Vertical evolution of exocometary gas - I. How vertical diffusion shortens the CO lifetime

Bright debris discs can contain large amounts of CO gas. This gas was thought to be a protoplanetary remnant until it was recently shown that it could be released in collisions of volatile-rich solids. As CO is released, interstellar UV radiation photodissociates CO producing CI, which can shield CO allowing a large CO mass to accumulate. However, this picture was challenged because CI is inefficient at shielding if CO and CI are vertically mixed. Here, we study for the first time the vertical evolution of gas to determine how vertical mixing affects the efficiency of shielding by CI. We present a 1D model that accounts for gas release, photodissociation, ionization, viscous evolution, and vertical mixing due to turbulent diffusion. We find that if the gas surface density is high and the vertical diffusion weak (alpha(v)/alpha < [H/r](2)) CO photodissociates high above the mid-plane, forming an optically thick CI layer that shields the CO underneath. Conversely, if diffusion is strong (alpha(v)/alpha > [H/r](2)) CI and CO become well mixed, shortening the CO lifetime. Moreover, diffusion could also limit the amount of dust settling. High-resolution ALMA observations could resolve the vertical distribution of CO and CI, and thus constrain vertical mixing and the efficiency of CI shielding. We also find that the CO and CI scale heights may not be good probes of the mean molecular weight, and thus composition, of the gas. Finally, we show that if mixing is strong the CO lifetime might not be long enough for CO to spread interior to the planetesimal belt where gas is produced.