IUCAA Preprints
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Item Magnetic helicity in stellar dynamos : new numerical experiments(2001-01-04) Axel, Brandenburg; Wolfgang, Dobler; Subramanian, KandaswamyThe theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super-equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of α. For solar parameters, typical magnetic helicity fluxes lie around 1047 Mx2 per cycle.Item Strong mean field dynamos require supercritical helicity fluxes(2006-01-10) Brandenburg, Axel; Subramanian, KandaswamySeveral one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak.Item Minimal tau approximation and simulations of the alpha effect(2005-08-01) Brandenburg, Axel; Subramanian, KandaswamyThe 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 relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic field – roughly independently of the magnetic Reynolds 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.Item Kinetic and magnetic alpha effects in nonlinear dynamo theory(2007-01-19) Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, AxelThe backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small scale magnetic field. These results hold for both steady and time dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in theτ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find α ∝ B−2 0 for delta-correlated forcing, in contrast to the well-known α ∝ B−3 0 behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows.Item Galactic dynamo and helicity losses through fountain flow(2006-01-19) Shukurov, A.; Sokoloff, Dmitry; Subramanian, KandaswamyNonlinear 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.Item Evolving turbulence and magnetic fields in galaxy clusters(2006-01-10) Subramanian, Kandaswamy; Shukurov, A.; Haugen, N. E. L.We discuss, using simple analytical models and 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 tur- bulent 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 typically 10⁴ in 5Gyr. Three physically distinct regimes can be identified in the evolution of turbulence and magnetic field in galaxy clusters. Firstly, the fluctuation dynamo will produce microgauss-strong, random magnetic fields during the epoch of cluster formation and major mergers. At this stage pervasive turbulent flows with r.m.s. velocity of about 300 kms−ᶥ can be maintained at scales 100–200 kpc. The magnetic field is intermittent, has a smaller scale of 20–30 kpc and average strength of 2 G. Secondly, turbulence will decay after the end of the major merger epoch; we discuss the dynamics of the decaying turbulence and the behavior of magnetic field in it. Magnetic field and turbulent speed undergo a power-law decay, decreasing by a factor of two 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 order 300 kms−ᶥ and 2 G, respectively, whereas the turbulent scales are of order 200 kpc for wakes behind subclusters of a mass 3 × 10ᶥᶟM⊙ and about 10 kpc in the galactic wakes. Magnetic field in the wakes is intermittent and has the scale of about 30 kpc and 1 kpc in the subcluster and galactic wakes, respectively. Random Faraday rotation measure is estimated to be typically 100–200 radm−², in agreement with observations. We predict detectable polarization of synchrotron emission from cluster radio halos at wavelengths 3–6 cm, if observed at sufficiently high resolution.Item Astrophysical magnetic fields and nonlinear dynamo theory(2006-01-10) Brandenburg, Axel; Subramanian, KandaswamyThe current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak ‘seed’ magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed.Item Kinematic alpha effect in isotropic turbulence simulations(2008-01) Sur, Sharanya; Brandenburg, Axel; Subramanian, KandaswamyUsing numerical simulations at moderate magnetic Reynolds numbers up to 220 it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha effect and a turbulent diffusivitywhose 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, alpha and turbulent diffusivity are proportional to Rm. Over finite time intervals meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that small-scale dynamo-generated fields do not make a correlated contribution to the mean electromotive force.