One of the best ways to improve our understanding of the stellar activity-induced signal in radial velocity (RV) measurements is through simultaneous high-precision photometric and RV observations. This is of prime importance to mitigate the RV signal induced by stellar activity and therefore unveil the presence of low-mass exoplanets. The K2 Campaign 7 and 8 fields of view were located in the southern hemisphere, and provided a unique opportunity to gather unprecedented simultaneous high-precision photometric observation with K2 and high-precision RV measurements with the HARPS spectrograph to study the relationship between photometric variability and RV jitter. We observed nine stars with different levels of activity, from quiet to very active. We first probed the presence of any meaningful relation between measured RV jitter and the simultaneous photometric variation, and also other activity indicators (such as BIS, FWHM, logR0'HK, and F8) by evaluating the strength and significance of the monotonic correlation between RVs and each indicator. We found that for the case of very active stars, strong and significant correlations exist between almost all the observables and measured RVs; however, when we move towards lower activity levels the correlations become random, and we could not reach any conclusion regarding the tendency of correlations depending on the stellar activity level. Except for the F8 whose strong correlation with RV jitter persists over a wide range of stellar activity level, and thus our result suggests that F8 might be a powerful proxy for activity-induced RV jitter over a wide range of stellar activity. Moreover, we examine the capability of two state-of-the-art modeling techniques, namely the FF' method and SOAP2.0, to accurately predict the RV jitter amplitude using the simultaneous photometric observation. We found that for the very active stars both techniques can predict the amplitude of the RV jitter reasonably well; however, at lower activity levels the FF' method underpredicts the RV jitter amplitude.
