Kandaswamy Subramanian

Astrophysical magnetic fields and nonlinear dynamo theory

The invention concerns a new process for the production of 2-alkoxy-4-propen-1-yl phenols of the formula (I), in which R represents the methyl or ethyl radical wherein 2-alkoxy phenols of the formula (II), in which R is as defined above, are initially condensed with propionaldehyde in the presence of acid catalysts, and the resulting condensation product is subsequently split by heating in the presence of a basic catalyst to form the phenols of formula I.

Evolving turbulence and magnetic fields in galaxy clusters

We discuss, using simple analytical models and magnetohydrodynamic (MHD) simulations, the origin and parameters of turbulence and magnetic fields in galaxy clusters. Any pre-existing tangled magnetic field must decay in a few hundred million years by generating gas motions even if the electric conductivity of the intracluster gas is high. We argue that turbulent motions can be maintained in the intracluster gas and its dynamo action can prevent such a decay and amplify a random seed magnetic field by a net factor of typically 104 in 5 Gyr. Three physically distinct regimes can be identified in the evolution of turbulence and magnetic field in galaxy clusters. First, the fluctuation dynamo will produce microgauss (μG)-strong, random magnetic fields during the epoch of cluster formation and major mergers. At this stage pervasive turbulent flows with rms velocity of about 300 km s -1 can be maintained at scales of 100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30 kpc and average strength of 2 μG. Secondly, turbulence will decay after the end of the major merger epoch; we discuss the dynamics of the decaying turbulence and the behaviour of magnetic field in it. Magnetic field and turbulent speed undergo a power-law decay, decreasing by a factor of 2 during this stage, whereas their scales increase by about the same factor. Thirdly, smaller-mass subclusters and cluster galaxies will produce turbulent wakes where magnetic fields will be generated as well. Although the wakes plausibly occupy only a small fraction of the cluster volume, we show that their area-covering factor can be close to unity, and thus they can produce some of the signatures of turbulence along virtually all lines of sight. The latter could potentially allow one to reconcile the possibility of turbulence with ordered filamentary gas structures, as in the Perseus cluster. The turbulent speeds and magnetic fields in the wakes are estimated to be of the order of 300 km s -1 and 2 μG, respectively, whereas the turbulent scales are of the order of 200 kpc for wakes behind subclusters of a mass 3 x 10 13 M ⊙ and about 10 kpc in the galactic wakes. Magnetic field in the wakes is intermittent and has the scale of about 30 and 1 kpc in the subcluster and galactic wakes, respectively. Random Faraday rotation measure is estimated to be typically 100-200 rad m -2 , in agreement with observations. We predict detectable polarization of synchrotron emission from cluster radio haloes at wavelengths 3-6 cm, if observed at sufficiently high resolution.

The Structure of Dark Matter Halos in Hierarchical Clustering Theories

During hierarchical clustering, smaller masses generally collapse earlier than larger masses and so are denser on the average. The core of a small-mass halo could be dense enough to resist disruption and survive undigested when it is incorporated into a larger object. We explore the possibility that a nested sequence of undigested cores in the center of the halo that have survived the hierarchical, inhomogeneous collapse to form larger and larger objects determines the halo structure in the inner regions. For a flat universe with P(k) ∝ kn, scaling arguments then suggest that the core density profile is ρ ∝ r-α, with α = (9 + 3n)/(5 + n). For any n < 1, the signature of undigested cores is a core density profile shallower than ρ ∝ 1/r2 and dependent on the power spectrum. For typical objects formed from a cold dark matter (CDM)-like power spectrum, the effective value of n is close to -2, and thus α could typically be near 1, the Navarro, Frenk, & White (NFW) value. Velocity dispersions should also decrease with decreasing radius within the core. However, whether such behavior holds depends on detailed dynamics. We first examine the dynamics using a fluid approach to the self-similar collapse solutions for the dark matter phase-space density, including the effect of velocity dispersions. We highlight the importance of tangential velocity dispersions to obtain density profiles shallower than 1/r2 in the core regions. If tangential velocity dispersions in the core are constrained to be less than the radial dispersion, a cuspy core density profile shallower than 1/r cannot hold in self-similar collapse. We then look at the profiles of the outer halos in low-density cosmological models in which the total halo mass is convergent. We find a limiting r-4 outer profile for the open case and a limiting outer profile for the Λ-dominated case, which approaches the form [1 - (r/λ)-3]1/2, where 3 is the logarithmic slope of the initial density profile. Finally, we analyze a suite of dark halo density and velocity dispersion profiles obtained in cosmological N-body simulations of models with n = 0, -1, and -2. The core-density profiles show considerable scatter in their properties, but nevertheless do appear to reflect a memory of the initial power spectrum, with steeper initial spectra producing flatter core profiles. These results apply as well for low-density cosmological models (Ωmatter = 0.2-0.3), since high-density cores were formed early, where Ωmatter ≈ 1.

Cosmic ray transport in galaxy clusters: implications for radio halos, gamma-ray signatures, and cool core heating

We investigate the interplay of cosmic ray (CR) propagation and advection in galaxy clusters. Propagation in form of CR diffusion and streaming tends to drive the CR radial profiles towards being flat, with equal CR number density everywhere. Advection of CR by the turbulent gas motions tends to produce centrally enhanced profiles. We assume that the CR streaming velocity is of the order of the sound velocity. This is motivated by plasma physical arguments. The CR streaming is then usually larger than typical advection velocities and becomes comparable or lower than this only for periods with trans- and super-sonic cluster turbulence. As a consequence a bimodality of the CR spatial distribution results. Strongly turbulent, merging clusters should have a more centrally concentrated CR energy density profile with respect to relaxed ones with very subsonic turbulence. This translates into a bimodality of the expected diffuse radio and gamma-ray emission of clusters, since more centrally concentrated CR will find higher target densities for hadronic CR proton interactions, higher plasma wave energy densities for CR electron and proton re-acceleration, and stronger magnetic fields. Thus, the observed bimodality of cluster radio halos appears to be a natural consequence of the interplay of CR transport processes, independent of the model of radio halo formation, be it hadronic interactions of CR protons or re-acceleration of low-energy CR electrons. Energy dependence of the CR propagation should lead to spectral steepening of dying radio halos. Furthermore, we show that the interplay of CR diffusion with advection implies first order CR re-acceleration in the pressure-stratified atmospheres of galaxy clusters. Finally, we argue that CR streaming could be important in turbulent cool cores of galaxy clusters since it heats preferentially the central gas with highest cooling rate.

Galactic dynamo and helicity losses through fountain flow

Aims. Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. Methods. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic α-effect is explored. Results. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.

Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

Kinematic α-effect in isotropic turbulence simulations

Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force.

MAGNETIC HELICITY DENSITY AND ITS FLUX IN WEAKLY INHOMOGENEOUS TURBULENCE

A gauge-invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small-scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge-independent fashion, which was not possible earlier. This evolution equation is governed by local sources (owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed.

Minimal tau approximation and simulations of the alpha effect

The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxat ion of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxat ion time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxat ion time is positive and, in units of the turnover time at the f orcing wavenumber, it is of the order of unity. It is quenched by the magnetic field - roughly independently of the magnetic Reynol ds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the flow.

Nonlinear Current Helicity Fluxes in Turbulent Dynamos and Alpha Quenching

Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e., intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.