Activity time series of old stars from late F to early K. VI. Exoplanet mass characterisation and detectability in radial velocity

Context. Stellar variability impacts radial velocities (hereafter RVs) at various timescales and therefore the detectability of exoplanets and the mass determination based on this technique. Detecting and characterising Earth-like planets in the habitable zone of solar-type stars represents an important challenge in the coming years, however. It is therefore necessary to implement systematic studies of this issue, for example to delineate the current limitations of RV techniques.
Aims: A first aim of this paper is to investigate whether the targeted 10% mass uncertainty from RV follow-up of transits detected by PLATO can be reached. A second aim of this paper is to analyse and quantify Earth-like planet detectability for various spectral types.
Methods: For this purpose, we implemented blind tests based on a large data set (more than 20 000) of realistic synthetic time series reproducing different phenomena leading to stellar variability such as magnetic activity patterns similar to the solar configuration as well as flows (oscillations, granulation, and supergranulation), covering F6-K4 stars and a wide range of activity levels.
Results: We find that the 10% mass uncertainty for a 1 M_Earth in the habitable zone of a G2 star cannot be reached, even with an improved version of the usual correction of stellar activity (here based on a non-linear relation with log R'_HK and cycle phase instead of a linear correlation) and even for long-duration (10 yr) well-sampled observations. This level can be reached, however, for masses above 3 M_Earth or for K4 stars alone. We quantify the maximum dispersion of the RV residuals needed to reach this 10% level, assuming the activity correction method and models do not affect the planetary signal. Several other methods, also based on a correction using log R'_HK in various ways (including several denoising techniques and Gaussian processes) or photometry, were tested and do not allow a significantly improvement of this limited performance. Similarly, such low-mass planets in the habitable zone cannot be detected with a similar correction: blind tests lead to very low detection rates for 1 M_Earth and to a very high level of false positives. We also studied the residuals after correction of the stellar signal, and found significant power in the periodogram at short and long timescales, corresponding to masses higher than 1 M_Earth in this period range.
Conclusions: We conclude that very significant and new improvements with respect to methods based on activity indicators to correct for stellar activity must be devised at all timescales to reach the objective of 10% uncertainty on the mass or to detect such planets in RV. Methods based on the correlation with activity indicators are unlikely to be sufficient.