Numerical Simulations of Incompressible MHD Turbulence

The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent works on direct three-dimensional numerical simulations for MHD turbulence in a periodic box. In those works, we use a pseudo-spectral code to solve the incompressible MHD equations. We first discuss the structure and properties of turbulence as functions of scale. The results are consistent with the scaling law recently proposed by Goldreich & Sridhar. The scaling law is based on the concept of scale-dependent isotropy: smaller eddies are more elongated than larger ones along magnetic field lines. This scaling law substantially changes our views on MHD turbulence. For example, as noted by Lazarian & Vishniac, the scaling law can provide a fast reconnection rate. We further discuss how the study of incompressible MHD turbulence can help us to understand physical processes in interstellar medium (ISM) by considering imbalanced cascade and viscous damped turbulence.Comment: 5 pages; 3 figures; Conference proceedin

Fast Diffusion of Magnetic Field in Turbulence and Origin of Cosmic Magnetism

Turbulence is believed to play important roles in the origin of cosmic magnetism. While it is well known that turbulence can efficiently amplify a uniform or spatially homogeneous seed magnetic field, it is not clear whether or not we can draw a similar conclusion for a localized seed magnetic field. The main uncertainty is the rate of magnetic field diffusion on scales larger than the outer scale of turbulence. To measure the diffusion rate of magnetic field on those large scales, we perform a numerical simulation in which the outer scale of turbulence is much smaller than the size of the system. We numerically compare diffusion of a localized seed magnetic field and a localized passive scalar. We find that diffusion of the magnetic field can be much faster than that of the passive scalar and that turbulence can efficiently amplify the localized seed magnetic field. Based on the simulation result, we construct a model for fast diffusion of magnetic field. Our model suggests that a localized seed magnetic field can fill the whole system in (L_sys/L) times the large-eddy turnover time and that growth of the magnetic field stops in max(15, L_sys/L) times the large-eddy turnover time, where L_sys is the size of the system and $L$ is the driving scale. Our finding implies that, regardless of the shape of the seed field, fast magnetization is possible in turbulent systems, such as large-scale structure of the universe or galaxies.Comment: 6 pages, 4 figures, published in PR

Statistics of Galactic Synchrotron and Dust Foregrounds: Spectra, PDFs and Higher-Order Moments

We present statistical analysis of diffuse Galactic synchrotron emission and polarized thermal emission from dust. Both Galactic synchrotron emission and polarized thermal emission from dust reflect statistics of magnetic field fluctuations and, therefore, Galactic turbulence. We mainly focus on the relation between observed angular spectra and underlying turbulence statistics. Our major findings are as follows. First, we find that magnetohydrodynamic (MHD) turbulence in the Galaxy can indeed explain diffuse synchrotron emission from high galactic latitude. Our model calculation suggests that either a one-component extended halo model or a two-component model, an extended halo component (scale height > 1kpc) plus a local component, can explain the observed angular spectrum of the synchrotron emission. However, discrete sources seem to dominate the spectrum for regions near the Galactic plane. Second, we study how star-light polarization is related with polarized emission from thermal dust. We also discuss the expected angular spectrum of polarized emission from thermal dust. Our model calculations suggest that C_l\propto l^{-11/3} for l > 1000 and a shallower spectrum for l < 1000.Comment: 15 pages, 11 figures; ApJ, submitted; We welcome comments from foreground experts on the possibility of the filtering procedur

Polarization of FIR emission from T Tauri Disks

Recent observation of 850 micron sub-mm polarization from T Tauri disks opens up the possibility of studying magnetic field structure within protostellar disks. The degree of polarization is around 3 % and the direction of polarization is perpendicular to the disk. Since thermal emission from dust grains dominates the spectral energy distribution at the sub-mm/FIR regime, dust grains are thought to be the cause of the polarization. We discuss grain alignment by radiation and we explore the efficiency of dust alignment in T Tauri disks. Calculations show that dust grains located far away from the Central proto-star are more efficiently aligned. In the presence of a regular magnetic field, the aligned grains produce polarized emission in sub-mm/FIR wavelengths. The direction of polarization is perpendicular to the local magnetic field direction. When we use a recent T Tauri disk model and take a Mathis-Rumpl-Nordsieck-type distribution with maximum grain size of 500-1000 $\mu$m, the degree of polarization is around 2-3 % level at wavelengths larger than $\sim100\mu$m. Our study indicates that multifrequency infrared polarimetric studies of protostellar disks can provide good insights into the details of their magnetic structure. We also provide predictions for polarized emission for disks viewed at different wavelengths and viewing angles.Comment: 8 pages, 8 figures; submitted to RevMexAA (conference series

Growth of a localized seed magnetic field in a turbulent medium

Turbulence dynamo deals with amplification of a seed magnetic field in a turbulent medium and has been studied mostly for uniform or spatially homogeneous seed magnetic fields. However, some astrophysical processes (e.g. jets from active galaxies, galactic winds, or ram-pressure stripping in galaxy clusters) can provide localized seed magnetic fields. In this paper, we numerically study amplification of localized seed magnetic fields in a turbulent medium. Throughout the paper, we assume that driving scale of turbulence is comparable to the size of the system. Our findings are as follows. First, turbulence can amplify a localized seed magnetic field very efficiently. The growth rate of magnetic energy density is as high as that for a uniform seed magnetic field. This result implies that a magnetic field ejected from an astrophysical object can be a viable source of magnetic field in a cluster. Second, the localized seed magnetic field disperses and fills the whole system very fast. If turbulence in a system (e.g. a galaxy cluster or a filament) is driven at large scales, we expect that it takes a few large-eddy turnover times for magnetic field to fill the whole system. Third, growth and turbulence diffusion of a localized seed magnetic field are also fast in high magnetic Prandtl number turbulence. Fourth, even in decaying turbulence, a localized seed magnetic field can ultimately fill the whole system. Although the dispersal rate of magnetic field is not fast in purely decaying turbulence, it can be enhanced by an additional forcing.Comment: 11 pages, 9 figures, ApJ (accepted

Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence

When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \$b_+^2/b_-^2 \propto (\epsilon_+/\epsilon_-)^n \$ with n>2). These results are consistent with those obtained for imbalanced non-relativistic Alfv\'enic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.Comment: 6 pages, 3 figure

Effects of multiple-scale driving on turbulence statistics

Turbulence is ubiquitous in astrophysical fluids such as the interstellar medium (ISM) and the intracluster medium (ICM). In turbulence studies, it is customary to assume that fluid is driven on a single scale. However, in astrophysical fluids, there can be many different driving mechanisms that act on different scales. If there are multiple energy-injection scales, the process of energy cascade and turbulence dynamo will be different compared with the case of single energy-injection scale. In this work, we perform three-dimensional incompressible/compressible magnetohydrodynamic (MHD) turbulence simulations. We drive turbulence in Fourier space in two wavenumber ranges, 2\$\leq k \leq \sqrt{12}\$ (large-scale) and 15 \$\lesssim k \lesssim \$ 26 (small-scale). We inject different amount of energy in each range by changing the amplitude of forcing in the range. We present the time evolution of the kinetic and magnetic energy densities and discuss the turbulence dynamo in the presence of energy injections at two scales. We show how kinetic, magnetic and density spectra are affected by the two-scale energy injections and we discuss the observational implications. In the case \$\epsilon_L < \epsilon_S\$, where \$\epsilon_L\$ and \$\epsilon_S\$ are energy-injection rates at the large and small scales, respectively, our results show that even a tiny amount of large-scale energy injection can significantly change the properties of turbulence. On the other hand, when \$\epsilon_L \gtrsim \epsilon_S\$, the small-scale driving does not influence the turbulence statistics much unless \$\epsilon_L \sim \epsilon_S\$.Comment: 17 pages, 6 figure

Scaling of ISM Turbulence: Implications for HI

Galactic HI is a gas that is coupled to magnetic field because of its fractional ionization. Many properties of HI are affected by turbulence. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time in the history of the subject we have a scaling model that is supported by numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We also discuss the new regime of MHD turbulence that happens below the scale at which conventional turbulent motions get damped by viscosity. The viscosity in the case of HI is being produced by neutrals and truncates the turbulent cascade at parsec scales. We show that below this scale magnetic fluctuations with a shallow spectrum persist and point out to a possibility of the resumption of the MHD cascade after ions and neutrals decouple. We discuss the implications of the new insight into MHD turbulence for cosmic ray transport and grain dynamics.Comment: 12pages, 12 figures, to appear in "Seeing Through the Dust: The Detection of HI and the Exploration of the ISM in Galaxies", R. Taylor, T. Landecker, & A. Willis (eds.), ASP Conference Serie

Origin of Magnetic Field in the Intracluster Medium: Primordial or Astrophysical?

The origin of magnetic fields in clusters of galaxies is still an unsolved problem, which is largely due to our poor understanding of initial seed magnetic fields. If the seed magnetic fields have primordial origins, it is likely that large-scale pervasive magnetic fields were present before the formation of the large-scale structure. On the other hand, if they were ejected from astrophysical bodies, they were highly localized in space at the time of injection. In this paper, using turbulence dynamo models for high magnetic Prandtl number fluids, we find constraints on the seed magnetic fields. The hydrodynamic Reynolds number based on the Spitzer viscosity in the intracluster medium (ICM) is believed to be less than $O(10^2)$, while the magnetic Reynolds number can be much larger than that. In this case, if the seed magnetic fields have primordial origins, they should be stronger than $O(10^{-11})$G, which is very close to the upper limit of $O(10^{-9})$G set by the cosmic microwave background (CMB) observations. On the other hand, if the seed magnetic fields were ejected from astrophysical bodies, any seed magnetic fields stronger than $O(10^{-9})$G can safely magnetize the intracluster medium. Therefore, it is less likely that primordial magnetic fields are the direct origin of present-day magnetic fields in the ICM.Comment: 11 pages, 10 figures, Accepted for publication in the Ap

Alignment of Irregular Grains by Mechanical Torques

We study the alignment of irregular dust grains by mechanical torques due to the drift of grains through the ambient gas. We first calculate mechanical torques (MATs) resulting from specular reflection of gas atoms for seven irregular shapes: one shape of mirror symmetry, three highly irregular shapes (HIS), and three weakly irregular shapes (WIS). We find that the grain with mirror symmetry experiences negligible MATs due to its mirror-symmetry geometry. Three highly irregular shapes can produce strong MATs which exhibit some generic properties as radiative torques, while three weakly irregular shapes produce less efficient MATs. We then study grain alignment by MATs for the different angles between the drift velocity and the ambient magnetic field, for paramagnetic and superparamagnetic grains assuming efficient internal relaxation. We find that for HIS grains, MATs can align subsonically drifting grains in the same way as radiative torques, with low-J and high-J attractors. For supersonic drift, MATs can align grains with low-J and high-J attractors, analogous to radiative alignment by anisotropic radiation. We also show that the joint action of MATs and magnetic torques in grains with iron inclusions can lead to perfect MAT alignment. Our results point out the potential importance of MAT alignment for HIS grains predicted by the analytical model of Lazarian \& Hoang (2007b), although more theoretical and observational studies are required due to uncertainty in the shape of interstellar grains. We outline astrophysical environments where MAT alignment is potentially important.Comment: 18 pages, 11 figures, accepted to Astrophysical Journa