Stacking transmission spectra of different exoplanets

TL;DR

This paper investigates the physical interpretation of stacked exoplanet transmission spectra, showing they approximate the geometric mean of individual spectra and providing guidelines for their use in population studies.

Contribution

It demonstrates that stacked spectra are mathematically similar to geometric means of abundance ratios and explores conditions under which stacking is valid for exoplanet atmospheres.

Findings

Stacked spectra approximate the geometric mean of individual spectra.

Stacking is valid for two dominant species with self-similar abundance ratios.

Temperature and surface gravity influence the validity of stacking across different planetary regimes.

Abstract

In many areas of astronomy, spectra of different objects are co-added or stacked to improve signal-to-noise and reveal population-level characteristics. As the number of exoplanets with measured transmission spectra grows, it becomes important to understand when stacking spectra from different exoplanets is appropriate and what stacked spectra represent physically. Stacking will be particularly valuable for long-period planets, where repeated observations of the same planet are time-consuming. Here, we show that stacked exoplanet transmission spectra are approximately mathematically equivalent to spectra generated from the geometric mean of each planet's abundance ratios. We test this by comparing stacked and geometric mean spectra across grids of forward models over JWST's NIRSpec/G395H wavelength range (2.8-5.2$\mu$m). For two dominant species (e.g., H$_2$O and CO$_2$), the geometric mean accurately reflects the stacked spectrum if abundance ratios are self-similar across planets. Introducing a third species (e.g., CH$_4$) makes temperature a critical factor, with stacking becoming inappropriate across the CO/CH$_4$ boundary. Surface gravity exerts only a minor influence when stacking within comparable planetary regimes. We further assess the number of stacked, distinct sub-Neptunes with high-metallicity atmospheres and low-pressure cloud decks required to rule out a flat spectrum at $>5\sigma$, as a function of both cloud deck pressure and per-planet spectral precision. These results provide guidance on when stacking is useful and on how to interpret stacked exoplanet spectra in the era of population studies of exoplanets.