129 research outputs found
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
Mineral Processing by Short Circuits in Protoplanetary Disks
Meteoritic chondrules were formed in the early solar system by brief heating
of silicate dust to melting temperatures. Some highly refractory grains (Type B
calcium-aluminum-rich inclusions, CAIs) also show signs of transient heating. A
similar process may occur in other protoplanetary disks, as evidenced by
observations of spectra characteristic of crystalline silicates. One possible
environment for this process is the turbulent magnetohydrodynamic flow thought
to drive accretion in these disks. Such flows generally form thin current
sheets, which are sites of magnetic reconnection, and dissipate the magnetic
fields amplified by a disk dynamo. We suggest that it is possible to heat
precursor grains for chondrules and other high-temperature minerals in current
sheets that have been concentrated by our recently described short-circuit
instability. We extend our work on this process by including the effects of
radiative cooling, taking into account the temperature dependence of the
opacity; and by examining current sheet geometry in three-dimensional, global
models of magnetorotational instability. We find that temperatures above 1600 K
can be reached for favorable parameters that match the ideal global models.
This mechanism could provide an efficient means of tapping the gravitational
potential energy of the protoplanetary disk to heat grains strongly enough to
form high-temperature minerals. The volume-filling nature of turbulent magnetic
reconnection is compatible with constraints from chondrule-matrix
complementarity, chondrule-chondrule complementarity, the occurrence of igneous
rims, and compound chondrules. The same short-circuit mechanism may perform
other high-temperature mineral processing in protoplanetary disks such as the
production of crystalline silicates and CAIs.Comment: 6 pages, 3 figures, ApJL published versio
Short Circuits in Thermally Ionized Plasmas: A Mechanism for Intermittent Heating of Protoplanetary Disks
Many astrophysical systems of interest, including protoplanetary accretion
disks, are made of turbu- lent magnetized gas with near solar metallicity.
Thermal ionization of alkali metals in such gas exceeds non-thermal ionization
when temperatures climb above roughly 1000 K. As a result, the conductiv- ity,
proportional to the ionization fraction, gains a strong, positive dependence on
temperature. In this paper, we demonstrate that this relation between the
temperature and the conductivity triggers an exponential instability that acts
similarly to an electrical short, where the increased conductivity concentrates
the current and locally increases the Ohmic heating. This contrasts with the
resistiv- ity increase expected in an ideal magnetic reconnection region. The
instability acts to focus narrow current sheets into even narrower sheets with
far higher currents and temparatures. We lay out the basic principles of this
behavior in this paper using protoplanetary disks as our example host system,
motivated by observations of chondritic meteorites and their ancestors, dust
grains in protoplanetary disks, that reveal the existence of strong, frequent
heating events that this instability could explain.Comment: 9 pages, 6 figures, 1 table Accepted, Ap
Phurbas: An Adaptive, Lagrangian, Meshless, Magnetohydrodynamics Code. II. Implementation and Tests
We present an algorithm for simulating the equations of ideal
magnetohydrodynamics and other systems of differential equations on an
unstructured set of points represented by sample particles. The particles move
with the fluid, so the time step is not limited by the Eulerian
Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to
ensure the particles fill the computational volume, and gives the algorithm
substantial flexibility and power. A target resolution is specified for each
point in space, with particles being added and deleted as needed to meet this
target. We have parallelized the code by adapting the framework provided by
GADGET-2. A set of standard test problems, including 1e-6 amplitude linear MHD
waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented.
Finally we demonstrate good agreement with analytic predictions of linear
growth rates for magnetorotational instability in a cylindrical geometry. This
paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.Comment: 14 pages, 14 figures, ApJS accepted, revised in accordance with
changes to paper I (arXiv:1110.0835
GLOBAL SIMULATIONS OF PROTOPLANETARY DISKS WITH OHMIC RESISTIVITY AND AMBIPOLAR DIFFUSION
Protoplanetary disks are believed to accrete onto their central T Tauri star
because of magnetic stresses. Recently published shearing box simulations
indicate that Ohmic resistivity, ambipolar diffusion and the Hall effect all
play important roles in disk evolution. In the presence of a vertical magnetic
field, the disk remains laminar between 1-5au, and a magnetocentrifugal disk
wind forms that provides an important mechanism for removing angular momentum.
Questions remain, however, about the establishment of a true physical wind
solution in the shearing box simulations because of the symmetries inherent in
the local approximation. We present global MHD simulations of protoplanetary
disks that include Ohmic resistivity and ambipolar diffusion, where the
time-dependent gas-phase electron and ion fractions are computed under FUV and
X-ray ionization with a simplified recombination chemistry. Our results show
that the disk remains laminar, and that a physical wind solution arises
naturally in global disk models. The wind is sufficiently efficient to explain
the observed accretion rates. Furthermore, the ionization fraction at
intermediate disk heights is large enough for magneto-rotational channel modes
to grow and subsequently develop into belts of horizontal field. Depending on
the ionization fraction, these can remain quasi-global, or break-up into
discrete islands of coherent field polarity. The disk models we present here
show a dramatic departure from our earlier models including Ohmic resistivity
only. It will be important to examine how the Hall effect modifies the
evolution, and to explore the influence this has on the observational
appearance of such systems, and on planet formation and migration.Comment: 18 pages, 12 figures, accepted for publication in Ap
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