A General Framework for Radial Velocity Calibration in Low-resolution Spectroscopic Surveys: Correcting Wavelength-dependent and Global Systematics with Application to LAMOST Data Release 9

Abstract Radial velocity (RV) is crucial for stellar kinematics and Galactic archaeology. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope has obtained over 10 million low-resolution spectra ( R ∼ 1800), yielding RVs for millions of stars, but these suffer from (1) wavelength-dependent inconsistencies (relative shifts between spectral segments) and (2) global zero-point offsets (uniform shifts of entire spectra). In this work, we comprehensively characterize and correct both. Each spectrum is first divided into eight ∼500 Å segments. We organize the data at the spectrograph and fiber levels, measure segment-wise RV offsets relative to the full spectrum at each level, then fit these offsets with low-order polynomials to correct wavelength-dependent systematics. We then correct zero-points hierarchically: at the spectrograph level by minimizing a joint χ 2 constrained by repeat observations and crossmatches with APOGEE and the Gaia Radial Velocity Spectrometer, and at the fiber level by averaging seasonal offsets. After correction, RV precision improves significantly; for cross-night repeats, the standard deviation of RV differences at high signal-to-noise ratios drops by a factor of 2 from ∼3.6 to ∼1.8 km s −1 , implying a single-measurement precision of ∼1.3 km s −1 . External checks with APOGEE and Gaia show dispersions drop from ∼4.0 to ∼2.0 km s −1 . The precision approaches, though slightly below, the theoretical limit at R ∼ 1800. We release a value-added RV catalog with corrected velocities for ∼5.7 million spectra, providing a homogeneous and systematically corrected dataset. The framework established in this work is also applicable to RV calibration in other large-scale spectroscopic surveys.