Self-consistent Stellar Radial Velocities from LAMOST Medium-Resolution Survey (MRS) DR7

Radial velocity (RV) is among the most fundamental physical quantities obtainable from stellar spectra and is rather important in the analysis of time-domain phenomena. The LAMOST Medium-Resolution Survey (MRS) DR7 contains 5 million single-exposure stellar spectra at spectral resolution $R\sim7\,500$. However, the temporal variation of the RV zero-points (RVZPs) of the MRS survey, which makes the RVs from multiple epochs inconsistent, has not been addressed. In this paper, we measure the RVs of the 3.8 million single-exposure spectra (for 0.6 million stars) with signal-to-noise ratio (SNR) higher than 5 based on cross-correlation function (CCF) method, and propose a robust method to self-consistently determine the RVZPs exposure-by-exposure for each spectrograph with the help of \textit{Gaia} DR2 RVs. Such RVZPs are estimated for 3.6 million RVs and can reach a mean precision of $\sim 0.38\,\mathrm{km\,s}^{-1}$. The result of the temporal variation of RVZPs indicates that our algorithm is efficient and necessary before we use the absolute RVs to perform time-domain analysis. Validating the results with APOGEE DR16 shows that our absolute RVs can reach an overall precision of 0.84/0.80 $\mathrm{km\,s}^{-1}$ in the blue/red arm at $50