is also applicable for other classes of planets.