Accretion onto stars with octupole magnetic fields: Matter flow, hot spots and phase shifts

Recent measurements of the surface magnetic fields of classical T Tauri stars (CTTSs) and magnetic cataclysmic variables show that their magnetic fields have a complex structure. Investigation of accretion onto such stars requires global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the complexity of simulations strongly increases with each higher-order multipole. Previously, we were able to model disc accretion onto stars with magnetic fields described by a superposition of dipole and quadrupole moments. However, in some stars, like CTTS V2129 Oph and BP Tau, the octupolar component is significant and it was necessary to include the next octupolar component. Here, we show results of global 3D MHD simulations of accretion onto stars with superposition of the dipole and octupole fields, where we vary the ratio between components. Simulations show that if octupolar field strongly dominates at the disc-magnetosphere boundary, then matter flows into the ring-like octupolar poles, forming ring-shape spots at the surface of the star above and below equator. The light-curves are complex and may have two peaks per period. In case where the dipole field dominates, matter accretes in two ordered funnel streams towards poles, however the polar spots are meridionally-elongated due to the action of the octupolar component. In the case when the fields are of similar strengths, both, polar and belt-like spots are present. In many cases the light-curves show the evidence of complex fields, excluding the cases of small inclinations angles, where sinusoidal light-curve is observed and ‘hides’ the information about the field complexity.We also propose new mechanisms of phase shift in stars with complex magnetic fields. We suggest that the phase shifts can be connected with: (1) temporal variation of the star’s intrinsic magnetic field and subsequent redistribution of main magnetic poles; (2) variation of the accretion rate, which causes the disc to interact with the magnetic fields associated with different magnetic moments. We use our model to demonstrate these phase shift mechanisms, and we discuss possible applications of these mechanisms to accreting millisecond pulsars and young stars.