Gradient expansion, curvature perturbations and magnetized plasmas

The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and pre-decoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, are derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate Universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.Comment: 40 pages, no figure

Relation of Astrophysical Turbulence and Magnetic Reconnection

Astrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHD turbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink, Lazarian & Vishniac 2011 to show that the expressions of fast magnetic reconnection in Lazarian & Vishniac 1999 can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of flux-freezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnection diffusion as it based on reconnection of magnetic field lines. The reconnection diffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.Comment: 8 pages, 4 figures, Physics of Plasma

Parameter dependence of magnetized CMB observables

Pre-decoupling magnetic fields affect the scalar modes of the geometry and produce observable effects which can be constrained also through the use of current (as opposed to forthcoming) data stemming from the Cosmic Microwave Background observations. The dependence of the temperature and polarization angular power spectra upon the parameters of an ambient magnetic field is encoded in the scaling properties of a set of basic integrals whose derivation is simplified in the limit of small angular scales. The magnetically-induced distortions patterns of the relevant observables can be computed analytically by employing scaling considerations which are corroborated by numerical results.Comment: 48 pages, 11 figures; corrected minor typos; discussions added; to appear in Physical Revie

Magneto-acoustic wave energy from numerical simulations of an observed sunspot umbra

We aim at reproducing the height dependence of sunspot wave signatures obtained from spectropolarimetric observations through 3D MHD numerical simulations. A magneto-static sunspot model based on the properties of the observed sunspot is constructed and perturbed at the photosphere introducing the fluctuations measured with the \SiI\ $\lambda$ 10827 \AA\ line. The results of the simulations are compared with the oscillations observed simultaneously at different heights from the \HeI\ $\lambda$ 10830 \AA\ line, the \CaIIH\ core and the \FeI\ blends in the wings of the \CaIIH\ line. The simulations show a remarkable agreement with the observations. They reproduce the velocity maps and power spectra at the formation heights of the observed lines, as well as the phase and amplification spectra between several pair of lines. We find that the stronger shocks at the chromosphere are accompanied with a delay between the observed signal and the simulated one at the corresponding height, indicating that shocks shift the formation height of the chromospheric lines to higher layers. Since the simulated wave propagation matches very well the properties of the observed one, we are able to use the numerical calculations to quantify the energy contribution of the magneto-acoustic waves to the chromospheric heating in sunspots. Our findings indicate that the energy supplied by these waves is too low to balance the chromospheric radiative losses. The energy contained at the formation height of the lowermost \SiI\ $\lambda$ 10827 \AA\ line in the form of slow magneto-acoustic waves is already insufficient to heat the higher layers, and the acoustic energy which reaches the chromosphere is around 3-9 times lower than the required amount of energy. The contribution of the magnetic energy is even lower.Comment: Accepted for publication in The Astrophysical Journa

Faraday rotation, stochastic magnetic fields and CMB maps

The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $\Lambda$CDM paradigm (m$\Lambda$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal m$\Lambda$CDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite.Comment: 53 pages, 15 included figure

Mathematical models of magnetospheric convection and its coupling to the ionosphere

Mathematical models of magnetospheric convection and its coupling to ionospher

Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.Comment: added references, revise

Cosmic polarimetry in magnetoactive plasmas

Polarimetry of the Cosmic Microwave Background (CMB) represents one of the possible diagnostics aimed at testing large-scale magnetism at the epoch of the photon decoupling. The propagation of electromagnetic disturbances in a magnetized plasma leads naturally to a B-mode polarization whose angular power spectrum is hereby computed both analytically and numerically. Combined analyses of all the publicly available data on the B-mode polarization are presented, for the first time, in the light of the magnetized $\Lambda$CDM scenario. Novel constraints on pre-equality magnetism are also derived in view of the current and expected sensitivities to the B-mode polarization.Comment: 34 pages, 13 figure

Structural Invariance of Sunspot Umbrae Over the Solar Cycle: 1993-2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the NASA/NSO spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for a confirming observation of umbral limb-darkening. Log-normal fits to the observed size distribution confirm that the size spectrum shape does not vary with time. The intensity-magnetic flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as testified by the invariant size-magnetic field relationship, as well as the mean size (i.e. strength) of sunspot umbrae do not significantly depend on solar cycle phase.Comment: 17 pages, 6 figures. Published in Solar Physic