tokens: must be taken into account when analysing gas observations and comparing it with dust levels. However, if CO is unshielded, its short lifetime (∼120 yr) means that its mass will be set by the present mass-loss rate. Conversely, atomic carbon has a longer lifetime as it will viscously evolve on longer time-scales which will depend on the kinematic viscosity. We used this new numerical code to produce the first population synthesis model for exocometary gas around A stars. Population synthesis studies are ideal to deal with degenerated problems and provide constraints on population properties rather than individual systems. Informed by previous studies that fit the dust evolution, we generated samples of 10 4 stars hosting planetesimal discs with random radius, mass, and stellar properties. We evolved these systems up to a random age between 3–100 Myr and compare the final distribution to the observed distribution by applying the same selection filters to our model population. We found that our model can reproduce the distribution of CO masses well when viscosities are high (α ≈ 0.1), even producing a bimodal distribution with a large population of unshielded CO discs and a small fraction of shielded ones. The shielded population is nevertheless common in our models among systems with bright debris discs, which explains why shielded discs are common among the sample of 17 A stars with bright and cold debris discs. The high-α value implies that gas needs to be lost on time-scales of ∼1–10 Myr. Otherwise, carbon readily accumulates shielding CO and producing a large population of shielded and massive CO discs, even around systems with low planetesimal disc masses, which is inconsistent with observations. Although, we focused on A stars, we also tested our model against observations of FGK stars. While massive and shielded CO gas discs are found around A stars, observations of FGK stars have showed that these have low CO gas masses, with only a few detections. Using our model, we showed that this is consistent with the collisional evolution studies of discs around FGK stars compared to A stars. Their lower initial disc masses means that gas release rates are lower. Our model quantitatively shows that massive CO gas discs should be very rare around FGK stars if they have similar viscosity levels compared to A stars. An important test of viscous evolution models of gas in debris discs, is whether gas is observed to extend inwards and accrete on to the star. In Section 5 , we discussed recent observations of neutral carbon around a few systems which seem to indicate that carbon has not spread inwards forming an accretion disc as expected in a viscous evolution scenario. This might suggest that either gas release started recently or is lost through another mechanism, e.g. radiation pressure. Nevertheless, our modelling constrains the gas loss time-scale to be ∼1–10 Myr (viscous time-scale), which could provide insights into alternative
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