Velocity shift and SNR limits for high-resolution spectroscopy of hot Jupiters using Keck/KPIC

High-resolution cross-correlation spectroscopy (HRCCS) is a technique for detecting the atmospheres of close-in planets using the change in the projected planet velocity over a few hours. To date, this technique has most often been applied to hot Jupiters, which show a large change in velocity on short timescales. Applying this technique to planets with longer orbital periods requires an improved understanding of how the size of the velocity shift and the observational signal-to-noise ratio impact detectability. We present grids of simulated Keck/KPIC observations of hot Jupiter systems, varying the observed planet velocity shift and signal-to-noise ratio (SNR), to estimate the minimum thresholds for a successful detection. These simulations realistically model the cross-correlation process, which includes a time-varying telluric spectrum in the simulated data and data detrending via PCA. We test three different planet models based on an ultra-hot Jupiter, a classical hot Jupiter, and a metal-rich hot Saturn. For a ${6}\sigma$ detection suitable for retrieval analysis, we estimate a minimum velocity shift of $\Delta v_\text{pl} \sim {30, 50, 60}$ km/s, compared to an instrumental resolution of 9 km/s, and minimum SNR $\sim 370, 800, 1200$ for the respective planet models. We find that reported KPIC detections to-date fall above or near the ${6}\sigma$ limit. These simulations can be efficiently re-run for other planet models and observational parameters, which can be useful in observation planning and detection validation.