Non-ideal Magnetohydrodynamic Effects in Protoplanetary Disks

Abstract

The gas dynamics in protoplanetary disks (PPDs), particularly the level of turbulence as well as their global structure and evolution, are of crucial importance to many aspects of planet formation. Magnetic field is widely believed to play a crucial role in the gas dynamics, mainly via the magneto-rotational instability (MRI) or the magneto-centrifugal wind (MCW). In PPDs, however, these mechanisms are strongly affected by non-ideal magnetohydrodynamics (MHD) effects, including Ohmic resistivity, Hall effect and ambipolar diffusion (AD), due to the weak ionization level in PPDs. While Ohmic resistivity has been routinely included in the study of PPD gas dynamics, the Hall effects and AD have been largely ignored, even though they play an equally, if not more, important role.

In this thesis, the effect of AD is thoroughly explored via numerical simulations and the results are applied to estimate the effectiveness of the MRI in PPDs. The simulations show that MRI can always operate in the presence of AD for appropriate magnetic field strength and geometry. Stronger AD requires weaker magnetic field, and the most favorable field geometry involves the presence of both net vertical and net toroidal magnetic fluxes. Applying these results to PPDs, together with the results in the literature on the effect of Ohmic resistivity and the Hall term, a new theoretical framework is proposed to make optimistic estimates of the MRI-driven accretion rate. It is found that the MRI inevitably becomes inefficient in driving rapid accretion in the inner regions ($\sim1$ AU) of PPDs. It becomes more efficient in the outer disk ($\gtrsim15$ AU), especially assisted by the presence of tiny grains.

The fact that MRI becomes inefficient at the inner PPDs makes the MCW scenario a promising alternative. By performing vertically stratified shearing-box simulations of PPDs that simultaneously include the effects of both Ohmic resistivity and AD in a self-consistent manner, it is found that in the presence of a weak net vertical magnetic field (plasma $\beta\sim10^5$ at midplane), the MRI is completely suppressed in the inner region of PPDs, where the gas flow is purely laminar. A strong MCW is launched robustly that efficiently carries away the disk angular momentum, with the resulting wind-driven accretion rate consistent with observations. This thesis concludes by proposing a new scenario on the accretion process in PPDs where the MCW and MRI operate at the inner and outer disks respectively.