Precision wavelength calibration for Radial Velocity measurements using Uranium lines between 3800-6900 \AA

We present here the precise wavelength calibration of a high-resolution spectrum using Uranium (U) lines in the wavelength range of 3809 - 6833 \AA\ for precision radial velocity measurements for exoplanet detection or related astrophysical sciences. We identify 1540 well-resolved U lines from a high-resolution (R=67,000) spectrum of the uranium-argon hollow cathode lamp (UAr HCL) using PARAS spectrograph in the aforesaid wavelength range. We calculate the neutral and first allowed transitions (Ritz wavelength) of U from its known energy levels and compare them with our observed central wavelengths. We measure an offset of -0.15 m\AA\space in our final U line list. The line list has an average measurement uncertainty of 15 m s$^{-1}$ (0.013 pixels or 0.28 m\AA). We included these lines to the PARAS data analysis framework to perform the wavelength calibration and then calculate the multi-order Radial Velocity (RV) of PARAS spectra. The typical dispersion of residuals around the wavelength solution of a UAr spectrum, using U lines, is found to be 0.8 m\AA\space($\sim$45 m s$^{-1}$). With the use of this line list, we present our results for the precision RV of an on-sky source (A RV standard star), and an off-sky source (A HCL) observed with PARAS along with UAr HCL. We measure the dispersion in absolute drift difference between two fibers (inter-fiber drift) for a span of 6.5 hours to be 88 cm s$^{-1}$, and the RV dispersion (${\sigma_{RV}}$) for a RV standard star, HD55575 over the course of $\sim$450 days to be 3.2 m s$^{-1}$. These results are in good agreement with the previous ones measured using the ThAr HCL. It proves that the ThAr HCL with $\sim$ 99\% pure-Th are replaceable with the UAr HCL for the wavelength calibration of the high-resolution spectrographs such as PARAS (R $\leq$ 67,000) to achieve a RV precision of 1-3 m s$^{-1}$ in the visible region.