Predictions for the secondary CO, C and O gas content of debris discs from the destruction of volatile-rich planetesimals

This paper uses observations of dusty debris discs, including a growing number of gas detections in these systems, to test our understanding of the origin and evolution of this gaseous component. It is assumed that all debris discs with icy planetesimals create second generation CO, C and O gas at some level, and the aim of this paper is to predict that level and assess its observability. We present a new semi-analytical equivalent of the numerical model of Kral et al. allowing application to large numbers of systems. That model assumes CO is produced from volatile-rich solid bodies at a rate that can be predicted from the debris discs fractional luminosity. CO photodissociates rapidly into C and O that then evolve by viscous spreading. This model provides a good qualitative explanation of all current observations, with a few exceptional systems that likely have primordial gas. The radial location of the debris and stellar luminosity explain some non-detections, e.g. close-in debris (like HD 172555) is too warm to retain CO, while high stellar luminosities (like n Tel) result in short CO lifetimes. We list the most promising targets for gas detections, predicting >15 CO detections and >30 C I detections with ALMA, and tens of C II and OI detections with future far-IR missions. We find that CO, C I, CII and OI gas should be modelled in non-LTE for most stars, and that CO, CI and OI lines will be optically thick for the most gas-rich systems. Finally, we find that radiation pressure, which can blow out C I around early-type stars, can be suppressed by self-shielding.