Analytic and numerical models of the 3D multipolar magnetospheres of pre-main sequence stars

Traditionally models of accretion of gas on to T Tauri stars have assumed a dipole stellar magnetosphere, partly for simplicity, but also due to the lack of information about their true magnetic field topologies. Before and since the first magnetic maps of an accreting T Tauri star were published in 2007 a new generation of magnetospheric accretion models have been developed that incorporate multipole magnetic fields. Three-dimensional models of the large-scale stellar magnetosphere with an observed degree of complexity have been produced via numerical field extrapolation from observationally derived T Tauri magnetic maps. Likewise, analytic and magnetohydrodynamic models with multipolar stellar magnetic fields have been produced. In this conference review article we compare and contrast the numerical field extrapolation and analytic approaches, and argue that the large-scale magnetospheres of some (but not all) accreting T Tauri stars can be well described by tilted dipole plus tilted octupole field components. We further argue that the longitudinal field curve, whether derived from accretion related emission lines, or from photospheric absorption lines, provides poor constrains on the large-scale magnetic field topology and that detailed modeling of the rotationally modulated Stokes V signal is required to recover the true field complexity. We conclude by examining the advantages, disadvantages and limitations of both the field extrapolation and analytic approaches, and also those of magnetohydrodynamic models