Uncovering Hidden Systematics in Extreme-Precision Radial Velocity Measurements

Abstract

We identify and correct for small but coherent instrumental drifts in seven years of radial velocity data from the EXtreme PREcision Spectrograph (EXPRES). The systematics are most notable for the six months before and after 2022 January, when EXPRES experienced larger temperature variations, and we see a systematic trough-to-peak amplitude of 2.8 m/s in the radial velocities. This is large enough to mimic or obscure planetary signatures. To isolate and correct these effects, we develop a suite of diagnostics that track two-dimensional \'echellogram shifts, scalings, and rotation, as well as line bisector spans (LBS) derived from laser frequency comb (LFC) lines. By combining these empirical tracers with instrument telemetry in a multi-dimensional regression, we reduce the EXPRES instrument trend traced with solar RVs from an RMS of 1.32 m/s to 0.43 m/s, a 67% improvement, and the aggregate of twelve chromospherically quiet stars show a 26% reduction in velocity scatter. Our injection-recovery simulations further demonstrate a doubling in sensitivity to low-amplitude planetary signals after correction. When applied to the stellar time series of $\rho$ Coronae Borealis ($\rho$CrB), the correction removes a spurious planet d signal, restoring the integrity of the data. These results highlight the need for long-term monitoring and multi-dimensional calibration diagnostics on the path toward true centimeter-per-second precision in next-generation EPRV instruments.