A Tale of Two Molecules: The Underprediction of CO$_2$ and Overprediction of PH$_3$ in Late T and Y Dwarf Atmospheric Models

The sensitivity and spectral coverage of JWST is enabling us to test our assumptions of ultracool dwarf atmospheric chemistry, especially with regards to the abundances of phosphine (PH$_3$) and carbon dioxide (CO$_2$). In this paper, we use NIRSpec PRISM spectra ($\sim$0.8$-$5.5 $\mu$m, $R\sim$100) of four late T and Y dwarfs to show that standard substellar atmosphere models have difficulty replicating the 4.1$-$4.4 $\mu$m wavelength range as they predict an overabundance of phosphine and an underabundance of carbon dioxide. To help quantify this discrepancy, we generate a grid of models using PICASO based on the Elf Owl chemical and temperature profiles where we include the abundances of these two molecules as parameters. The fits to these PICASO models show a consistent preference for orders of magnitude higher CO$_2$ abundances and a reduction in PH$_3$ abundance as compared to the nominal models. This tendency means that the claimed phosphine detection in UNCOVER$-$BD$-$3 could instead be explained by a CO$_2$ abundance in excess of standard atmospheric model predictions; however the signal-to-noise of the spectrum is not high enough to discriminate between these cases. We discuss atmospheric mechanisms that could explain the observed underabundance of PH$_3$ and overabundance of CO$_2$, including a vertical eddy diffusion coefficient ($K_{\mathrm{zz}}$) that varies with altitude, incorrect chemical pathways, or elements condensing out in forms such as NH$_4$H$_2$PO$_4$. However, our favored explanation for the required CO$_2$ enhancement is that the quench approximation does not accurately predict the CO$_2$ abundance, as CO$_2$ remains in chemical equilibrium with CO after CO quenches.