Grzegorz Kowal

Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields

We study the effects of turbulence on magnetic reconnection using three-dimensional direct numerical simulations. This is the first attempt to test a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian & Vishniac. This model predicts that weak turbulence, which is generically present in most astrophysical systems, enhances the rate of reconnection by reducing the transverse scale for reconnection events and by allowing many independent flux reconnection events to occur simultaneously. As a result, the reconnection speed becomes independent of Ohmic resistivity and is determined by the magnetic field wandering induced by turbulence. We test the dependence of the reconnection speed on turbulent power, the energy injection scale, and resistivity. We apply the open and experiment with the outflow boundary conditions in our numerical model and discuss the advantages and drawbacks of various setups. To test our results, we also perform simulations of turbulence with the same outflow boundaries but without a large-scale field reversal, thus without large-scale reconnection. To quantify the reconnection speed we use both an intuitive definition, i.e., the speed of the reconnected flux inflow, and a more sophisticated definition based on a formally derived analytical expression. Our results confirm the predictions of the Lazarian and Vishniac model. In particular, we find that the reconnection speed is proportional to the square root of the injected power, as predicted by the model. The dependence on the injection scale for some of our models is a bit weaker than expected, i.e., l 3/4 inj, compared to the predicted linear dependence on the injection scale, which may require some refinement of the model or may be due to effects such as the finite size of the excitation region, which are not a part of the model. The reconnection speed was found to depend on the expected rate of magnetic field wandering and not on the magnitude of the guide field. In our models, we see no dependence on the guide field when its strength is comparable to the reconnected component. More importantly, while in the absence of turbulence we successfully reproduce the Sweet-Parker scaling of reconnection, in the presence of turbulence we do not observe any dependence on Ohmic resistivity, confirming that the reconnection of the weakly stochastic field is fast. We also do not observe a dependence on anomalous resistivity, which suggests that the presence of anomalous effects, e.g., Hall MHD effects, may be irrelevant for astrophysical systems with weakly stochastic magnetic fields.

Density fluctuations in mhd turbulence : Spectra, intermittency, and topology

We perform three-dimensional (3D) compressible MHD simulations over many dynamical times for an extended range of sonic and Alfven Mach numbers and analyze the statistics of 3D density and 2D column density, which include probability distribution functions, spectra, skewness, kurtosis, She-Leveque exponents, and genus. In order to establish the relation between the statistics of the observables, i.e., column densities, and the underlying 3D statistics of density, we analyze the effects of cloud boundaries. We define the parameter space for 3D measures to be recovered from column densities. In addition, we show that for subsonic turbulence the spectra of density fluctuations are consistent with k-7/3 in the case of a strong magnetic field and k-5/3 in the case of a weak magnetic field. For supersonic turbulence we confirm the earlier findings of the shallow spectra of density and Kolmogorov spectra of the logarithm of density. We find that the intermittencies of the density and velocity are very different.

DENSITY STUDIES OF MHD INTERSTELLAR TURBULENCE: STATISTICAL MOMENTS, CORRELATIONS AND BISPECTRUM

We present a number of statistical tools that show promise for obtaining information on turbulence in molecular clouds (MCs) and diffuse interstellar medium (ISM). For our tests we make use of three-dimensional 5123 compressible MHD isothermal simulations performed for different sonic, i.e., , where VL is the injection velocity, Vs is the sound velocity, and Alfvenic , where VA is the Alfven velocity, Mach numbers. We introduce the bispectrum, a new tool for statistical studies of the interstellar medium which, unlike an ordinary power spectrum of turbulence, preserves the phase information of the stochastic field. We show that the bispectra of the three-dimensional stochastic density field and of column densities, available from observations, are similar. This opens good prospects for studies of MCs and diffuse media with the new tool. We use the bispectrum technique to define the role of nonlinear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. As expected, a strong correlation is obtained for wave modes k 1 = k 2 for all models. Larger values of result in increased correlations for modes with k 1 ≠ k 2. This effect becomes more evident with increasing magnetic field intensity. We believe that the different MHD wave modes, e.g., Alfven and magneto-acoustic, which arise in strongly magnetized turbulence, may be responsible for the increased correlations compared to purely hydrodynamical perturbations. In addition to the bispectrum, we calculated the third and fourth statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with . In particular, as increases, so does the Gaussian asymmetry of the density distribution. We also studied the correlations of two-dimensional column density with dispersion of velocities and magnetic field, as well as the correlations of three-dimensional density with magnetic and kinetic energy and for comparison. Our results show that column density is linearly correlated with magnetic field for high . This trend is independent of the turbulent kinetic energy and can be used to characterize inhomogeneities of physical properties in low density clumps in the ISM.

Studies of Regular and Random Magnetic Fields in the ISM: Statistics of Polarization Vectors and the Chandrasekhar-Fermi Technique

Polarimetry is extensively used as a tool to trace the interstellar magnetic field projected on the plane of sky. Moreover, it is also possible to estimate the magnetic field intensity from polarimetric maps based on the Chandrasekhar-Fermi method. In this work, we present results for turbulent, isothermal, three-dimensional simulations of sub/supersonic and sub/super-Alfvenic cases. With the cubes, assuming perfect grain alignment, we created synthetic polarimetric maps for different orientations of the mean magnetic field with respect to the line of sight (LOS). We show that the dispersion of the polarization angle depends on the angle of the mean magnetic field regarding the LOS and on the Alfvenic Mach number. However, the second-order structure function of the polarization angle follows the relation SF ∝ lα, α being dependent exclusively on the Alfvenic Mach number. The results show an anticorrelation between the polarization degree and the column density, with exponent γ ~ − 0.5, in agreement with observations, which is explained by the increase in the dispersion of the polarization angle along the LOS within denser regions. However, this effect was observed exclusively on supersonic, but sub-Alfvenic, simulations. For the super-Alfvenic, and the subsonic model, the polarization degree showed to be independent of the column density. Our major quantitative result is a generalized equation for the CF method, which allowed us to determine the magnetic field strength from the polarization maps with errors <20%. We also account for the role of observational resolution on the CF method.

VELOCITY FIELD OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE: WAVELET DECOMPOSITION AND MODE SCALINGS

We study compressible magnetohydrodynamic turbulence, which holds the key to many astrophysical processes, including star formation and cosmic-ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid, we use wavelet decomposition of the turbulent velocity field into Alfven, slow, and fast modes, which presents an extension of the Cho & Lazarian decomposition approach based on Fourier transforms. The wavelets allow us to follow the variations of the local direction of the magnetic field and therefore improve the quality of the decomposition compared to the Fourier transforms, which are done in the mean field reference frame. For each resulting component, we calculate the spectra and two-point statistics such as longitudinal and transverse structure functions as well as higher order intermittency statistics. In addition, we perform a Helmholtz- Hodge decomposition of the velocity field into incompressible and compressible parts and analyze these components. We find that the turbulence intermittency is different for different components, and we show that the intermittency statistics depend on whether the phenomenon was studied in the global reference frame related to the mean magnetic field or in the frame defined by the local magnetic field. The dependencies of the measures we obtained are different for different components of the velocity; for instance, we show that while the Alfven mode intermittency changes marginally with the Mach number, the intermittency of the fast mode is substantially affected by the change.

THE TURBULENT WARM IONIZED MEDIUM: EMISSION MEASURE DISTRIBUTION AND MHD SIMULATIONS

We present an analysis of the distribution of Hemission measures for the warm ionized medium (WIM) of the GalaxyusingdatafromtheWisconsinHMapper(WHAM)NorthernSkySurvey.OursampleisrestrictedtoGalactic latitudes jbj > 10 � .Weremovedsightlinesintersecting19high-latitudeclassicalHiiregions,leavingonlysightlines that sample the diffuse WIM. The distribution of EM sin jbjfor the diffuse WIM sample is poorly characterized by a single normal distribution, but is extraordinarily wellfit by a lognormal distribution, with hlog EM sin jbj(pc cm � 6 ) � 1 i¼ 0:146 � 0:001 and standard deviationlog EM sin jbj ¼ 0:190 � 0:001. The value of log EM sin jbj hi drops from 0:260 � 0:002 at Galactic latitude 10 < jbj < 30 to 0:038 � 0:002 at Galactic latitude 60 < jbj < 90. The distribution maywidenslightly atlowGalacticlatitude.WecomparetheobservedEMdistributionfunctiontothepredictionsof three- dimensional magnetohydrodynamic simulations of isothermal turbulence within a nonstratified interstellar medium. We find that the distribution of EM sin jbj is well described by models of mildly supersonic turbulence with a sonic Mach number of � 1.4Y2.4. The distribution is weakly sensitive to the magnetic field strength. The model also successfully predictsthedistributionof dispersionmeasuresof pulsarsandHlineprofiles.InthebestfittingmodeltheturbulentWIM occupies a vertical path length of 400Y500 pc within the 1.0Y1.8 kpc scale height of the layer. The WIM gas has a lognormal distribution of densities with a most probable electron density npk � 0:03 cm � 3 . We also discuss the impli- cations of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM. Subject headingg ISM: structure — MHD — turbulence

Scaling Relations of Compressible MHD Turbulence

We study scaling relations of compressible and strongly magnetized turbulence using isothermal numerical simulations with resolution 5123. We find a good correspondence of our results with the Fleck model of compressible hydrodynamic turbulence. In particular, we find that the density-weighted velocity, i.e., ≡ ρ1/3, proposed by Kritsuk and coworkers obeys the Kolmogorov scaling, i.e., v(k) ~ k-5/3, for the high Mach number turbulence. Similarly, we find that the exponents of the third-order structure functions for stay equal to unity for all Mach numbers studied. The higher order correlations obey the She-Leveque scalings corresponding to the two-dimensional dissipative structures, and this result does not change with the Mach number either. In contrast to velocity , which exhibits different scaling parallel and perpendicular to the local magnetic field, the scaling of is similar in both directions. In addition, we find that the peaks of density create a hierarchy in which both physical and column densities decrease with the scale in accordance to the Fleck predictions. This hierarchy can be related to ubiquitous small ionized and neutral structures (SINS) in the interstellar gas. We believe that studies of statistics of the column density peaks can provide both a consistency check for the turbulence velocity studies and insight into supersonic turbulence, when the velocity information is not available.

Particle acceleration in turbulence and weakly stochastic reconnection.

In this Letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in and demonstrated numerically in . When turbulence is included within the current sheet, the acceleration rate is highly enhanced, because reconnection becomes fast and independent of resistivity and allows the formation of a thick volume filled with multiple simultaneously reconnecting magnetic fluxes. Charged particles trapped within this volume suffer several head-on scatterings with the contracting magnetic fluctuations, which significantly increase the acceleration rate and results in a first-order Fermi process. For comparison, we also tested acceleration in MHD turbulence, where particles suffer collisions with approaching and receding magnetic irregularities, resulting in a reduced acceleration rate. We argue that the dominant acceleration mechanism approaches a second order Fermi process in this case.

Fast magnetic reconnection and energetic particle acceleration

Abstract Our numerical simulations show that the reconnection of magnetic field becomes fast in the presence of weak turbulence in the way consistent with the Lazarian and Vishniac (1999) model of fast reconnection. We trace particles within our numerical simulations and show that the particles can be efficiently accelerated via the first order Fermi acceleration. We discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers.

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e.g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew-Goldberger-Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL- MHD subsonic and supersonic turbulences show small differences compared