Data Reduction Pipeline of the TOU Optical Very High Resolution Spectrograph and Its sub-m s−1 Performance

TOU is an extremely high resolution optical spectrograph (R=$100,000$, 380-900~nm), which is designed to detect low mass exoplanets using the radial velocity technique.We describe an IDL-based radial velocity (RV) data reduction pipeline for the TOU spectrograph and its performance with stable stars. This pipeline uses a least-squares fitting algorithm to match observed stellar spectra to a high signal-to-noise template created for each star. By carefully controlling all of the error contributions to RV measurements in both the hardware and data pipeline, we have achieved $\sim$0.9\ms long-term RV precision with one of the most RV stable stars, Tau Ceti, similar to what has been achieved with HARPS. This paper presents steps and details in our data pipeline on how to reach the \sms RV precision and also all major error sources which contribute to the final RV measurement uncertainties. The lessons learned in this pipeline development can be applied to other environmentally controlled, very high resolution optical spectrographs to improve RV precision.