Dependence of coronal X-ray emission on spot-induced brightness variations in cool main sequence stars

The maximum amplitude (A(max)) of spot-induced brightness variations from long-term V-band photometry and the ratio L-X/L-bol between X-ray and bolometric luminosities are suitable indicators of the level of magnetic activity in the photosphere and in the corona of late-type stars, respectively. By using these activity indicators we investigate the dependence of coronal X-ray emission on the level of photospheric starspot activity in a homogeneous sample of low mass main sequence field and cluster stars of different ages (IC 2602, IC 4665, IC 2391, alpha Persei, Pleiades and Hyades). First, the activity-rotation connection at the photospheric level is re-analysed, as well as its dependence on spectral type and age. The upper envelope of Amax increases monotonically with decreasing rotational period (P) and Rossby number (R-0) showing a break around 1.1 d that separates two rotation regimes where the starspot activity shows different behaviours. The A(max)-P and A(max)-R-0 relations are fitted with linear, exponential and power laws to look for the function which best represents the trend of the data. The highest values of Amax are found among K-type stars and at the ages of a Persei and Pleiades. We also analyse the activity-rotation connection at the coronal level as well as its dependence on spectral type. The level of X-ray emission increases with increasing rotation rate up to a saturation level. The rotational period at which saturation occurs is colour-dependent and increases with advancing spectral type. Also the L-X/L-bol-P and L-X/L-bol-R-0 relations are fitted with linear, exponential and power laws to look for the best fitting function. Among the fastest rotating stars (P less than or equal to 0.3 d) there is evidence of super-saturation. Also the highest values of L-X/L-bol are found among K-type stars. Finally, the photospheric-coronal activity connection is investigated by using for the first time the largest ever sample of light curve amplitudes as indicators of the magnetic filling factor. The activity parameters L-X/L-bol and A(max) are found to be correlated with each other, thus confirming the dependence of coronal activity on photospheric magnetic fields. More precisely, the L-X/L-bol-A(max) distribution shows the presence of an upper envelope, which is constant at the L-X/L-bol similar or equal to -3.0 saturation level, and of a lower envelope. The best fit to the lower envelope is given by a power law with steepness decreasing from F-G to M spectral types. However, it is considered a tentative result, since the fit reduced chi-squares are large. Such spectral-type dependence may be related to a colour dependence of Amax on the total starspot filling factor, as well as to the coronal emission being possibly more sensitive to starspot activity variations in F- and G-type than in M-type stars. The L-X/L-bol-A(max) mean values for each cluster in our sample decrease monotonically with increasing age, showing that the levels of photospheric and coronal activity evolve in time according to a single power law till the Sun's age.