Warping and Precession of Accretion Disks around Magnetic Stars: Nonlinear Evolution

Abstract

The inner region of the accretion disk around a magnetized star (T Tauri star, white dwarf, or neutron star) is subjected to magnetic torques that induce warping and precession of the disk. These torques arise from the interaction between the stellar field and the induced electric currents in the disk. We carry out numerical simulations of the nonlinear evolution of warped, viscous accretion disks driven by the magnetic torques. We show that the disk can develop into a highly warped steady state in which the disk attains a fixed (warped) shape and precesses rigidly. The warp is most pronounced at the disk inner radius (near the magnetosphere boundary). As the system parameters (such as accretion rate) change, the disk can switch between a completely flat state (warping-stable) and a highly warped state. The precession of warped disks may be responsible for a variety of quasi-periodic oscillations or radiation flux variabilities observed in many different systems, including young stellar objects and X-ray binaries.

Modelling the photopolarimetric variability of AA Tau

“…Naturally, it is quite possible to surmise that any variations in mass transfer rate will impact on the size and nature of the warping of the disc. This scenario is discussed in a recent paper by Pfeiffer & Lai (2004). We comment that another factor that may affect the long‐term behaviour of any warp is magnetic diffusivity, which we do not consider here.…”

Characterizing X-ray binary long-term variability

“…Pfeiffer & Lai (2004) carried out numerical simulations of viscous accretion discs driven by the magnetic torque in the inner disc, resulting from the interaction between the induced electric currents in the disc and the accreting object’s magnetic field ( B ). They show that an accretion disc surrounding a magnetic star (T Tauri star, WD or NS) can develop warps in the inner disc that steadily precess.…”

Statistical Trends in the Obliquity Distribution of Exoplanet Systems

“…The precession rate due to a rapidly spinning star is proportional to the oblateness quadrupole moment J 2 M * R 2 * and scales with orbital radius as ∝ r −7/2 . Alternatively, a magnetized protostar for which the magnetic moment µ and spin vector are misaligned can also induce precessional torques, which act at a rate proportional to µ 2 and scale with radius as ∝ r −11/2 (Lai 1999;Pfeiffer & Lai 2004). Of these two effects, the magnetic torque seems to be the most efficient one, as Pfeiffer & Lai (2004) state that r BP ∼ 3r in ∼ 10R * , where r in ∝ µ 4/7 is the is the magnetospheric truncation radius.…”

“…Alternatively, a magnetized protostar for which the magnetic moment µ and spin vector are misaligned can also induce precessional torques, which act at a rate proportional to µ 2 and scale with radius as ∝ r −11/2 (Lai 1999;Pfeiffer & Lai 2004). Of these two effects, the magnetic torque seems to be the most efficient one, as Pfeiffer & Lai (2004) state that r BP ∼ 3r in ∼ 10R * , where r in ∝ µ 4/7 is the is the magnetospheric truncation radius. On the other hand, for a rapidly spinning oblate star (say, rotating at a tenth of the breakup rate) the transition radius is smaller: r BP ≈ R * ( 3 2 J 2 αh −2 ) 1/2 ∼ O(R * ).…”