Generalized investigation of the rotation-activity relation: Favouring rotation period instead of Rossby number

摘要

Magnetic activity in Sun-like and low-mass stars causes X-ray coronalemission, which is stronger for more rapidly rotating stars. This relation isoften interpreted in terms of the Rossby number, i.e., the ratio of rotationperiod to convective overturn time. We reconsider this interpretation on thebasis of the observed X-ray emission and rotation periods of 821 stars withmasses below 1.4 Msun. A generalized analysis of the relation between X-rayluminosity normalized by bolometric luminosity, L_X/L_bol, and combinations ofrotational period, P, and stellar radius, R, shows that the Rossby formulationdoes not provide the solution with minimal scatter. Instead, we find that therelation L_X/L_bol ~ P^{-2}R^{-4} optimally describes the non-saturatedfraction of the stars. This relation is equivalent to L_X ~ P^{-2}, indicatingthat the rotation period alone determines the total X-ray emission. Since L_Xis directly related to the magnetic flux at the stellar surface, this meansthat the surface flux is determined solely by the star's rotation and isindependent of other stellar parameters. While a formulation in terms of aRossby number would be consistent with these results if the convective overturntime scales exactly as L_bol^{-1/2}, our generalized approach emphasizes theneed to test a broader range of mechanisms for dynamo action in cool stars.