Atmospheric carbon depletion as a tracer of water oceans and biomass on temperate terrestrial exoplanets

The conventional observables to identify a habitable or inhabited environment in exoplanets, such as an ocean glint or abundant atmospheric O$_2$, will be challenging to detect with present or upcoming observatories. Here we suggest a new signature. A low carbon abundance in the atmosphere of a temperate rocky planet, relative to other planets of the same system, traces the presence of substantial amount of liquid water, plate tectonic and/or biomass. We show that JWST can already perform such a search in some selected systems like TRAPPIST-1 via the CO$_2$ band at $4.3\,\rm \mu m$, which falls in a spectral sweet spot where the overall noise budget and the effect of cloud/hazes are optimal. We propose a 3-step strategy for transiting exoplanets: 1) detection of an atmosphere around temperate terrestrial planets in $\sim 10$ transits for the most favorable systems, (2) assessment of atmospheric carbon depletion in $\sim 40$ transits, (3) measurements of O$_3$ abundance to disentangle between a water- vs biomass-supported carbon depletion in $\sim100$ transits. The concept of carbon depletion as a signature for habitability is also applicable for next-generation direct imaging telescopes.