Magnetic Braking by a Stellar Wind--I

Abstract

The stellar wind theory is formulated for a rotating magnetic star, surrounded by an isothermal corona, and with the magnetic and rotation axes parallel. A critical surface C is defined by the Alfvénic points on each field-line, at which the wind-speed just equals the local Alfvén speed. The limiting field-line, with its Alfvenic point on the equator, separates the wind zone (which includes the polar regions) from the dead zone, in which outward expansion is prevented by the magnetic pressure. Within C , the roughly dipolar field is strong enough to force the flow to follow the field, and to keep the gas approximately co-rotating with the star. Beyond C , the gas flow drags the field to follow the flow, and each element approximately conserves its angular momentum. If the coronal temperature is too low for a thermal wind, the magnetically-controlled centrifugal forces drive a centrifugal wind, so that there is again a surface C limiting the zone of co-rotation. The rate of mass-loss, $$-\dot M$$ and angular momentum loss, $$-\dot J$$ are found as functions of the coronal base density ρ ₈ , the star's rotation Ω ₈ and three non-dimensional numbers: l , the ratio of gravitational to thermal energy density, ζ , the ratio of magnetic to thermal energy density, and κ , the ratio of centrifugal force to gravity, all three computed at the coronal base r ₈ . For $$\zeta\gg1,-\dot J$$ varies slowly with ζ , but $$-\dot M$$ decreases sharply with increasing ζ , so illustrating Schatzman's suggestion that angular momentum loss per unit mass-loss may be greatly increased by magnetic control of the outflowing gas. When the corona is hot, $$-\dot J/\Omega_8r_{8}\text{}^{2}$$ is almost independent of κ —the wind is essentially thermal; but at lower temperatures it is high only when κ ≃1—the wind is essentially centrifugal. The theory is applied to stars in thermal equilibrium, and to pre-main sequence stars contracting along the Hayashi and post-Hayashi tracks. In a close binary system of proto-stars, coupling between spin and orbital motion may be sufficiently strong to ensure that spin angular momentum lost is restored at the expense of the orbital angular momentum, so that the system remains a close binary in spite of the contraction of the individual stars.