Spectropolarimetric observations combined with tomographic imaging techniques have revealed that all pre-main sequence (PMS) stars host multipolar magnetic fields, ranging from strong and globally axisymmetric with ~>kilo-Gauss dipole components, to
complex and non-axisymmetric with weak dipole components (<~0.1 kG). Many host dominantly octupolar large-scale fields. We argue that the large-scale magnetic properties of a PMS star are related to its location in the Hertzsprung-Russell diagram. This conference paper is a synopsis of Gregory et al. (2012), updated to include the latest results from magnetic mapping studies of PMS stars.
ZDI studies have shown that the magnetic fields of T Tauri stars can be significantly more complex than a simple dipole and can vary markedly between sources. We collect and summarize the magnetic field topology information obtained to date and prese
nt Hertzsprung-Russell (HR) diagrams for the stars in the sample. Intriguingly, the large scale field topology of a given pre-main sequence (PMS) star is strongly dependent upon the stellar internal structure, with the strength of the dipole component of its multipolar magnetic field decaying rapidly with the development of a radiative core. Using the observational data as a basis, we argue that the general characteristics of the global magnetic field of a PMS star can be determined from its position in the HR diagram. Moving from hotter and more luminous to cooler and less luminous stars across the PMS of the HR diagram, we present evidence for four distinct magnetic topology regimes. Stars with large radiative cores, empirically estimated to be those with a core mass in excess of ~40 per cent of the stellar mass, host highly complex and dominantly non-axisymmetric magnetic fields, while those with smaller radiative cores host axisymmetric fields with field modes of higher order than the dipole dominant (typically, but not always, the octupole). Fully convective stars stars above ~0.5 MSun appear to host dominantly axisymmetric fields with strong (kilo-Gauss) dipole components. Based on similarities between the magnetic properties of PMS stars and main sequence M-dwarfs with similar internal structures, we speculate that a bistable dynamo process operates for lower mass stars (<~0.5 MSun at an age of a few Myr) and that they will be found to host a variety of magnetic field topologies. If the magnetic topology trends across the HR diagram are confirmed they may provide a new method of constraining PMS stellar evolution models.
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 m
aps 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.
Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surfac
e magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplaces equation for the magnetostatic potential.
Magnetic fields play a crucial role at all stages of the formation of low mass stars and planetary systems. In the final stages, in particular, they control the kinematics of in-falling gas from circumstellar discs, and the launching and collimation
of spectacular outflows. The magnetic coupling with the disc is thought to influence the rotational evolution of the star, while magnetised stellar winds control the braking of more evolved stars and may influence the migration of planets. Magnetic reconnection events trigger energetic flares which irradiate circumstellar discs with high energy particles that influence the disc chemistry and set the initial conditions for planet formation. However, it is only in the past few years that the current generation of optical spectropolarimeters have allowed the magnetic fields of forming solar-like stars to be probed in unprecedented detail. In order to do justice to the recent extensive observational programs new theoretical models are being developed that incorporate magnetic fields with an observed degree of complexity. In this review we draw together disparate results from the classical electromagnetism, molecular physics/chemistry, and the geophysics literature, and demonstrate how they can be adapted to construct models of the large scale magnetospheres of stars and planets. We conclude by examining how the incorporation of multipolar magnetic fields into new theoretical models will drive future progress in the field through the elucidation of several observational conundrums.
