Stacking transmission spectra of different exoplanets

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 physically represent. 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 can, under well-defined conditions, be represented by 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, which is the primary chemical transition considered in this work. 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, grey 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.