2022A&A...661A..24F

Stellar activity manifests itself in a variety of different phenomena, some of which we can measure as activity tracers from different atmospheric layers of the star, typically at different wavelengths. Stellar activity is furthermore inherently time variable, therefore simultaneous measurements are necessary to study the correlation between different activity indicators. In this study we compare X-ray fluxes measured within the first all-sky survey conducted by the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) instrument on board the Spectrum-Roentgen-Gamma observatory to CaII H&K excess flux measurements R_HK⁺, using observations made with the robotic TIGRE telescope. We created the largest sample of simultaneous X-ray and spectroscopic CaII H&K observations of late-type stars obtained so far, and in addition, previous measurements of CaII H&K for all sample stars were obtained. We find the expected correlation between our log(L_X/L_bol) to log(R_HK⁺) measurements, but when the whole stellar ensemble is considered, the correlation between coronal and chromospheric activity indicators does not improve when the simultaneously measured data are used. A more detailed analysis shows that the correlation of log(L_X/L_bol) to log(R_HK⁺) measurements of the pseudo-simultaneous data still has a high probability of being better than that of a random set of non-simultaneous measurements with a long time baseline between the observations. Cyclic variations on longer timescales are therefore far more important for the activity flux-flux relations than short-term variations in the form of rotational modulation or flares, regarding the addition of "noise" to the activity flux-flux correlations. Finally, regarding the question of predictability of necessarily space-based log (L_X/L_bol) measurements by using ground-based chromospheric indices, we present a relation for estimating log (L_X/L_bol) from R_HK⁺ values and show that the expected error in the calculated minus observed (C-O) log (L_X/L_bol) values is 0.35 dex.