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 $144^3$ 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 $\alpha-\Omega$ 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 $\partial_r\Omega>0$. 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 $-\partial_r\Omega$, 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