2019MNRAS.482.1406Z

The advent of the laser-frequency comb as the wavelength calibration unit allows us to measure the radial velocity (RV) at cm s^–1 precision level with high stability in the long term, which enables the possibility of the detection of Earth twins around solar-like stars. A recent study shows that the laser-frequency comb can also be used to measure and study the precision of the instrumental system including the variations of line profile and the systematic uncertainty and instrumental drift. In this paper, we present the stringent analysis of a laser-frequency comb (LFC) system with 25 GHz repetition frequency on an R ∼ 50 000 spectrograph with the wavelength spanning from 5085-7380 Å. We report a novel fitting model optimized for the comb line profile, the constrained double Gaussian. The constraint condition is set as µ_1,2 - µ< sqrt(2 ln 2σ). We introduce a Bayesian information criterion to test various models. Compared to the traditional Gaussian model, the CDG (constrained double Gaussian) model provides a much better goodness of fit. We apply the CDG model to the observed comb data to demonstrate the improvement of the RV precision with the CDG model. We find that the improvement of the CDG model is about 40-60 per cent for wavelength calibration precision. We also consider the use of the LFC and CDG model as a tool to characterize the line-shape variation across the detector. The aim of this work is to measure and understand the details of the comb lines including their asymmetry and behaviours under various conditions, which play a significant role in the simultaneous calibration process and cross-correlation function method to determine the Doppler shift at high precision level.