A CO-to-H$_2$ ratio of $\approx 10^{-5}$ towards the Herbig Ae star HK Ori
Measurements of gas mass in protoplanetary gas disks form the basis for estimating the conditions of planet formation. Among the most important constraints derived from disk diagnostics are the abundances of gas-phase species critical for understanding disk chemistry. Towards this end, we present direct line-of-sight measurements of H$_{2}$ and CO, employing UV absorption spectroscopy from $HST$-COS to characterize disk composition, molecular excitation temperatures, and spatial distribution in the circumstellar material around the Herbig Ae stars HK Ori and T Ori. We observe strong CO (N(CO) = 10$^{15.5}$ cm$^{-2}$; T$_{rot}$(CO) = 19 K) and H$_{2}$ (N(H$_{2}$) = 10$^{20.34}$ cm$^{-2}$; T$_{rot}$(H$_{2}$) = 141 K) absorption towards HK Ori with a CO/H$_{2}$ ratio ($\equiv$ N(CO)/N(H$_{2}$)) = 1.3$^{+1.6}_{-0.7}$~$\times$~10$^{-5}$. These measurements place direct empirical constraints on the CO-to-H$_{2}$ conversion factor in the disk around a Herbig Ae star for the first time, although there is uncertainty concerning the exact viewing geometry of the disk. The spectra of T Ori show CO (N(CO) = 10$^{14.9}$ cm$^{-2}$; T$_{rot}$(CO) = 124 K) absorption. Interestingly, we do not detect any H$_{2}$ absorption towards this star (N(H$_{2}$) $<$ 10$^{15.9}$ cm$^{-2}$). We discuss a potential scenario for the detection of CO without H$_{2}$, which deserves further investigation. The low abundance ratio measured around HK Ori suggests significant depletion of CO in the circumstellar gas, which conforms with the handful of other recent CO abundance measurements in protoplanetary disks.