Magnetocentrifugally Driven Flows from Young Stars and Disks. VI.   Accretion with a Multipole Stellar Field
  Previous analyses of magnetospheric accretion and outflow in classical T Tauri stars (CTTSs), within the context of both the X-wind model and other theoretical scenarios, have assumed a dipolar geometry for the stellar magnetic field if it were not perturbed by the presence of an accreting, electrically conducting disk. However, CTTS surveys reveal that accretion hot spots cover a small fraction of the stellar surface, and that the net field polarization on the stellar surface is small. Both facts imply that the magnetic field generated by the star has a complex non-dipolar structure. To address this discrepancy between theory and observations, we re-examine X-wind theory without the dipole constraint. Using simple physical arguments based on the concept of trapped flux, we show that a dipole configuration is in fact not essential. Independent of the precise geometry of the stellar magnetosphere, the requirement for a certain level of trapped flux predicts a definite relationship among various CTTS observables. Moreover, superposition of multipole stellar fields naturally yield small observed hot-spot covering fractions and small net surface polarizations. The generalized X-wind picture remains viable under these conditions, with the outflow from a small annulus near the inner disk edge little affected by the modified geometry, but with inflow highly dependent on the details of how the emergent stellar flux is linked and trapped by the inner disk regions. Our model is consistent with data, including recent spectropolarimetric measurements of the hot spot sizes and field strengths in V2129 Oph and BP Tau. 
Subhanjoy Mohanty, Frank H. Shu