78 research outputs found
Sustained Turbulence in Differentially Rotating Magnetized Fluids at Low Magnetic Prandtl Number
We show for the first time that sustained turbulence is possible at low
magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our
results indicate that increasing the vertical domain size is equivalent to
increasing the dynamical range between the energy injection scale and the
dissipative scale. This has important implications for a large variety of
differentially rotating systems with low magnetic Prandtl number such as
protostellar disks and laboratory experiments.Comment: 5 pages, 6 figures, submitted to ApJ, changes made in response to
referee repor
The Stability of Weakly Collisional Plasmas with Thermal and Composition Gradients
Over the last decade, substantial efforts have been devoted to understanding
the stability properties, transport phenomena, and long-term evolution of
weakly-collisional, magnetized plasmas which are stratified in temperature.
These studies have improved our understanding of the physics governing the
intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This,
however, might not be a good approximation if heavy elements sediment in the
inner region of the galaxy cluster. In this paper, we analyze the stability of
a weakly-collisional, magnetized plane-parallel atmosphere which is stratified
in both temperature and composition. This allows us to discuss for the first
time the dynamics of weakly-collisional environments where heat conduction,
momentum transport, and ion-diffusion are anisotropic with respect to the
direction of the magnetic field. We show that, depending on the relative signs
and magnitudes of the gradients in the temperature and the mean molecular
weight, the plasma can be subject to a wide variety of unstable modes which
include modifications to the magnetothermal instability (MTI), the
heat-flux-driven buoyancy instability (HBI), and overstable gravity modes
previously studied in homogeneous media. We discuss the astrophysical
implications of our findings for a representative galaxy cluster where helium
has sedimented. Our findings suggest that the core insulation that results from
the magnetic field configurations that arise as a natural consequence of the
HBI, which would be MTI stable in a homogeneous medium, could be alleviated if
the mean molecular weight gradient is steep enough, i.e., . This study constitutes a first step toward understanding the
interaction between magnetic turbulence and the diffusion of heavy elements in
the ICM. (abridged)Comment: 16 pages, 7 figures. This article supersedes arXiv:1111.3372 (5
pages, 3 figures). The present version of this article is published in Ap
Spectral Analysis of Non-Ideal MRI Modes: The effect of Hall diffusion
The effect of magnetic field diffusion on the stability of accretion disks is
a problem that has attracted considerable interest of late. In particular, the
Hall effect has the potential to bring about remarkable changes in the
dynamical behavior of disks that are without parallel. In this paper, we
conduct a systematic examination of the linear eigenmodes in a weakly
magnetized differentially rotating gas with special focus on Hall diffusion. We
first develop a geometrical representation of the eigenmodes and provide a
detailed quantitative description of the polarization properties of the
oscillatory modes under the combined influence of the Coriolis and Hall
effects. We also analyze the effects of magnetic diffusion on the structure of
the unstable modes and derive analytical expressions for the kinetic and
magnetic stresses and energy densities associated with the non-ideal MRI. Our
analysis explicitly demonstrates that, if the dissipative effects are
relatively weak, the kinetic stresses and energies make up the dominant
contribution to the total stress and energy density when the equilibrium
angular momentum and magnetic field vectors are anti-parallel. This is in sharp
contrast to what is observed in the case of the ideal or dissipative MRI. We
conduct shearing box simulations and find very good agreement with the results
derived from linear analysis. As the modes in consideration are also exact
solutions of the non-linear equations, the unconventional nature of the kinetic
and magnetic stresses may have significant implications for the non-linear
evolution in some regions of protoplanetary disks.Comment: 16 pages, 11 figures, accepted by Ap
On Vertically Global, Horizontally Local Models for Astrophysical Disks
Disks with a barotropic equilibrium structure, for which the pressure is only
a function of the density, rotate on cylinders in the presence of a
gravitational potential, so that the angular frequency of such a disk is
independent of height. Such disks with barotropic equilibria can be
approximately modeled using the shearing box framework, representing a small
disk volume with height-independent angular frequency. If the disk is in
baroclinic equilibrium, the angular frequency does generally depend on height,
and it is thus necessary to go beyond the standard shearing box approach. In
this paper, we show that given a global disk model, it is possible to develop
approximate models that are local in horizontal planes without an expansion in
height with shearing-periodic boundary conditions. We refer to the resulting
framework as the vertically global shearing box (VGSB). These models can be
non-axisymmetric for globally barotropic equilibria but should be axisymmetric
for globally baroclinic equilibria. We provide explicit equations for this VGSB
which can be implemented in standard magnetohydrodynamic codes by generalizing
the shearing-periodic boundary conditions to allow for a height-dependent
angular frequency and shear rate. We also discuss the limitations that result
from the radial approximations that are needed in order to impose
height-dependent shearing periodic boundary conditions. We illustrate the
potential of this framework by studying a vertical shear instability and
examining the modes associated with the magnetorotational instability.Comment: 24 pages, 8 figures, updated to match published versio
On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks
The magnetorotational instability is thought to play an important role in
enabling accretion in sufficiently ionized astrophysical disks. The rate at
which MRI-driven turbulence transports angular momentum is related to both the
strength of the amplitudes of the fluctuations on various scales and the degree
of anisotropy of the underlying turbulence. This has motivated several studies
of the distribution of turbulent power in spectral space. In this paper, we
investigate the anisotropic nature of MRI-driven turbulence using a
pseudo-spectral code and introduce novel ways to robustly characterize the
underlying turbulence. We show that the general flow properties vary in a
quasi-periodic way on timescales comparable to 10 inverse angular frequencies
motivating the temporal analysis of its anisotropy. We introduce a 3D tensor
invariant analysis to quantify and classify the evolution of the anisotropic
turbulent flow. This analysis shows a continuous high level of anisotropy, with
brief sporadic transitions towards two- and three-component isotropic turbulent
flow. This temporal-dependent anisotropy renders standard shell-average,
especially when used simultaneously with long temporal averages, inadequate for
characterizing MRI-driven turbulence. We propose an alternative way to extract
spectral information from the turbulent magnetized flow, whose anisotropic
character depends strongly on time. This consists of stacking 1D Fourier
spectra along three orthogonal directions that exhibit maximum anisotropy in
Fourier space. The resulting averaged spectra show that the power along each of
the three independent directions differs by several orders of magnitude over
most scales, except the largest ones. Our results suggest that a
first-principles theory to describe fully developed MRI-driven turbulence will
likely have to consider the anisotropic nature of the flow at a fundamental
level.Comment: 13 pages, 13 figures, submitted to Ap
On the dynamics of pebbles in protoplanetary disks with magnetically-driven winds
We present an analytical model to investigate the production of pebbles and
their radial transport through a protoplanetary disk (PPD) with magnetically
driven winds. While most of the previous analytical studies in this context
assume that the radial turbulent coefficient is equal to the vertical dust
diffusion coefficient, in the light of the results of recent numerical
simulations, we relax this assumption by adopting effective parametrisations of
the turbulent coefficients involved in terms of the strength of the magnetic
fields driving the wind. Theoretical studies have already pointed out that even
in the absence of winds, these coefficients are not necessarily equal, though
its consequences regarding pebble production have not been explored. In this
paper, we investigate the evolution of the pebble production line, the radial
mass flux of the pebbles and their corresponding surface density as a function
of the plasma parameter at the disk midplane. Our analysis explicitly
demonstrates that the presence of magnetically-driven winds in a PPD leads to
considerable reduction of the rate and duration of the pebble delivery. We show
that when the wind is strong, the core growth in mass due to the pebble
accretion is so slow that it is unlikely that a core could reach a pebble
isolation mass during a PPD lifetime. When the mass of a core reaches this
critical value, pebble accretion is halted due to core-driven perturbations in
the gas. With decreasing wind strength, however, pebble accretion may, in a
shorter time, increase the mass of a core to the pebble isolation mass.Comment: 15 pages, accepted for publication in Ap
Structure of Protoplanetary Discs with Magnetically-driven Winds
We present a new set of analytical solutions to model the steady state
structure of a protoplanetary disc with a magnetically-driven wind. Our model
implements a parametrization of the stresses involved and the wind launching
mechanism in terms of the plasma parameter at the disc midplane, as suggested
by the results of recent, local MHD simulations. When wind mass-loss is
accounted for, we find that its rate significantly reduces the disc surface
density, particularly in the inner disc region. We also find that models that
include wind mass-loss lead to thinner dust layers. As an astrophysical
application of our models, we address the case of HL Tau, whose disc exhibits a
high accretion rate and efficient dust settling at its midplane. These two
observational features are not easy to reconcile with conventional accretion
disc theory, where the level of turbulence needed to explain the high accretion
rate would prevent a thin dust layer. Our disc model that incorporates both
mass-loss and angular momentum removal by a wind is able to account for HL Tau
observational constraints concerning its high accretion rate and dust layer
thinness.Comment: Accepted for publication in MNRAS, 13 pages, 8 figure
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