The watery atmosphere of HD~209458~b revealed by joint $K$- and $L$-band high-resolution spectroscopy

We present a joint analysis of high-resolution $K$- and $L$-band observations of the benchmark hot Jupiter \hdb\ from the Keck Planet Imager and Characterizer (KPIC). One half night of observations were obtained in each bandpass covering similar pre-eclipse phases. The two epochs were then jointly analyzed using our atmospheric retrieval pipeline based on \petit\ to constrain the atmospheric pressure-temperature profile and chemical composition. Consistent with recent results from \textit{JWST} observations at lower spectral resolution, we obtain an oxygen-rich composition for \hdb\ ($\rm C/O < 10^{-3}$ at 95\% confidence) and a lower limit on the volatile metallicity similar to the solar value ($\rm [(C+O)/H] > -0.2$ at 95\% confidence). Leveraging the large spectral grasp of the multi-band observations, we constrain the H$_2$O mixing ratio to $\rm \log H_2O_{VMR} > -3.1$ at 95\% confidence, and obtain 95\% upper limits on the atmospheric mixing ratios of CO ($<10^{-4.8}$), CH$_4$ ($<10^{-4.5}$), NH$_3$ ($<10^{-5.8}$), H$_2$S ($<10^{-3.3}$), and HCN ($<10^{-5.6}$). The limits on CH$_4$, NH$_3$, and HCN are consistent with recent results from \textit{JWST} transmission spectroscopy, demonstrating the value of multi-band ground-based high resolution spectroscopy for precisely constraining trace species abundances in exoplanet atmospheres. The retrieved low-C/O, moderate-metallicity composition for \hdb\ is consistent with formation scenarios involving late accretion of substantial quantities of oxygen-rich refractory solids and/or ices.