Activity-rotation Relationship: Interpretation of an X-ray Derived Rossby Number

Astronomy and Astrophysics – Astrophysics

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In this work we present results of a new study on the relationship between X-ray emission and an empirical Rossby number. Using an extended sample of 238 dwarfs in the B-V range 0.5 -- 1.6, including 102 field stars and 136 members of clusters, we have first established power-law correlation functions between the X-ray to bolometric luminosity ratio and the rotation period for stars in 7 selected color ranges. We have then determined a color-dependent function, τe(B-V), which allows us to derive a single "optimized" relation between Lx/Lbol and an empirical X-ray-derived Rossby number Roemp=Prot/τe.
We show that τe scales with B-V as Lbol-0.5 and for B-V>1.3 it is significantly lower than the theoretical convective turnover time. Our result demonstrates that for non-saturated coronae the Lx -- Prot relation is equivalent to the Lx/Lbol vs. Roemp relation.

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