The Epoch of Giant Planet Migration Planet Search Program. I. Near-Infrared Radial Velocity Jitter of Young Sun-like Stars

We present early results from the Epoch of Giant Planet Migration program, a precise RV survey of over one hundred intermediate-age ($\sim$20$-$200 Myr) G and K dwarfs with the Habitable-Zone Planet Finder spectrograph (HPF) at McDonald Observatory's Hobby-Eberly Telescope (HET). The goals of this program are to determine the timescale and dominant physical mechanism of giant planet migration interior to the water ice line of Sun-like stars. Here, we summarize results from the first 14 months of this program, with a focus on our custom RV pipeline for HPF, a measurement of the intrinsic near-infrared RV activity of young Solar analogs, and modeling the underlying population-level distribution of stellar jitter. We demonstrate on-sky stability at the sub-2 m s$^{-1}$ level for the K2 standard HD 3765 using a least-squares matching method to extract precise RVs. Based on a subsample of 29 stars with at least three RV measurements from our program, we find a median RMS level of 34 m s$^{-1}$. This is nearly a factor of 2 lower than the median RMS level in the optical of 60 m s$^{-1}$ for a comparison sample with similar ages and spectral types as our targets. The observed near-infrared jitter measurements for this subsample are well reproduced with a log-normal parent distribution with $\mu=4.15$ and $\sigma=1.02$. Finally, by compiling RMS values from previous planet search programs, we show that near-infrared jitter for G and K dwarfs generally decays with age in a similar fashion to optical wavelengths, albeit with a shallower slope and lower overall values for ages $\lesssim$1 Gyr.