The multipolar magnetic fields of accreting pre-main-sequence stars: B at the inner disk, B along the accretion flow, and B at the accretion shock

Zeeman-Doppler imaging studies have revealed the complexity of the large-scale magnetic fields of accreting pre-main-sequence stars. All have multipolar magnetic fields with the octupole component being the dominant field mode for many of the stars studied thusfar. Young accreting stars with fully convective interiors often feature simple axisymmetric magnetic fields with dipole components of order a kilo-Gauss (at least those of mass $\gtrsim0.5\,{\rm M}_\odot$), while those with substantially radiative interiors host more complex non-axisymmetric magnetic fields with dipole components of order a few 0.1 kilo-Gauss. Here, via several simple examples, we demonstrate that i). in most cases, the dipole component alone can be used to estimate the disk truncation radius (but little else); ii) due the presence of higher order magnetic field components, the field strength in the accretion spots is far in excess of that expected if a pure dipole magnetic field is assumed. (Fields of $\sim$6$\,{\rm kG}$ have been measured in accretion spots.); iii) if such high field strengths are taken to be representative of the polar strength of a dipole magnetic field, the disk truncation radius would be overestimated. The effects of multipolar magnetic fields must be considered in both models of accretion flow and of accretion shocks.