Reflected spectroscopy of small exoplanets III: probing the UV band to measure biosignature gasses

Direct-imaging observations of terrestrial exoplanets will enable characterizing their atmospheric compositions and assessing their habitability. Using Earth as a template, the key atmospheric signatures for the biosphere is O$_2$ and the photochemical product O$_3$, while this O$_2$-O$_3$ biosignature is not detectable in the visible wavelengths for most of the time after the emergence of oxygenic photosynthesis life (i.e., the Proterozoic Earth). Here we demonstrate spectroscopic observations in the ultraviolet wavelengths for detecting and characterizing O$_2$ and O$_3$ in terrestrial exoplanets like Proterozoic Earth, using a spectral retrieval framework developed for future exoplanet direct-imaging missions. For an O$_2$ mixing ratio 2--3 orders of magnitude less than the present-day Earth, and an O$_3$ mixing ratio of $10^{-7}-10^{-6}$, we find that O$_3$ can be detected and its mixing ratio can be measured precisely (to within $~1$ order of magnitude) with the addition of the ultraviolet ($0.25-0.4\ \mu$m) spectra to visible-wavelength spectroscopy. With a modest spectral resolution ($R=7$) in the ultraviolet, the O$_3$ detection is robust against other potential gases absorbing in the ultraviolet (e.g., H$_2$S and SO$_2$), as well as the short-wavelength cutoff between 0.2 and 0.25 $\mu$m. While the O$_3$ detection does not rely on the near-infrared spectra, extending the wavelength coverage to the near-infrared ($1-1.8\ \mu$m) would provide essential information to interpret the O$_3$ biosignature, including the mixing ratio of H$_2$O, the cloud pressure, as well as the determination that the atmosphere is N$_2$- rather than CO$_2$-dominated. Overall, this work indicates that the capabilities of ultraviolet spectroscopy are essential for characterizing Earth-like exoplanets, and reaffirms the importance of the near-infrared. The ultraviolet and near-infrared capabilities should thus be evaluated as critical components for the future missions aiming at imaging and characterizing terrestrial exoplanets, such as the Habitable World Observatory.