EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS

By Xue-Ning Bai, James M. Stone. 2011

149 citations recorded by the source corpus.

We study the role of ambipolar diffusion (AD) on the nonlinear evolution of the magnetorotational instability (MRI) in protoplanetary disks using the strong coupling limit, which applies in very weakly ionized gas with electron recombination time much shorter than the orbital time so that a single-fluid treatment is sufficient. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency at which neutral particles collides with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress αmax. For Am ≲ 1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wavenumber with a growth rate exceeding that of the pure vertical field case. We find there is a very tight correlation between the turbulent stress α and the plasma 〈β〉 ≡ Pgas/Pmag ≈ 1/2α at the saturated state of the MRI turbulence regardless of field geometry, and αmax rapidly decreases with decreasing Am. In particular, we find αmax ≈ 7 × 10−3 for Am = 1 and αmax ≈ 6 × 10−4 for Am = 0.1.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/1ab845b6e8d230c3834b078930baff56931daf85

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In Astronomy and Astrophysics

1. Xue-Ning Bai
2. D. Wilner
3. S. Andrews
4. A. Hughes
5. E. Chiang
6. K. Rosenfeld
7. T. Birnstiel
8. E. Bergin

Citations in the corpus

• WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. I. SUPPRESSION OF THE MAGNETOROTATIONAL INSTABILITY AND LAUNCHING OF THE MAGNETOCENTRIFUGAL WIND (2013, methodology): “…cells if one defines the scale height to be √ 2H , as in a number of works) to properly resolve the MRI turbulence (Davis et al. 2010; Sorathia et al. 2012; Bai & Stone 2011), and have a relatively large simulation box to capture the mesoscale structures of the MRI turbulence (Simon et al. 2012).”
• EXCLUSION OF COSMIC RAYS IN PROTOPLANETARY DISKS: STELLAR AND MAGNETIC EFFECTS (2013, background): “In the weakly ionized limit, Bai & Stone (2011) show that a disk can become MRI unstable at any value of Am, as long as the disk is weakly magnetic.”
• WEAK TURBULENCE IN THE HD 163296 PROTOPLANETARY DISK REVEALED BY ALMA CO OBSERVATIONS (2015, background): “Simulations have also found that a net vertical magnetic field is required to produce strong turbulence (Bai & Stone 2011; Simon et al. 2013); in the HD 163296 system the MRI may still operate but simply with a weak magnetic field that results in weak turbulence.”
• LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW (2012, background): “Such a tilt angle is related to the empirical correlation between the plasma β and the stress parameter α ≈ 1/2β (Guan et al. 2009; Bai & Stone 2011), which also applies for the midplane region of our run B4 as we can compare Figures 3 and 6.”
• Global simulations of protoplanetary disks with net magnetic flux: I. Non-ideal MHD case (2016, background): “Both diffusive effects can damp magnetic structures, and potentially quench the MRI (Jin 1996; Kunz & Balbus 2004), as supported by numerous non-linear simulations (e.g., Hawley & Stone 1998; Fleming et al. 2000; Bai & Stone 2011).”
• Multiple Disk Gaps and Rings Generated by a Single Super-Earth (2017, background): “…than non-ideal MHD effects, in particular ambipolar diffusion, can significantly suppress the magnetorotational instability in disks at tens of AUs, resulting in practically zero turbulence at disk midplanes (Bai & Stone 2011; Perez-Becker & Chiang 2011b,a; Bai 2013; Turner et al. 2014; Bai 2015).”
• Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics (2017, background): “For AD, Am 1 can suppress or damp the MRI depending on vertical field strength (Bai & Stone 2011).”