We formulate the time-steady, axisymmetric problem of stellar magnetospheric inflow of gas from a surrounding accretion disk. The computational domain is bounded on the outside by a surface of given shape containing the open field lines associated with an induced disk wind. The mechanism for this wind has been investigated in previous publications in this journal. Our zeroth-order solution incorporates an acceptable accounting of the pressure balance between the magnetic field lines loaded with accreting gas (funnel flow) and those empty of matter (dead zone). In comparison with previous models, our funnel-flow/dead-zone solution has the following novel features: (1) Because of a natural tendency for the trapped stellar magnetic flux to pinch toward the corotation radius Rx (X-point of the effective potential), most of the interesting magnetohydrodynamics is initiated within a small neighborhood of Rx (X-region), where the Keplerian angular speed of rotation in the disk equals the spin rate of the star. (2) Unimpeded funnel flow from the inner portion of the X-region to the star can occur when the amount of trapped magnetic flux equals or exceeds 1.5 times the unperturbed dipole flux that would lie outside Rx in the absence of an accretion disk. (3). Near the equatorial plane, radial infall from the X-point is terminated at a "kink" point Rk = 0.74Rx that deflects the flow away from the midplane, mediating thereby between the field topology imposed by a magnetic fan of trapped flux at Rx and the geometry of a strong stellar dipole. (4) The excess angular momentum of accretion that would otherwise spin up the star rapidly is deposited by the magnetic torques of the funnel flow into the inner portion of the X-region of the disk. (5) An induced disk wind arises in the outer portion of the X-region, where the stellar field lines have been blown open, and removes whatever excess angular momentum that viscous torques do not transport to the outer disk. (6) The interface between open field lines loaded with outflowing matter (connected to the disk) and those not loaded (connected to the star) forms a "helmet streamer," along which major mass-ejection and reconnection events may arise in response to changing boundary conditions (e.g., stellar magnetic cycles), much the way that such events occur in the active Sun. (7) Pressure balance across the dead-zone/wind interface will probably yield an asymptotically vertical (i.e., "jetlike") trajectory for the matter ejected along the helmet streamer, but mathematical demonstration of this fact is left for future studies. (8) In steady state the overall balance of angular momentum in the star/disk/ magnetosphere system fixes the fractions, f and 1 - f, of the disk mass accretion rate into the X-region carried away, respectively, by the wind and funnel flows.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science
- Accretion, accretion disks
- Stars: pre-main-sequence