MINDS. The detection of $^{13}$CO$_{2}$ with JWST-MIRI indicates abundant CO$_{2}$ in a protoplanetary disk

We present JWST-MIRI MRS spectra of the protoplanetary disk around the low-mass T Tauri star GW Lup from the MIRI mid-INfrared Disk Survey (MINDS) GTO program. Emission from $^{12}$CO$_{2}$, $^{13}$CO$_{2}$, H$_{2}$O, HCN, C$_{2}$H$_{2}$, and OH is identified with $^{13}$CO$_{2}$ being detected for the first time in a protoplanetary disk. We characterize the chemical and physical conditions in the inner few au of the GW Lup disk using these molecules as probes. The spectral resolution of JWST-MIRI MRS paired with high signal-to-noise data is essential to identify these species and determine their column densities and temperatures. The $Q$-branches of these molecules, including those of hot-bands, are particularly sensitive to temperature and column density. We find that the $^{12}$CO$_{2}$ emission in the GW Lup disk is coming from optically thick emission at a temperature of $\sim$400 K. $^{13}$CO$_{2}$ is optically thinner and based on a lower temperature of $\sim$325 K, may be tracing deeper into the disk and/or a larger emitting radius than $^{12}$CO$_{2}$. The derived $N_{\rm{CO_{2}}}$/$N_{\rm{H_{2}O}}$ ratio is orders of magnitude higher than previously derived for GW Lup and other targets based on \textit{Spitzer}-IRS data. This high column density ratio may be due to an inner cavity with a radius in between the H$_{2}$O and CO$_{2}$ snowlines and/or an overall lower disk temperature. This paper demonstrates the unique ability of JWST to probe inner disk structures and chemistry through weak, previously unseen molecular features.