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Stellar activity is the ultimate source of radial-velocity (RV) noise in thesearch for Earth-mass planets orbiting late-type main-sequence stars. Weanalyse the performance of four different indicators and the chromosphericindex $\log R'_{\rm HK}$ in detecting RV variations induced by stellar activityin 15 slowly rotating ($v\sin i \leq 5$ km/s), weakly active ($\log R'_{\rm HK}\leq -4.95$) solar-like stars observed with the high-resolution spectrographHARPS-N. We consider indicators of the asymmetry of the cross-correlationfunction (CCF) between the stellar spectrum and the binary weighted line maskused to compute the RV, that is the bisector inverse span (BIS), $\Delta V$,and a new indicator $V_{\rm asy(mod)}$ together with the full width at halfmaximum (FWHM) of the CCF. We present methods to evaluate the uncertainties ofthe CCF indicators and apply a kernel regression (KR) between the RV, the time,and each of the indicators to study their capability of reproducing the RVvariations induced by stellar activity. The considered indicators together withthe KR prove to be useful to detect activity-induced RV variations in $47 \pm18$ percent of the stars over a two-year time span when a significance(two-sided p-value) threshold of one percent is adopted. In those cases, KRreduces the standard deviation of the RV time series by a factor ofapproximately two. The BIS, the FWHM, and the newly introduced $V_{\rmasy(mod)}$ are the best indicators, being useful in $27 \pm 13$, $13 \pm 9$,and $13 \pm 9$ percent of the cases, respectively. The relatively limitedperformances of the activity indicators are related to the very low activitylevel and $v\sin i$ of the considered stars. For the application of ourapproach to sun-like stars, a spectral resolution of at least $10^5$ and highlystabilized spectrographs are recommended.

astronomy and astrophysics

The GAPS Programme with HARPS-N at TNG XVII. Line profile indicators and  kernel regression as diagnostics of radial-velocity variations due to stellar  activity in solar-like stars