High CO/H_2 ratio supports an exocometary origin for a CO-rich debris disc

Over 20 exocometary belts host detectable circumstellar gas, mostly in the form of CO. Two competing theories for its origin have emerged, positing that the gas is either primordial or secondary. Primordial gas survives from the belt's parent protoplanetary disc and is therefore H_2-rich. Secondary gas is outgassed in situ by exocomets and is relatively H_2-poor. Discriminating between these scenarios has not been possible for belts that host unexpectedly large quantities of CO. We aim to break this gas origin dichotomy through direct measurement of H_2 column densities in two edge-on, CO-rich exocometary belts around ∼15 Myr-old A-type stars, constraining the frac CO H _2 ratio and CO gas lifetimes. Observing edge-on belts enables rovibrational absorption spectroscopy against the stellar background. We present near-IR CRIRES+ spectra of HD 110058 and HD 131488, which provide the first direct probe of H_2 gas in CO-rich exocometary belts. We targeted the H_2 (v=1-0 S(0)) line at 2223.3 nm and the 12 CO v=2̊ightarrow0 rovibrational lines in the range 2333.8-2335.5 nm and derived constraints on column densities along the line of sight to the stars. We detect 12 CO strongly, but not H_2, in the CRIRES+ spectra. This allows us to place 3σ lower limits on the frac CO H ₂ ratios of> 1.35 $ and $> 3.09 $ for HD 110058 and HD 131488, respectively. These constraints demonstrate that, at least for HD 110058, the exocometary gas is compositionally distinct and significantly H_2-poor compared to the <10^-4 frac 10^ -3 10^ -5 CO H _2 ratios typical of protoplanetary discs. For HD 131488, we further compared the CO photodissociation timescale to the age of the system through simple shielding arguments, and find that we cannot formally rule out a primordial origin; however, we suggest that a more realistic model of CO survival likely supports a secondary origin for this system as well. Overall, a high $ ratio for HD 110058 indicates that the gas in this CO-rich belt is most likely not primordial in composition, supporting the presence of exocometary gas. CO H _2