Constraints Imposed by the Square-root Spin-down Law on Coronal Wind Parameters

We derive an explicit expression for the coronal wind mass-loss rate in terms of either the surface field or the surface rotation rate. This result is based on a currently used generalized torque interpolation formula (per unit rotational velocity) expressed as a product of known monomials, separately for the magnetic field and the mass-loss rate. The latter is assumed here to be given by an unknown monomial power of the magnetic field. This yields a torque dependent solely on the magnetic field that must yield the square-root spin-down law. A monomial field-rotation relation, defining the rotational power index for the field, is derived from the congruity of the decay with age of the observed Ca II emission luminosity (with an arbitrary magnetic field power dependence) with the decay with age of the rotational velocity. This allows one to express the mass-loss rate power index in terms of the rotational index. We apply this constraining equation to a variety of observations. We find that even though there is considerable scatter in the data, there is sufficient observational evidence for the reality of a linear field-rotation relation associated with a linear temporal decay of the mass-loss rate.