A self-consistent reduced model for dusty magnetorotationally unstable discs


  • Emmanuel Jacquet,

    Corresponding author
    1. Laboratoire de Minéralogie et de Cosmochimie du Muséum, Muséum National d’Histoire Naturelle, 57 rue Cuvier, 75005 Paris, France
      E-mail: ejacquet@mnhn.fr
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  • Steven Balbus

    1. Laboratoire de Radioastronomie, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
    2. Institut universitaire de France, Maison des Universités, 103 blvd. Saint-Michel, 75005 Paris, France
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E-mail: ejacquet@mnhn.fr


The interaction between settling of dust grains and magnetorotational instability (MRI) turbulence in protoplanetary discs is analysed. We use a reduced system of coupled ordinary differential equations to represent the interaction between the diffusion of grains and the inhibition of the MRI. The coupled equations are styled on a Landau equation for the turbulence and a Fokker–Planck equation for the diffusion. The turbulence–grain interaction is probably most relevant near the outer edge of the disc’s quiescent, or ‘dead’ zone. Settling is most pronounced near the mid-plane, where a high dust concentration can self-consistently suppress the MRI. Under certain conditions, however, grains can reach high altitudes, a result of some observational interest. Finally, we show that the equilibrium solutions are linearly stable.