Expectations for the confirmation of Proxima c from a long-term radial velocity follow-up

Abstract

Proxima c, a candidate second planet orbiting Proxima Centauri, was detected with the radial velocity method. The announced long orbital period (5.21$^{+0.26}_{-0.22}$ years), and small semi-amplitude of the induced Doppler signal (1.2$\pm$0.4 m/s), make this detection challenging and the target worthy of a follow-up in the next years. We intend to evaluate the impact of future data on the statistical significance of the detection through realistic simulated radial velocities to be added to the published dataset, spanning up to one orbital period of Proxima c in the time range 2019-2023. We find that the detection significance of Proxima c increases depending not only on the amount of data collected, but also on the number of instruments used, and especially on the timespan covered by the observational campaign. However, on average we do not get strong statistical evidence and we predict that, in the best-case scenario, in the next 5 years the detection of Proxima c can become significant at 4$\sigma$ level. If instead Proxima c does not exist, the detected signal may lower its significance down to 2$\sigma$.