Nonlinear mean-field dynamo and prediction of solar activity

We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations.Comment: 15 pages, 6 figures, jpp.cls, final versio

The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journa

RXTE and ASCA Constraints on Non-thermal Emission from the A2256 Galaxy Cluster

An 8.3 hour observation of the Abell 2256 galaxy cluster using the Rossi X-ray Timing Explorer proportional counter array produced a high quality spectrum in the 2 - 30 keV range. Joint fitting with the 0.7 - 11 keV spectrum obtained with the Advanced Satellite for Astrophysics and Cosmology gas imaging spectrometer gives an upperlimit of 2.3x10^-7 photons/cm^2/sec/keV for non-thermal emission at 30 keV. This yields a lower limit to the mean magnetic field of 0.36 micro Gauss (uG) and an upperlimit of 1.8x10^-13 ergs/cm^3 for the cosmic-ray electron energy density. The resulting lower limit to the central magnetic field is ~1 - 3 uG While a magnetic field of ~0.1 - 0.2 uG can be created by galaxy wakes, a magnetic field of several uG is usually associated with a cooling flow or, as in the case of the Coma cluster, a subcluster merger. However, for A2256, the evidence for a merger is weak and the main cluster shows no evidence of a cooling flow. Thus, there is presently no satisfactory hypothesis for the origin of an average cluster magnetic field as high as >0.36 uG in the A2256 cluster.Comment: 8 pages, Astrophysical Journal (in press

Memory Effects in Turbulent Dynamo: Generation and Propagation of Large Scale Magnetic Field

We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the growth rate several times compared to the conventional gradient transport expression. Moreover, the integral turbulent transport term leads to a large decrease of the speed of magnetic front propagation.Comment: 13 pages, 2 figure

Reconnection in a Weakly Stochastic Field

We examine the effect of weak, small scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows, and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich and Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find that the lower limit for the reconnection speed is the Alfven speed times the Lundquist number to the power (-3/16). The upper limit on the reconnection speed is typically a large fraction of Alfven speed. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as Lundquist number to the power (-2/5) and the thickness of the current sheet scales as the Lundquist number to the power (-3/5). A significant fraction of the magnetic energy goes into high frequency Alfven waves. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and Solar dynamos are generically fast, i.e. do not depend on the plasma resistivity.Comment: Extended version accepted to ApJ, 44pages, 2 figure

Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 6-9 \times 10^{-16}$, for a magnetic field of $B_0 \sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \approx -1.4 \times 10^{-16}$. These values are more than $\sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 \sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.Comment: 9 page