MRI is considered to be the most promising mechanism driving angular-momentum transport in protoplanetary disks (Balbus & Hawley 1991; Brandenburg et al. 1995; Hawley et al. 1995; Balbus et al. 1996; Balbus & Hawley 1998). However, protoplanetary disks are cold, dense, and, therefore, poorly ionized. The low level of ionization tends to decouple the disk gas from magnetic fields, which generates non-ideal MHD effects: Ohmic dissipation, ambipolar diffusion (AD), and the Hall effect (e.g., Armitage 2011; Turner et al. 2014). These effects quench MRI in different ways: Ohmic dissipation originates from collisions between electrons and neutrals, AD from collisions between ions and neutrals, and the Hall effect from drift between electrons and ions (Fleming et al. 2000; Sano & Stone 2002; Bai & Stone 2011). Ohmic dissipation operates in high-density regions with weak field, AD dominates in highly ionized and low-density regions, and the Hall effect lies in between (Fleming & Stone 2003; Bai & Stone 2011; Bai 2014). So far, the effect of Ohmic dissipation has been best studied. Investigations show the layered accretion in the inner disk, where the midplane region is “dead” due to low ionization while the surface layer is “active” due to sufficient ionization (Gammie 1996; Jin 1996; Fleming et al. 2000; Fleming & Stone 2003; Turner et al. 2007; Ilgner & Nelson 2008; Oishi & Mac Low 2009; Okuzumi & Hirose 2011). Recent works that take into account both Ohmic dissipation and AD show that AD may render the surface layer and portions of the outer disk inactive (Bai & Stone 2011; Landry et al. 2013; Kalyaan et al. 2015). Bai & Stone (2013) find that MRI is completely suppressed in the inner disk and a strong magnetocentrifugal wind is launched. Three-dimensional simulations that include all three non-ideal MHD effects are also performed (Bai 2014, 2015; Lesur et al. 2014; Simon et al. 2015). In the inner disk, the influence of the Hall effect on midplane angular-momentum transport depends on the orientation of the vertical magnetic field with the disk rotation axis. When the field is aligned with the axis, the enhanced Maxwell stress promotes angular-momentum transport. When the field is anti-aligned with the axis, the midplane remains quiescent. In the outer disk, the Hall effect has little influence on the disk turbulence. Although the inclusion of AD and the Hall effect substantially changes the level of turbulence in the protoplanetary disks, the feature that the viscosity is low in the inner disk and high in the outer disk is still valid. In this study, we assume that gas giant planets form in situ via the core accretion scenario, which implies that their formation locations are always in the low-viscosity region. Since in this study we focus on the relation between photoevaporation and planet formation and gap opening by planets in the disk, we adopt Ohmic dissipation to represent the non-ideal MHD effects on the MRI. We consider that this simplification has little influence on our main calculation results.
Citation: Bai 2014
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Citation: Ilgner & Nelson 2008
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Citation: Bai 2014
Citation function: Background