Magnetic Braking by a Stellar Wind-IV: THE EFFECT OF DIFFERENT POLOIDAL FIELD STRUCTURES

Abstract

The theory of magnetic braking by a stellar wind is extended to cover a variety of assumed poloidal fields, all symmetric about the rotation axis, all dipolar angular structure, but with radial structures varying from the curl-free at one extreme to the quasi-monopolar at the other. The rates of mass-loss $$\dot M$$ and angular momentum-loss $$\dot J$$ are computed as functions of four non-dimensional parameters: l , the ratio of gravitational to thermal energy density, ζ , the ratio of magnetic to thermal density, κ , the ratio of the centrifugal force to gravity, all measured at the coronal base r_s ; and a parameter λ that describes the structure of the poloidal field. Except for small values of ζ , and large values of κ , an equatorial dead zone is formed, separated from the wind zone. It is confirmed that $$\dot J/(\Omega_\text sr_{\text s^2})$$ is insensitive to changes in ζ for the dipolar field, where Ω _s is the star's angular velocity at the coronal base, but as the field structure changes from the dipolar to the radial, it becomes rather sensitive to ζ . For ζ ≫ 1, $$\dot J/(\Omega_\text sr_{\text s^2}\dot M)$$ increases very rapidly as κ decreases. Even in a hot corona, when κ is large the centrifugal force contributes as much to the braking effect of the wind as the thermal pressure. In reality, the field structure parameter λ is not independent of l , κ and ζ but will be fixed by the trans-field component of the equation of motion. This will be discussed in a later paper.