254 research outputs found
Numerical Studies of Weakly Stochastic Magnetic Reconnection
We study the effects of turbulence on magnetic reconnection using
three-dimensional numerical simulations. This is the first attempt to test a
model of fast magnetic reconnection proposed by Lazarian & Vishniac (1999),
which assumes the presence of weak, small-scale magnetic field structure near
the current sheet. This affects the rate of reconnection by reducing the
transverse scale for reconnection flows and by allowing many independent flux
reconnection events to occur simultaneously. We performed a number of
simulations to test the dependencies of the reconnection speed, defined as the
ratio of the inflow velocity to the Alfven speed, on the turbulence power, the
injection scale and resistivity. Our results show that turbulence significantly
affects the topology of magnetic field near the diffusion region and increases
the thickness of the outflow region. We confirm the predictions of the Lazarian
& Vishniac model. In particular, we report the growth of the reconnection speed
proportional to ~ V^2, where V is the amplitude of velocity at the injection
scale. It depends on the injection scale l as ~ (l/L)^(2/3), where L is the
size of the system, which is somewhat faster but still roughly consistent with
the theoretical expectations. We also show that for 3D reconnection the Ohmic
resistivity is important in the local reconnection events only, and the global
reconnection rate in the presence of turbulence does not depend on it.Comment: 8 pages, 8 figure
Gravitational Instability in Collisionless Cosmological Pancakes
The gravitational instability of cosmological pancakes composed of
collisionless dark matter in an Einstein-de Sitter universe is investigated
numerically to demonstrate that pancakes are unstable with respect to
fragmentation and the formation of filaments. A ``pancake'' is defined here as
the nonlinear outcome of the growth of a 1D, sinusoidal, plane-wave, adiabatic
density perturbation. We have used high resolution, 2D, N-body simulations by
the Particle-Mesh (PM) method to study the response of pancakes to perturbation
by either symmetric (density) or antisymmetric (bending or rippling) modes,
with corresponding wavevectors k_s and k_a transverse to the wavevector k_p of
the unperturbed pancake plane-wave. We consider dark matter which is initially
``cold'' (i.e. with no random thermal velocity in the initial conditions). We
also investigate the effect of a finite, random, isotropic, initial velocity
dispersion (i.e. initial thermal velocity) on the fate of pancake collapse and
instability. Pancakes are shown to be gravitationally unstable with respect to
all perturbations of wavelength l<l_p (where l_p= 2pi/k_p). These results are
in contradiction with the expectations of an approximate, thin-sheet energy
argument.Comment: To appear in the Astrophysical Journal (1997), accepted for
publication 10/10/96, single postscript file, 61 pages, 19 figure
A Numerical Gamma-Ray Burst Simulation Using Three-Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jet-like Expansion
We present the first unrestricted, three-dimensional relativistic
hydrodynamical calculations of the blob of gas associated with the jet
producing a gamma-ray burst. We investigate the deceleration phase of the blob
corresponding to the time when afterglow radiation is produced, concentrating
on the transition in which the relativistic beaming 1/gamma goes from being
less than theta, where gamma is the bulk Lorentz factor and theta is the
angular width of the jet, to 1/gamma > theta. We study the time dependent
evolution of the physical parameters associated with the jet, both parallel to
the direction of motion and perpendicular to it. We calculate light curves for
observers at varying angles with respect to the velocity vector of the blob,
assuming optically thin emission that scales with the local pressure. Our main
findings are that (i) gas ahead of the advancing blob does not accrete onto and
merge with the blob material but rather flows around the blob, (ii) the decay
light curve steepens at a time corresponding roughly to 1/gamma equals theta
(in accord with earlier studies), and (iii) the rate of decrease of the forward
component of momentum in the blob is well-fit by a simple model in which the
gas in front of the blob exerts a drag force on the blob, and the cross
sectional area of the blob increases quadratically with laboratory time (or
distance).Comment: 30 pages, 10 Postscript figures, uses aasms4.st
The 21cm angular-power spectrum from the dark ages
At redshifts z >~ 30 neutral hydrogen gas absorbs CMB radiation at the 21cm
spin-flip frequency. In principle this is observable and a high-precision probe
of cosmology. We calculate the linear-theory angular power spectrum of this
signal and cross-correlation between redshifts on scales much larger than the
line width. In addition to the well known redshift-distortion and density
perturbation sources a full linear analysis gives additional contributions to
the power spectrum. On small scales there is a percent-level linear effect due
to perturbations in the 21cm optical depth, and perturbed recombination
modifies the gas temperature perturbation evolution (and hence spin temperature
and 21cm power spectrum). On large scales there are several post-Newtonian and
velocity effects; although negligible on small scales, these additional terms
can be significant at l <~ 100 and can be non-zero even when there is no
background signal. We also discuss the linear effect of reionization
re-scattering, which damps the entire spectrum and gives a very small
polarization signal on large scales. On small scales we also model the
significant non-linear effects of evolution and gravitational lensing. We
include full results for numerical calculation and also various approximate
analytic results for the power spectrum and evolution of small scale
perturbations.Comment: 29 pages; significant extensions including: self-absorption terms
(i.e. change to background radiation due to 21cm absorption); ionization
fraction perturbations; estimates of non-linear effects; approximate analytic
results; results for sharp redshift window functions. Code available at
http://camb.info/sources
Magnetic Field Structure and Stochastic Reconnection in a Partially Ionized Gas
We consider stochastic reconnection in a magnetized, partially ionized
medium. Stochastic reconnection is a generic effect, due to field line
wandering, in which the speed of reconnection is determined by the ability of
ejected plasma to diffuse away from the current sheet along magnetic field
lines, rather than by the details of current sheet structure. We consider the
limit of weak stochasticity, so that the mean magnetic field energy density is
greater than either the turbulent kinetic energy density or the energy density
associated with the fluctuating component of the field. We consider field line
stochasticity generated through a turbulent cascade, which leads us to consider
the effect of neutral drag on the turbulent cascade of energy. In a
collisionless plasma, neutral particle viscosity and ion-neutral drag will damp
mid-scale turbulent motions, but the power spectrum of the magnetic
perturbations extends below the viscous cutoff scale. We give a simple physical
picture of the magnetic field structure below this cutoff, consistent with
numerical experiments. We provide arguments for the reemergence of the
turbulent cascade well below the viscous cut-off scale and derive estimates for
field line diffusion on all scales. We note that this explains the persistence
of a single power law form for the turbulent power spectrum of the interstellar
medium, from scales of tens of parsecs down to thousands of kilometers. We find
that under typical conditions in the ISM stochastic reconnection speeds are
reduced by the presence of neutrals, but by no more than an order of magnitude.Comment: Astrophysical Journal in pres
The Generation of Magnetic Fields Through Driven Turbulence
We have tested the ability of driven turbulence to generate magnetic field
structure from a weak uniform field using three dimensional numerical
simulations of incompressible turbulence. We used a pseudo-spectral code with a
numerical resolution of up to collocation points. We find that the
magnetic fields are amplified through field line stretching at a rate
proportional to the difference between the velocity and the magnetic field
strength times a constant. Equipartition between the kinetic and magnetic
energy densities occurs at a scale somewhat smaller than the kinetic energy
peak. Above the equipartition scale the velocity structure is, as expected,
nearly isotropic. The magnetic field structure at these scales is uncertain,
but the field correlation function is very weak. At the equipartition scale the
magnetic fields show only a moderate degree of anisotropy, so that the typical
radius of curvature of field lines is comparable to the typical perpendicular
scale for field reversal. In other words, there are few field reversals within
eddies at the equipartition scale, and no fine-grained series of reversals at
smaller scales. At scales below the equipartition scale, both velocity and
magnetic structures are anisotropic; the eddies are stretched along the local
magnetic field lines, and the magnetic energy dominates the kinetic energy on
the same scale by a factor which increases at higher wavenumbers. We do not
show a scale-free inertial range, but the power spectra are a function of
resolution and/or the imposed viscosity and resistivity. Our results are
consistent with the emergence of a scale-free inertial range at higher Reynolds
numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?
Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales II: Perturbative and numerical analyses of power spectrum and bispectrum
We explore observational constraints on possible deviations from Newtonian
gravity by means of large-scale clustering of galaxies. We measure the power
spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare
the result with predictions in an empirical model of modified gravity. Our
model assumes an additional Yukawa-like term with two parameters that
characterize the amplitude and the length scale of the modified gravity. The
model predictions are calculated using two methods; the second-order
perturbation theory and direct N-body simulations. These methods allow us to
study non-linear evolution of large-scale structure. Using the simulation
results, we find that perturbation theory provides reliable estimates for the
power spectrum and the bispectrum in the modified Newtonian model. We also
construct mock galaxy catalogues from the simulations, and derive constraints
on the amplitude and the length scale of deviations from Newtonian gravity. The
resulting constraints from power spectrum are consistent with those obtained in
our earlier work, indicating the validity of the previous empirical modeling of
gravitational nonlinearity in the modified Newtonian model. If linear biasing
is adopted, the bispectrum of the SDSS galaxies yields constraints very similar
to those from the power spectrum. If we allow for the nonlinear biasing
instead, we find that the ratio of the quadratic to linear biasing
coefficients, b_2/b_1, should satisfy -0.4 < b_2/b_1<0.3 in the modified
Newtonian model.Comment: 12 pages, 7 figure
Stochastic Biasing and Weakly Non-linear Evolution of Power Spectrum
Distribution of galaxies may be a biased tracer of the dark matter
distribution and the relation between the galaxies and the total mass may be
stochastic, non-linear and time-dependent. Since many observations of galaxy
clustering will be done at high redshift, the time evolution of non-linear
stochastic biasing would play a crucial role for the data analysis of the
future sky surveys. In this paper, we develop the weakly non-linear analysis
and attempt to clarify the non-linear feature of the stochastic biasing. We
compute the one-loop correction of the power spectrum for the total mass, the
galaxies and their cross correlation. Assuming the local functional form for
the initial galaxy distribution, we investigate the time evolution of the
biasing parameter and the correlation coefficient. On large scales, we first
find that the time evolution of the biasing parameter could deviate from the
linear prediction in presence of the initial skewness. However, the deviation
can be reduced when the initial stochasticity exists. Next, we focus on the
quasi-linear scales, where the non-linear growth of the total mass becomes
important. It is recognized that the scale-dependence of the biasing
dynamically appears and the initial stochasticity could affect the time
evolution of the scale-dependence. The result is compared with the recent
N-body simulation that the scale-dependence of the halo biasing can appear on
relatively large scales and the biasing parameter takes the lower value on
smaller scales. Qualitatively, our weakly non-linear results can explain this
trend if the halo-mass biasing relation has the large scatter at high redshift.Comment: 29pages, 7 postscript figures, submitted to Ap
Magnetic Helicity Conservation and Astrophysical Dynamos
We construct a magnetic helicity conserving dynamo theory which incorporates
a calculated magnetic helicity current. In this model the fluid helicity plays
a small role in large scale magnetic field generation. Instead, the dynamo
process is dominated by a new quantity, derived from asymmetries in the second
derivative of the velocity correlation function, closely related to the `twist
and fold' dynamo model. The turbulent damping term is, as expected, almost
unchanged. Numerical simulations with a spatially constant fluid helicity and
vanishing resistivity are not expected to generate large scale fields in
equipartition with the turbulent energy density. The prospects for driving a
fast dynamo under these circumstances are uncertain, but if it is possible,
then the field must be largely force-free. On the other hand, there is an
efficient analog to the dynamo. Systems whose turbulence is
driven by some anisotropic local instability in a shearing flow, like real
stars and accretion disks, and some computer simulations, may successfully
drive the generation of strong large scale magnetic fields, provided that
. We show that this
criterion is usually satisfied. Such dynamos will include a persistent,
spatially coherent vertical magnetic helicity current with the same sign as
, that is, positive for an accretion disk and negative for
the Sun. We comment on the role of random magnetic helicity currents in storing
turbulent energy in a disordered magnetic field, which will generate an
equipartition, disordered field in a turbulent medium, and also a declining
long wavelength tail to the power spectrum. As a result, calculations of the
galactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa
- …