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

Ideal kink instability of a magnetic loop equilibrium

The force-free coronal loop model by Titov & D\'emoulin (1999} is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength ($m=1$) mode grows for average twists \Phi\ga3.5\pi (at a loop aspect ratio of $\approx$ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increases. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field, which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.Comment: Astron. Astrophys. Lett., accepte

High-Lundquist Number Scaling in Three-Dimensional Simulations of Parker's Model of Coronal Heating

Parker's model is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit, the coronal heating rate obtained so far is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis as well as 2D simulations. In the same limit the average magnetic energy built up by the random footpoint motion tends to have a much weaker dependence on the Lundquist number than that in the 2D simulations, due to the formation of strong current layers and subsequent disruption when the equilibrium becomes unstable. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly.Comment: Accepted for publication in Astrophysical Journa

Influence of the definition of dissipative events on their statistics

A convenient and widely used way to study the turbulent plasma in the solar corona is to do statistics of properties of events (or structures), associated with flares, that can be found in observations or in numerical simulations. Numerous papers have followed such a methodology, using different definitions of an event, but the reasons behind the choice of a particular definition (and not another one) is very rarely discussed. We give here a comprehensive set of possible event definitions starting from a one-dimensional data set such as a time-series of energy dissipation. Each definition is then applied to a time-series of energy dissipation issued from simulations of a shell-model of magnetohydrodynamic turbulence as defined in Giuliani and Carbone (1998), or from a new model of coupled shell-models designed to represent a magnetic loop in the solar corona. We obtain distributions of the peak dissipation power, total energy, duration and waiting-time associated to each definition. These distributions are then investigated and compared, and the influence of the definition of an event on statistics is discussed. In particular, power-law distributions are more likely to appear when using a threshold. The sensitivity of the distributions to the definition of an event seems also to be weaker for events found in a highly intermittent time series. Some implications on statistical results obtained from observations are discussed.Comment: 8 pages, 13 figures. Submitted to Astronomy&Astrophysic

Structures in magnetohydrodynamic turbulence: detection and scaling

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D) magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536^3 points, and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X-point configuration embedded in 3D, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8,000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with MHD. We suggest that this range can be governed by turbulence dynamics as opposed to criticality, and propose an interpretation of intermittency in terms of propagation of local instabilities.Comment: 17 pages, 9 figures, 5 table

Sex attribution, gender identity and quality of life in disorders of sex development due to 45,X/46,XY mosaicism: methods for clinical and psychosocial assessment.

The choice of sex in newborns with genital ambiguity is challenging. Information concerning the satisfaction of subjects with disorders of sex development from childhood to adulthood is required in order to address sex attribution policies. This study focuses on the methods that enable clinicians to investigate the alignment of phenotypes with gender identity and quality of life in people with disorders of this kind. These methods are presented as tools for studying a cohort of ten subjects with 45,X/46,XY mosaicism examined between 1985 and 2014 in the Department of Pediatric Endocrinology, Regina Margherita Children's Hospital, Turin: five children and five young adults, four reared as females and six as males. Clinical outcome was assessed by means of a clinical scoring system considering height, genital appearance, gonads and pubertal development. The Gender Identity Questionnaire for Children and the World Health Organization Quality of Life assessment were adopted. The four male children strongly identified with their assigned sex: male attribution was satisfactory until pubertal age. In young adults the clinical scores ranged between 55-65% for both genders. In the young male, the reduced sexual activity and the poor body image perception strongly affected his quality of life. The clinical scores of the two young female adults (60% for both) were not balanced with their quality of life scores (87.5% and 68.75% respectively): individual traits and social-familial context should be investigated in order to explain these differences. Clinical and psychosocial assessment in people with disorders of sex development is mandatory in order to plan care procedures; a detailed analysis requires adequate tools. Clinical scoring system, Gender Identity Questionnaire for Children and World Health Organization Quality of Life assessment can be used to investigate the alignment of physical phenotype with gender identity and quality of life

Coronal Heating, Weak MHD Turbulence and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity $B_0$, which depends on the spectral index of total energy for given loop parameters, must vary from $B_0^{3/2}$ for weak fields to $B_0^{2}$ for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet Sun coronal energy losses.Comment: 4 pages, 5 figures, uses emulateapj, complies with published versio