111 research outputs found
Simulations of MHD Instabilities in Intracluster Medium Including Anisotropic Thermal Conduction
We perform a suite of simulations of cooling cores in clusters of galaxies in
order to investigate the effect of the recently discovered heat flux buoyancy
instability (HBI) on the evolution of cores. Our models follow the
3-dimensional magnetohydrodynamics (MHD) of cooling cluster cores and capture
the effects of anisotropic heat conduction along the lines of magnetic field,
but do not account for the cosmological setting of clusters or the presence of
AGN. Our model clusters can be divided into three groups according to their
final thermodynamical state: catastrophically collapsing cores, isothermal
cores, and an intermediate group whose final state is determined by the initial
configuration of magnetic field. Modeled cores that are reminiscent of real
cluster cores show evolution towards thermal collapse on a time scale which is
prolonged by a factor of ~2-10 compared with the zero-conduction cases. The
principal effect of the HBI is to re-orient field lines to be perpendicular to
the temperature gradient. Once the field has been wrapped up onto spherical
surfaces surrounding the core, the core is insulated from further conductive
heating (with the effective thermal conduction suppressed to less than 1/100th
of the Spitzer value) and proceeds to collapse. We speculate that, in real
clusters, the central AGN and possibly mergers play the role of "stirrers,"
periodically disrupting the azimuthal field structure and allowing thermal
conduction to sporadically heat the core.Comment: 16 pages, 3 tables, 17 figures, accepted to ApJ with minor revisions,
to appear in Volume 704, Oct 20, 2009 issu
Can conduction induce convection? The non-linear saturation of buoyancy instabilities in dilute plasmas
We study the effects of anisotropic thermal conduction on low-collisionality,
astrophysical plasmas using two and three-dimensional magnetohydrodynamic
simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable
for either sign of the temperature gradient: the heat-flux-driven buoyancy
instability (HBI) operates when the temperature increases with radius while the
magnetothermal instability (MTI) operates in the opposite limit. In contrast to
previous results, we show that, in the presence of a sustained temperature
gradient, the MTI drives strong turbulence and operates as an efficient
magnetic dynamo (akin to standard, adiabatic convection). Together, the
turbulent and magnetic energies contribute up to ~10% of the pressure support
in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5%
of rho c_s^3. These findings are robust even in the presence of an external
source of strong turbulence. Our results on the nonlinear saturation of the HBI
are consistent with previous studies but we explain physically why the HBI
saturates quiescently by re-orienting the magnetic field (suppressing the
conductive heat flux through the plasma), while the MTI saturates by generating
sustained turbulence. We also systematically study how an external source of
turbulence affects the saturation of the HBI: such turbulence can disrupt the
HBI only on scales where the shearing rate of the turbulence is faster than the
growth rate of the HBI. In particular, our results provide a simple mapping
between the level of turbulence in a plasma and the effective isotropic thermal
conductivity. We discuss the astrophysical implications of these findings, with
a particular focus on the intracluster medium of galaxy clusters.Comment: 18 pages, 14 figures. Submitted to MNRA
Anisotropic Thermal Conduction and the Cooling Flow Problem in Galaxy Clusters
We examine the long-standing cooling flow problem in galaxy clusters with 3D
MHD simulations of isolated clusters including radiative cooling and
anisotropic thermal conduction along magnetic field lines. The central regions
of the intracluster medium (ICM) can have cooling timescales of ~200 Myr or
shorter--in order to prevent a cooling catastrophe the ICM must be heated by
some mechanism such as AGN feedback or thermal conduction from the thermal
reservoir at large radii. The cores of galaxy clusters are linearly unstable to
the heat-flux-driven buoyancy instability (HBI), which significantly changes
the thermodynamics of the cluster core. The HBI is a convective,
buoyancy-driven instability that rearranges the magnetic field to be
preferentially perpendicular to the temperature gradient. For a wide range of
parameters, our simulations demonstrate that in the presence of the HBI, the
effective radial thermal conductivity is reduced to less than 10% of the full
Spitzer conductivity. With this suppression of conductive heating, the cooling
catastrophe occurs on a timescale comparable to the central cooling time of the
cluster. Thermal conduction alone is thus unlikely to stabilize clusters with
low central entropies and short central cooling timescales. High central
entropy clusters have sufficiently long cooling times that conduction can help
stave off the cooling catastrophe for cosmologically interesting timescales.Comment: Submitted to ApJ, 14 pages, 14 figure
The Dynamics of Rayleigh-Taylor Stable and Unstable Contact Discontinuities with Anisotropic Thermal Conduction
We study the effects of anisotropic thermal conduction along magnetic field
lines on an accelerated contact discontinuity in a weakly collisional plasma.
We first perform a linear stability analysis similar to that used to derive the
Rayleigh-Taylor instability (RTI) dispersion relation. We find that anisotropic
conduction is only important for compressible modes, as incompressible modes
are isothermal. Modes grow faster in the presence of anisotropic conduction,
but growth rates do not change by more than a factor of order unity. We next
run fully non-linear numerical simulations of a contact discontinuity with
anisotropic conduction. The non-linear evolution can be thought of as a
superposition of three physical effects: temperature diffusion due to vertical
conduction, the RTI, and the heat flux driven buoyancy instability (HBI). In
simulations with RTI-stable contact discontinuities, the temperature
discontinuity spreads due to vertical heat conduction. This occurs even for
initially horizontal magnetic fields due to the initial vertical velocity
perturbation and numerical mixing across the interface. The HBI slows this
temperature diffusion by reorienting initially vertical magnetic field lines to
a more horizontal geometry. In simulations with RTI-unstable contact
discontinuities, the dynamics are initially governed by temperature diffusion,
but the RTI becomes increasingly important at late times. We discuss the
possible application of these results to supernova remnants, solar prominences,
and cold fronts in galaxy clusters.Comment: 18 pages, 15 figures, submitted to MNRA
Buoyancy Instabilities in Galaxy Clusters: Convection Due to Adiabatic Cosmic Rays and Anisotropic Thermal Conduction
Using a linear stability analysis and two and three-dimensional nonlinear
simulations, we study the physics of buoyancy instabilities in a combined
thermal and relativistic (cosmic ray) plasma, motivated by the application to
clusters of galaxies. We argue that cosmic ray diffusion is likely to be slow
compared to the buoyancy time on large length scales, so that cosmic rays are
effectively adiabatic. If the cosmic ray pressure is of
the thermal pressure, and the cosmic ray entropy (;
is the thermal plasma density) decreases outwards, cosmic rays drive an
adiabatic convective instability analogous to Schwarzschild convection in
stars. Global simulations of galaxy cluster cores show that this instability
saturates by reducing the cosmic ray entropy gradient and driving efficient
convection and turbulent mixing. At larger radii in cluster cores, the thermal
plasma is unstable to the heat flux-driven buoyancy instability (HBI), a
convective instability generated by anisotropic thermal conduction and a
background conductive heat flux. Cosmic-ray driven convection and the HBI may
contribute to redistributing metals produced by Type 1a supernovae in clusters.
Our calculations demonstrate that adiabatic simulations of galaxy clusters can
artificially suppress the mixing of thermal and relativistic plasma;
anisotropic thermal conduction allows more efficient mixing, which may
contribute to cosmic rays being distributed throughout the cluster volume.Comment: submitted to ApJ; 15 pages and 12 figures; abstract shortened to < 24
lines; for high resolution movies see
http://astro.berkeley.edu/~psharma/clustermovie.htm
Thermal Instability with Anisotropic Thermal Conduction and Adiabatic Cosmic Rays: Implications for Cold Filaments in Galaxy Clusters
Observations of the cores of nearby galaxy clusters show H and
molecular emission line filaments. We argue that these are the result of {\em
local} thermal instability in a {\em globally} stable galaxy cluster core. We
present local, high resolution, two-dimensional magnetohydrodynamic simulations
of thermal instability for conditions appropriate to the intracluster medium
(ICM); the simulations include thermal conduction along magnetic field lines
and adiabatic cosmic rays. Thermal conduction suppresses thermal instability
along magnetic field lines on scales smaller than the Field length (10
kpc for the hot, diffuse ICM). We show that the Field length in the cold medium
must be resolved both along and perpendicular to the magnetic field in order to
obtain numerically converged results. Because of negligible conduction
perpendicular to the magnetic field, thermal instability leads to fine scale
structure in the perpendicular direction. Filaments of cold gas along magnetic
field lines are thus a natural consequence of thermal instability with
anisotropic thermal conduction. Nonlinearly, filaments of cold ( K)
gas should have lengths (along the magnetic field) comparable to the Field
length in the cold medium pc! Observations show, however, that
the atomic filaments in clusters are far more extended, kpc. Cosmic
ray pressure support (or a small scale turbulent magnetic pressure) may resolve
this discrepancy: even a small cosmic ray pressure in the diffuse ICM, of the thermal pressure, can be adiabatically compressed to provide
significant pressure support in cold filaments. This is qualitatively
consistent with the large population of cosmic rays invoked to explain the
atomic and molecular line ratios observed in filaments.Comment: submitted to ApJ; 13 figs. 31 pages; abstract shortened; figures
reduced in size; see http://astro.berkeley.edu/~psharma/TI-v6.pdf for a copy
with high resolution figure
The Magnetothermal Instability in the Intracluster Medium
The electron mean free path in the intracluster medium (ICM) of galaxy
clusters is much larger than the gyroradius; thus, heat is transported
anisotropically along magnetic field lines. We show that the intracluster
medium is unstable to the magnetothermal instability (MTI) using MHD
simulations with anisotropic thermal conduction. As a result of the MTI, we
find that the temperature profile of the ICM can be substantially modified on
timescales of several billion years while the magnetic field is amplified by
dynamo action up to more than fifty times the original energy. We also show
that the instability drives field lines to become preferentially radial leading
to conduction that is a highly efficient fraction of the Spitzer conductivity.
As such, we present the first self-consistent calculation of the effective
thermal conductivity in the ICM.Comment: Submitted to Ap
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