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I describe recent advances made in Doppler spectroscopy of low mass star and discuss how they perform on public observations ontained with the HARPS spectrograph. This work is possible thanks to the recent development of the HARPS-TERRA software (Template Enhanced Radial velocity Re-analysis Application), which obtains precision RV measurements by least-squares matching each spectrum to a high SNR template built from the same observations. As a result, we obtain a substantial increase in precision compared to the traditional cross-correlation methods. The increase in precision is demonstrated with RV measurements on stable M dwarfs (80 cm/s over time-scales of years) and the early detection of several very low mass candidates. Moreover, the ability of HARPS-TERRA in reproducing the observed spectra at high fidelity allows us to explore new effects including : wavelength dependence of activity induced Doppler signals, simultaneous measurement of orbital obliquities and stellar rotation profiles and, when combined with advanced Bayesian data analysis techniques, small Doppler signals likely caused by new super-Earth mass candidates in the habitable zones of nearby stars

Advances in precision Doppler spectroscopy on cool stars