How does pressure balance work in the magnetosphere?

Thread starter ergospherical
Start date Jan 1, 2024
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Balance Magnetosphere Pressure

Jan 1, 2024

ergospherical

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Homework Statement: How does the radius of the magnetosphere of a neutron star, accreting from a binary companion, scale with the surface magnetic field ##B##, the radius ##R## and the accretion rate ##\dot{M}##?

Relevant Equations: Spin down rate ##\dot{\Omega} = -B^2 R^6 \Omega^3 / (I \mu_0 c^3)##

I'm not sure how to set up the pressure balance at the magnetosphere? Maybe some energy equation relating ##\frac{1}{2} \dot{M} v^2 \sim## magnetic energy density?

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