eROSITA's cool star population explained

Abstract

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, $\text{Ro}$, 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. 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$_{\text{bol}}$ ratio and {\it Gaia} BP-RP color.