Angular momentum conservation: 1

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Presentation transcript:

Angular momentum conservation: 1 Azimuthal component x R gives torque balance: Couple exerted by Lorentz force on unit volume Angular momentum transported by flow

Angular momentum conservation: 2 Equation of motion becomes: constant

Net angular momentum flux Integrate azimuthal equation of motion to get: Constant of integration on each field-streamline. L is the net angular momentum per unit mass carried in the plasma motion and the magnetic stresses Wind carries angular momentum away from star. Lorentz force transmits torque to stellar surface. Star spins down.

The story so far: Induction 1 Mass continuity 2 3 Torque balance

The Alfvénic point Use (1) - 0/R2 (3) to eliminate B: Substitute: to get: u is singular at Alfvenic point up=uA unless:

Weber-Davis radial-field model Radial field lines close to star (“split monopole”). Spherical Alfvénic surface, radius rA. Isotropic mass loss. Angular momentum flux across area ds is: Mass flux Net specific angular momentum transported along field line anchored at latitude  Area of surface element ds =4/3

Net spindown torque on star Density at Alfven radius: Net torque on star: Radial or dipole field For thermal driving, uA~ 2 to 3 cs, indep. of . For linear dynamo law, B0 ~ . If stellar moment of inertia is constant:

General braking laws Asymptotically: Hence for p = 3, cf. Skumanich.