Magnetospheric truncation radius ($r_m$)

The inner radius at which a stellar magnetic dipole field disrupts a surrounding accretion disk. In a free fall pressure-balance estimate with fixed aspect ratio $ϵ=H/r$, $r_m\sim ({ϵ}^2{\mu }^4/(GM{\dot{M}}^2){)}^{1/7}$. Geometry and inflow structure change its numerical coefficient.

The accretion Alfvén radius estimates where the magnetic stress of an accreting star competes with inflow stress and disrupts an approximately Keplerian disk. It is distinct from the Alfvén critical radius of an outgoing stellar wind. A dipole and a free-fall pressure estimate give the characteristic $B_{\ast }^{4/7}{\dot{M}}^{-2/7}$ scaling; the numerical coefficient depends on flow geometry, and an inferred radius inside the star is outside the model's domain.

A dipole's magnetic pressure scales as $B_{\ast }^2{R}_{\ast }^6/({\mu }_0{r}^6)$. Spherical free fall with $\rho =\dot{M}/(4\pi r^{2}v)$ and $v\propto (GM/r{)}^{1/2}$ has ram pressure proportional to $\dot{M}(GM{)}^{1/2}{r}^{-5/2}$. Equating them gives the seventh-root scaling. Disc geometry changes the coefficient; the estimate ceases to describe an exterior magnetosphere if the resulting radius lies inside the star.