Automatic Echelle Spectrograph Wavelength Calibration

Time domain astronomy and the increasing number of exoplanet candidates call for reliable, robust and automatic wavelength calibration. We present an algorithm for wavelength calibrating \'echelle spectrographs that uses only the two-dimensional spectrum and a list of laboratory wavelengths. Our approach is fully automatic and does not rely on a-priori knowledge such as the pixel locations of certain emission lines with which to anchor the wavelength solution, nor the true order number of each diffraction order. We demonstrate our method on all four spectrographs in Las Cumbres Observatory's Network of Robotic \'Echelle Spectrographs (NRES), on the High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph, and on synthetic data modelled after NRES. For NRES, we achieve a velocity-equivalent absolute precision of $\sim$10 m/s, limited by not accounting for effects like modal noise and astigmatism. We achieve $\sim$1 m/s on HARPS, which agrees with the absolute precision reported by the HARPS team. On synthetic data of varying quality, we achieve the velocity precision set by Gaussian centroiding errors. Accordingly, our algorithm likely holds for a wide range of spectrographs beyond the five presented here. We provide an open-source Python package, xwavecal (https://github.com/gmbrandt/xwavecal/), which outputs wavelength calibrated spectra as well as the pixel and order locations of emission lines and their wavelengths in the reference list.