Turbulent Coronal Heating Mechanisms: Coupling of Dynamics and Thermodynamics

Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets where energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a system where energy is deposited at unresolved small-scales. Methods. Fully compressible three-dimensional magnetohydrodynamic simulations are carried out to understand the thermodynamics of coronal heating in the magnetically confined solar corona. Results. We show that temperature is highly structured at scales below observational resolution and nonhomogeneously distributed so that only a fraction of the coronal mass and volume gets heated at each time. Conclusions. This is a multi-thermal system where hotter and cooler plasma strands are found one next to the other also at sub-resolution scales and exhibit a temporal dynamics.Comment: A&A Letter, in pres

Heating of coronal loops: weak MHD turbulence and scaling laws

To understand the nonlinear dynamics of the Parker scenario for coronal heating, long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out. A loop is modeled as a box extended along the direction of the strong magnetic field $B_0$ in which the system is embedded. At the top and bottom plates, which represent the photosphere, velocity fields mimicking photospheric motions are imposed. We show that the nonlinear dynamics is described by different regimes of MHD anisotropic turbulence, with spectra characterized by intertial range power laws whose indexes range from Kolmogorov-like values ($\sim 5/3$) up to $\sim 3$. We briefly describe the bearing for coronal heating rates.Comment: 8 pages, 4 figure

Nonlinear Dynamics of the Parker Scenario for Coronal Heating

The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled, nevertheless current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions ($\sim 1,000 km$) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive ``bursty'' heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine bright in these wavelengths with little evidence of entangled features. The different regimes of weak and strong MHD turbulence that develop, and their influence on coronal heating scalings, are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in {\it stronger loop fields} and lead to {\it larger heating rates} than in weak field regions.Comment: 22 pages, 18 figures, uses emulateapj, for mpeg file associated to Figure 17e see (temporarily) http://www.df.unipi.it/~rappazzo/arxiv/jfl.mpg, ApJ, in pres

Expression of SPANX proteins in normal prostatic tissue and in prostate cancer

The sperm protein associated with the nucleus in the X chromosome (SPANX) gene family encodes for proteins that are not only expressed in germ cells, but also in a number of tumors. In addition, SPANX genes map in an interval of the X chromosome (namely, Xq27), which has been found to be associated with familial prostate cancer by linkage analysis. The aim of this study was therefore to evaluate SPANX protein expression in normal prostate tissues and in prostate carcinoma. For this purpose, formalin-fixed and paraffin-embedded sections obtained from 15 normal (at autopsy) donors and 12 men with prostate cancer were analyzed by immunohistochemistry. About 40% of both normal and tumor prostate samples resulted SPANX positive. Signals were exclusively within the nucleus in normal prostate cells, whereas both nuclear and cytoplasmic positivity was observed in tumor cells. In conclusion, these findings showed that SPANX genes are expressed in both normal and tumor prostate gland, but the latter showed a peculiar cytoplasmic staining positivity. This suggests a possible association between SPANX over expression and prostate cancer development. Additional studies are needed to corroborate this hypothesis

Magnetic moment non-conservation in magnetohydrodynamic turbulence models

The fundamental assumptions of the adiabatic theory do not apply in presence of sharp field gradients as well as in presence of well developed magnetohydrodynamic turbulence. For this reason in such conditions the magnetic moment $\mu$ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width $\Delta \mu$ (defined as the half peak-to-peak difference in the particle magnetic moment) and the bounce frequency $\omega_b$. We perform test-particle simulations to investigate magnetic moment behavior when resonances overlapping occurs and during the interaction of a ring-beam particle distribution with a broad-band slab spectrum. We find that magnetic moment dynamics is strictly related to pitch angle $\alpha$ for a low level of magnetic fluctuation, $\delta B/B_0 = (10^{-3}, \, 10^{-2})$, where $B_0$ is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function $f(\alpha)$. This is a transient regime during which magnetic moment distribution $f(\mu)$ exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance $$ grows linearly in time as in normal diffusion. With strong fluctuations $f(\alpha)$ isotropizes completely, spatial diffusion sets in and $f(\mu)$ behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.Comment: 13 pages, 10 figures, submitted to PR

Spontaneous non-steady magnetic reconnection within the solar environment

This work presents a 2.5-dimensional simulation study of the instability of current-sheets located in a medium with a strong density variation along the current layer. The initial force-free configuration is observed to undergo a two-stage evolution consisting of an abrupt regime transition from a slow to a fast reconnection process leading the system to a final chaotic configuration. Yet, the onset of the fast phase is not determined by the presence of any anomalous enhancement in plasma's local resistivity, but rather is the result of a new mechanism discovered in Lapenta (2008)* and captured only when sufficient resolution is present. Hence, the effects of the global resistivity, the global viscosity and the plasma beta on the overall dynamics are considered. This mechanism allowing the transition from slow to fast reconnection provides a simple but effective model of several processes taking place within the solar atmosphere from the high chromosphere up to the low corona. In fact, the understanding of a spontaneous transition to a self-feeding fast reconnection regime as well as its macroscopic evolution is the first and fundamental step to produce realistic models of all those phenomena requiring fast (and high power) triggering events (* Lapenta G. 2008, Phys. Rev. Lett., 100, 235001).Comment: 29 pages, 10 figure