Benjamin D. G. Chandran

Scattering of Energetic Particles by Anisotropic Magnetohydrodynamic Turbulence with a Goldreich-Sridhar Power Spectrum

Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors nearly perpendicular to the background magnetic field, scattering is too weak to provide either the mean-free paths commonly used in Galactic cosmic-ray propagation models or the mean-free paths required for acceleration of cosmic rays at quasiparallel shocks. Where strong pitch-angle scattering occurs, it is due to fluctuations not described by the GS spectrum, such as fluctuations generated by streaming cosmic rays.

Turbulent Heating of Galaxy-Cluster Plasmas

A number of studies suggest that turbulent heating plays an important role in the thermal balance of galaxy-cluster plasmas. In this paper, we construct a model of intracluster plasmas in which radiative cooling is balanced by heating from viscous dissipation of turbulent motions, turbulent diffusion of high-specific-entropy plasma into low-specific-entropy regions, and thermal conduction. We solve for the rms turbulent velocity u by setting Γ + Q + H = R throughout a cluster, where Γ, Q, and H are the heating rates from dissipation of turbulence, turbulent diffusion, and conduction, respectively, and R is the rate of radiative cooling. We account for the effects of buoyancy in our expression for the eddy diffusivity and neglect nonthermal pressure. We take the conductivity to be a fixed fraction (typically one-fifth) of the Spitzer value for a nonmagnetized plasma and the density and temperature to be given by analytical fits to published data. We set the dominant velocity length scale l equal to αr + l0, where α is a constant, r is distance from cluster center, and l0 = 0.5 kpc. For 0.05 0.5, although there are exceptions to this rule. For some values of α, we find that at some locations the heat flux from turbulent diffusion has positive divergence, so that turbulent diffusion locally cools the plasma. Buoyancy inhibits turbulent diffusion of heat in the radial direction to a degree that increases with increasing α. This leads to an increase in the computed value of u relative to models that neglect buoyancy; the magnitude of the increase is moderate for α = 0.5 and large for α > 1.

Confinement and Isotropization of Galactic Cosmic Rays by Molecular-Cloud Magnetic Mirrors When Turbulent Scattering Is Weak

Theoretical studies of magnetohydrodynamic (MHD) turbulence and observations of solar wind —uc- tuations suggest that MHD turbulence in the interstellar medium is anisotropic at small scales, with smooth variations along the background magnetic —eld and sharp variations perpendicular to the back- ground —eld. Turbulence with this anisotropy is inefficient at scattering cosmic rays, and thus the scat- tering rate l may be smaller than has been traditionally assumed in diUusion models of Galactic cosmic-ray propagation, at least for cosmic-ray energies E above 1011¨1012 eV at which self-con—nement is not possible. In this paper, it is shown that Galactic cosmic rays can be eUectively con—ned through magnetic re—ection by molecular clouds, even when turbulent scattering is weak. Elmegreens quasi- fractal model of molecular-cloud structure is used to argue that a typical magnetic —eld line passes through a molecular cloud complex once every D300 pc. Once inside the complex, the —eld line will in most cases be focused into one or more dense clumps in which the magnetic —eld can be much stronger than the average —eld in the intercloud medium (ICM). Cosmic rays following —eld lines into cloud com- plexes are most often magnetically re—ected back into the ICM, since strong-—eld regions act as magnetic mirrors. For a broad range of cosmic-ray energies, a cosmic ray initially following some particular —eld line separates from that —eld line sufficiently slowly that the cosmic ray can be trapped between neigh- boring cloud complexes for long periods of time. The suppression of cosmic-ray diUusion due to mag- netic trapping is calculated in this paper with the use of phenomenological arguments, asymptotic analysis, and Monte Carlo particle simulations. Formulas for the coefficient of diUusion perpendicular to the Galactic disk are derived for several diUerent parameter regimes within the E-l plane. In one of these parameter regimes in which scattering is weak, it is shown that molecular-cloud magnetic mirrors strongly reduce cosmic-ray anisotropy in the ICM, and analytic formulas for the angular harmonics are derived. Subject headings: acceleration of particlescosmic raysISM: cloudsISM: magnetic —elds ¨ turbulence

Magnetic Flux Accumulation at the Galactic Center and Its Implications for the Strength of the Pregalactic Magnetic Field

We study the in—ow of disk gas toward the Galactic center during the lifetime of the Galaxy and its eUect on magnetic —eld lines frozen-in to the interstellar plasma. While compression leads to a large ampli—cation of the ii vertical ˇˇ magnetic —eld (pointing perpendicular to the disk), ambipolar diUusion efficiently removes from the disk magnetic —ux components oriented parallel to the Galactic plane. Turb- ulent interchange motions of nearly parallel vertical —eld lines at the Galactic center enhance the effi- ciency of magnetic reconnection of neighboring regions of oppositely directed vertical —eld. This suggests that the sign of the present-day vertical —eld at the Galactic center is uniform. If the Galactic-center —eld originates in the entrainment of a pregalactic —eld in radially in—owing interstellar plasma, then B 0 observations of the vertical —ux through the central 200 pc of our Galaxy yield a measure of the prega- lactic —eld that depends on the total mass accreted into the central 200 pc during the Galaxys lifetime. If this mass is 3 ) 109 and if the surface density of disk gas is roughly constant over the lifetime of the M _ Galaxy, then G, regardless of the angle of the pregalactic —eld with respect to the Galac- B 0 Z 2 ) 10~7 tic plane. The abundance of mechanisms for radial accretion of disk gas suggests that strong magnetic —elds should be a generic feature of the centers of spiral galaxies. We also note that cosmic-ray con—ne- ment in the strong vertical —eld at the Galactic center is expected to be poor. Subject headings: diUusionGalaxy: centerGalaxy: evolutionMHDISM: magnetic —elds ¨ turbulence

CONVECTION IN GALAXY-CLUSTER PLASMAS DRIVEN BY ACTIVE GALACTIC NUCLEI AND COSMIC-RAY BUOYANCY

Turbulent heating may play an important role in galaxy-cluster plasmas, but if turbulent heating is to balance radiative cooling in a quasi-steady state, some mechanism must regulate the turbulent velocity so that it is neither too large nor too small. This paper explores one possible regulating mechanism associated with an active galactic nucleus at cluster center. A steady-state model for the intracluster medium is presented in which radiative cooling is balanced by a combination of turbulent heating and thermal conduction. The turbulence is generated by convection driven by the buoyancy of cosmic rays produced by a central radio source. The cosmic-ray luminosity is powered by the accretion of intracluster plasma onto a central black hole. The model makes the rather extreme assumption that the cosmic rays and thermal plasma are completely mixed. Although the intracluster medium is convectively unstable near cluster center in the model solutions, the specific entropy of the thermal plasma still increases outward because of the cosmic-ray modification to the stability criterion. The model provides a self-consistent calculation of the turbulent velocity as a function of position but fails to reproduce the steep central density profiles observed in clusters. The principal difficulty is that in order for the fully mixed intracluster medium to become convectively unstable, the cosmic-ray pressure must become comparable to or greater than the thermal pressure within the convective region. The large cosmic ray pressure gradient then provides much of the support against gravity, reducing the thermal pressure gradient near cluster center and decreasing the central plasma density gradient. A more realistic active galactic nucleus (AGN)-feedback model of intracluster turbulence, in which relativistic and thermal plasmas are only partially mixed, may have greater success.

Particle Acceleration by Slow Modes in Strong Compressible Magnetohydrodynamic Turbulence, with Application to Solar Flares

Energetic particles that undergo strong pitch-angle scattering and diffuse through a plasma containing strong compressible MHD turbulence undergo diffusion in momentum space with diffusion coefficient Dp. If the rms turbulent velocity is of the order of the Alfven speed vA, the contribution to Dp from slow-mode eddies is (2p2vA/9l)[ln(lvA/D||) + 2γ - 3], where l is the outer scale of the turbulence, γ 0.577 is Eulers constant, and D|| is the spatial diffusion coefficient of energetic particles, which is assumed to satisfy D|| lvA. The energy spectrum of accelerated particles is derived for this value of Dp, taking into account Coulomb losses and particle escape from the acceleration region with an energy-independent escape time. Slow modes in the D|| lvA limit are an unlikely explanation for electron acceleration in solar flares to energies of 10-100 keV, because for solar flare conditions, the predicted acceleration times are too long, and the predicted energy spectra are too hard. The acceleration mechanism discussed in this paper could in principle explain the relatively hard spectra of gyrosynchrotron-emitting electrons in the 100-5000 keV range, but only if D|| lvA for such particles.

ACCELERATION OF ENERGETIC PARTICLES BY LARGE-SCALE COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE

Fast particles diffusing along magnetic field lines in a turbulent plasma can diffuse through and then return to the same eddy many times before the eddy is randomized in the turbulent flow. This leads to an enhancement of particle acceleration by large-scale compressible turbulence relative to previous estimates in which isotropic particle diffusion is assumed.

Radio Wave Propagation through a Medium Containing Electron Density Fluctuations Described by an Anisotropic Goldreich-Sridhar Spectrum

We study the propagation of radio waves through a medium possessing density fluctuations that are elongated along the ambient magnetic field and described by an anisotropic Goldreich-Sridhar power spectrum. We derive general formulae for the wave phase structure function D, visibility, angular broadening, diffraction pattern length scales, and scintillation timescale for arbitrary distributions of turbulence along the line of sight and specialize these formulae to idealized cases. In general, D (?r)5/3 when the baseline ?r is in the inertial range of the turbulent density spectrum, and D (?r)2 when ?r is in the dissipation range, just as for an isotropic Kolmogorov spectrum of fluctuations. When the density structures that dominate the scattering have an axial ratio R 1 (typically R ~ 103), the axial ratio of the broadened image of a point source in the standard Markov approximation is at most ~R1/2, and this maximum value is obtained in the unrealistic case that the scattering medium is confined to a thin screen in which the magnetic field has a single direction. If the projection of the magnetic field within the screen onto the plane of the sky rotates through an angle ?? along the line of sight from one side of the screen to the other, and if R-1/2 ?? 1, then the axial ratio of the resulting broadened image of a point source is 2(8/3)3/5/?? 3.6/??. The error in this formula increases with ?? but reaches only ~15% when ?? = ?. This indicates that a moderate amount of variation in the direction of the magnetic field along the line of sight dramatically decreases the anisotropy of a broadened image. When R 1, the observed anisotropy will in general be determined by the degree of variation of the field direction along the sight line and not by the degree of density anisotropy. Although this makes it difficult to determine observationally the degree of anisotropy in interstellar density fluctuations, observed anisotropies in broadened images provide general support for anisotropic models of interstellar turbulence. Regions in which the angle ? between the magnetic field and line of sight is small cause enhanced scattering due to the increased coherence of density structures along the line of sight. In the exceedingly rare and probably unrealized case that scattering is dominated by regions in which ? (?r/l)1/3, where l is the outer scale (stirring scale) of the turbulence, D (?r)4/3 for ?r in the inertial range. In a companion paper (Backer & Chandran) we discuss the semiannual modulation in the scintillation time of a nearby pulsar for which the field direction variation along the line of sight is expected to be moderately small.

Rayleigh-Taylor Stability of a Strong Vertical Magnetic Field at the Galactic Center Confined by a Disk Threaded with Horizontal Magnetic Field

Observations of narrow radio-emitting filaments near the Galactic center have been interpreted in previous studies as evidence of a pervasive vertical (i.e., perpendicular to the Galactic plane) milligauss magnetic field in the central ~150 pc of the Galaxy. A simple cylindrically symmetric model for the equilibrium in this central region is proposed in which horizontal (i.e., parallel to the Galactic plane) magnetic fields embedded in an annular band of partially ionized molecular material of radius ~150 pc are wrapped around vertical magnetic fields threading low-density hot plasma. The central vertical magnetic field, which has a pressure that significantly exceeds the thermal pressure of the medium, is confined by the weight of the molecular material. The stability of this equilibrium is studied indirectly by analyzing a uniformly rotating cylinder of infinite extent along the z-axis in cylindrical coordinates (r,θ,z), with low-density plasma and an axial magnetic field at r 150 pc, and a gravitational acceleration g* ∝ r directed in the - direction. Simple profiles are assumed for the density ρ, pressure p, and field strength B, with the sound speed and Alfven speeds ∝r within the dense plasma. The density profile and gravity tend to destabilize the plasma, but the plasma tends to be stabilized by rotation and magnetic tension—since the interface between the high- and low-density plasmas cannot be perturbed without bending either the horizontal or vertical field. Normal modes proportional to e with kz = 0 and m ≠ 0 are studied. Such modes neither bend nor compress the axial field at r < 150 pc but allow compressions of the dense plasma along the azimuthal magnetic field that enhance the destabilizing role of gravity. It is shown analytically that when β = 8πp/B2 is small and the dense plasma is supported against gravity primarily by rotation, the necessary and sufficient condition for stability to kz = 0 modes is |g| < 2|Ω|a, where g = g* - Ω2r is the effective gravity, Ω is the uniform angular velocity, and a is the sound speed in the dense plasma. Since the effective gravity is determined by the degree to which magnetic (and to a lesser degree pressure) forces support the dense plasma, the stability criterion gives an upper limit on the strength of the axial magnetic field, which is ~1 mG for Galactic center parameters.

A Review of the Theory of Incompressible MHD Turbulence

This brief review provides an introduction to key ideas in the theory of incompressible magnetohydrodynamic (MHD) turbulence.