Magnetospheric Accretion
The magnetic field of a young protostar plays a pivotal role in how matter is accreted from the surrounding protostellar disc. Here we consider a dipolar stellar magnetic field aligned with the rotation axis of the star, which carves an inner cavity out of the protostellar disc up to the truncation radius. This is the point at which the gas ram pressure is equal to the magnetic pressure, and at which the magnetic field lines couple to the disc.
\[\frac{B^2(R_{trunc})}{2\mu} = \rho u^2\] \[\frac{R_{trunc}}{R_*} = 2m_s^{2/7} \left ( \frac{B_*}{140G}\right )^{4/7}\left ( \frac{\dot M}{10^{-8}M_\odot yr^{-1}}\right )^{-\frac{2}{7}} \left ( \frac{M_*}{0.8M_\odot}\right )^{-1/7} \left ( \frac{R_*}{2R_\odot}\right )^{5/7}\] For typical values of \(B_* = 1kG\) and \(\dot M_A = 10^{-8}\; M_\odot \; yr^{-1}\), we find that \[R_{trunc} \approx 3-7R_* \approx 0.03-0.07AU\]Corotation vs truncation radius
Whether accretion occurs depends on the relation between the truncation and corotation radii.
Accretion regimeStellar field lines which couple to the disc at a radius less than the corotation radius \(r < r_{cor}\) will act to spin the star up. The disc material will be locked to the field lines and will move at the same angular velocity as the star. This is how accretion columns are formed.
DippersIn the case that \(r_{trunc} \sim r_{cor}\), field lines couple to the disc at the corotation radius and result in "disk locking". Accretion columns will form, but there will be no net spin-up or spin-down of the star. Dippers can be identified in light curves by their relatively flat maxima and quasi-periodic dips in brightness, which are caused by dust being lifted into accretion columns and temporarily eclipsing the star.
Propeller regimeStellar field lines which couple at \(r > r_{cor}\) will act to slow down the star as the stellar angular velocity is greater than the Keplerian velocity. This means that any disc material which becomes linked to the field lines will experience a centrifugal force which attempts to fling it away from the system. No accretion columns appear in this situation.
What causes magnetospheric accretion to stop?
- If the truncation radius shifts beyond the corotation radius, magnetospheric accretion will cease
- Photoevaporative winds can carry material away before it reaches the star
- planet formation can remove mass that would otherwise be accreted