125 research outputs found
Self-Sustained Ionization and Vanishing Dead Zones in Protoplanetary Disks
We analyze the ionization state of the magnetohydrodynamically turbulent
protoplanetary disks and propose a new mechanism of sustaining ionization.
First, we show that in the quasi-steady state of turbulence driven by
magnetorotational instability in a typical protoplanetary disk with dust
grains, the amount of energy dissipation should be sufficient for providing the
ionization energy that is required for activating magnetorotational
instability. Second, we show that in the disk with dust grains the energetic
electrons that compose electric currents in weakly ionized gas can provide
collisional ionization, depending on the actual saturation state of
magnetorotational turbulence. On the other hand, we show that in the
protoplanetary disks with the reduced effect of dust grains, the turbulent
motion can homogenize the ionization degree, leading to the activation of
magnetorotational instability even in the absence of other ionization
processes. The results in this Letter indicate that most of the regions in
protoplanetary disks remain magnetically active, and we thus require a change
in the theoretical modeling of planet formation.Comment: 11 pages, 2 figures. Accepted for publication in The Astrophysical
Journal Letter
The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: II. Saturation Level and Critical Magnetic Reynolds Number
The nonlinear evolution of the magnetorotational instability (MRI) in weakly
ionized accretion disks, including the effect of the Hall term and ohmic
dissipation, is investigated using local three-dimensional MHD simulations and
various initial magnetic field geometries. When the magnetic Reynolds number,
Re_M \equiv v_A^2 / \eta \Omega (where v_A is the Alfven speed, \eta the
magnetic diffusivity, and \Omega the angular frequency), is initially larger
than a critical value Re_{M, crit}, the MRI evolves into MHD turbulence in
which angular momentum is transported efficiently by the Maxwell stress. If
Re_M < Re_{M, crit}, however, ohmic dissipation suppresses the MRI, and the
stress is reduced by several orders of magnitude. The critical value is in the
range of 1 - 30 depending on the initial field configuration. The Hall effect
does not modify the critical magnetic Reynolds number by much, but enhances the
saturation level of the Maxwell stress by a factor of a few. We show that the
saturation level of the MRI is characterized by v_{Az}^2 / \eta \Omega, where
v_{Az} is the Alfven speed in the nonlinear regime along the vertical component
of the field. The condition for turbulence and significant transport is given
by v_{Az}^2 / \eta \Omega \gtrsim 1, and this critical value is independent of
the strength and geometry of the magnetic field or the size of the Hall term.
If the magnetic field strength in an accretion disk can be estimated
observationally, and the magnetic Reynolds number v_A^2 / \eta \Omega is larger
than about 30, this would imply the MRI is operating in the disk.Comment: 43 pages, 8 tables, 20 figures, accepted for publication in ApJ,
postscript version also available from
http://www.astro.umd.edu/~sano/publications
Axisymmetric Magnetorotational Instability in Viscous Accretion Disks
Axisymmetric magnetorotational instability (MRI) in viscous accretion disks
is investigated by linear analysis and two-dimensional nonlinear simulations.
The linear growth of the viscous MRI is characterized by the Reynolds number
defined as , where is the Alfv{\'e}n
velocity, is the kinematic viscosity, and is the angular
velocity of the disk. Although the linear growth rate is suppressed
considerably as the Reynolds number decreases, the nonlinear behavior is found
to be almost independent of . At the nonlinear evolutionary stage,
a two-channel flow continues growing and the Maxwell stress increases until the
end of calculations even though the Reynolds number is much smaller than unity.
A large portion of the injected energy to the system is converted to the
magnetic energy. The gain rate of the thermal energy, on the other hand, is
found to be much larger than the viscous heating rate. Nonlinear behavior of
the MRI in the viscous regime and its difference from that in the highly
resistive regime can be explained schematically by using the characteristics of
the linear dispersion relation. Applying our results to the case with both the
viscosity and resistivity, it is anticipated that the critical value of the
Lundquist number for active turbulence
depends on the magnetic Prandtl number in
the regime of and remains constant when , where and is the magnetic diffusivity.Comment: Accepted for publication in ApJ -- 18 pages, 9 figures, 1 tabl
Saturation and Thermalization of the Magnetorotational Instability: Recurrent Channel Flows and Reconnections
The nonlinear evolution and the saturation mechanism of the magnetorotational
instability (MRI) are investigated using three-dimensional resistive MHD
simulations. A local shearing box is used for our numerical analysis and the
simulations begin with a purely vertical magnetic field. We find that the
magnetic stress in the nonlinear stage of the MRI is strongly fluctuating. The
time evolution shows the quasi-periodic recurrence of spike-shape variations
typically for a few orbits which correspond to the rapid amplification of the
magnetic field by the nonlinear growth of a two-channel solution followed by
the decay through magnetic reconnections. The increase rate of the total energy
in the shearing box system is analytically related to the volume-averaged
torque in the system. We find that at the saturated state this energy gain of
the system is balanced with the increase of the thermal energy mostly due to
the joule heating. The spike-shape time evolution is a general feature of the
nonlinear evolution of the MRI in the disks threaded by vertical fields and can
be seen if the effective magnetic Reynolds number is larger than about unity.Comment: 11 pages, 4 figures, accepted for publication in ApJ
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