Empirical Constraints on the CO Snowline Transition in HD 163296: The Local CO Column and $^{13}$C$^{18}$O Optical Depth

Abstract

CO isotopologue emission is widely used to infer gas masses and volatile carbon abundances in protoplanetary disks, but converting line emission into a CO column depends on optical depth, temperature structure, linewidth, and isotope ratios. Inferring CO/H$_2$ additionally requires an independent constraint on the local hydrogen column. We use high-resolution $^{13}$C$^{18}$O $2$-$1$ observations of HD 163296 to derive a spatially localized empirical constraint on the CO column at the resolved CO snowline edge. We focus on the 70-75 au annulus, on the inner, high-column side of the observed profile steepening near 75 au. Using RADEX slab calculations conditioned on a two-dimensional temperature structure, we infer an effective beam-averaged CO column from the absolute integrated intensity. Across representative temperatures, isotope-ratio pairs, and effective local linewidths of 0.30 and 0.50 km s$^{-1}$, we find $N_{\rm CO}^{\rm beam}=(1.6-2.4)\times10^{20}$ cm$^{-2}$ and $^{13}$C$^{18}$O line-center optical depths $τ=0.39-0.97$. Thus, even this rare isotopologue is not safely optically thin at the snowline edge. Adopting $N_{\rm H2}=2.5\times10^{24}$ cm$^{-2}$ from a published parametric gas surface-density profile gives the conditional abundance ${\rm CO/H_2}=(6.4-9.5)\times10^{-5}$. A beam-forward radial-profile analysis gives consistent columns, and a physical disk model with a near-canonical warm-layer CO abundance supplies a comparable CO column. The measurement is consistent with the higher C$^{17}$O-based MAPS estimate. For the adopted hydrogen column, the inferred CO/H$_2$ ratio is consistent with a near-canonical abundance on the warm side of the snowline.