eROSITA's cool star population explained

The rotation-activity connection is the standard paradigm for interpreting chromospheric and coronal activity in late-type stars, namely, stars with outer convection zones. This paradigm states that activity increases with decreasing rotation period until a saturation limit is reached. By scaling rotation periods with the convective turnover time via the Rossby number, ≈ 10^ saturation is expected to occur at a universal value across all spectral types. In our paper, we systematically investigate the relationship between rotation and activity as measured though X-ray emission for a large sample of late-type stars to test the universal applicability of this paradigm. To this end, we utilized TESS short-cadence space photometry to determine the rotation periods for late-type stars identified in the eROSITA all-sky survey. This combined dataset provides rotation and X-ray measurements for 14004 stars, representing a sample size increase of more than an order of magnitude compared to previous studies. Our results show that F-type stars do not reach the "classical" saturation limit of L_X/L_ bol -3 , instead exhibiting significantly lower L_X/L_ bol values. We find that the convective turnover times derived from this sample closely agree with theoretical computations, supporting the idea that Rossby number-activity relations hold for all late-type main sequence stars. The lower level of activity in earlier spectral types (e.g., F-type and late A-type stars) is a physical consequence of their short convective turnover times, which prevent them from rotating rapidly enough to ever reach the saturation regime. We demonstrate that a simple model incorporating our derived turnover times versus color can successfully reproduce the observed characteristics of the eROSITA X-ray activity distribution, as measured by the L_X/L_ bol ratio and Gaia BP-RP color.