How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?

The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measurements are often due to measurement errors and finite nonmagnetic forces inconsistent as a boundary for a force-free field in the corona. In order to deal with these uncertainties, we developed two improvements: 1.) Preprocessing of the surface measurements in order to make them compatible with a force-free field 2.) The new code keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which have to be optimized for use with data from SDO/HMI. Within this work we describe the corresponding analysis method and evaluate the force-free equilibria by means of how well force-freeness and solenoidal conditions are fulfilled, the angle between magnetic field and electric current and by comparing projections of magnetic field lines with coronal images from SDO/AIA. We also compute the available free magnetic energy and discuss the potential influence of control parameters.Comment: 17 Pages, 6 Figures, Sol. Phys., accepte

Thin accretion disc with a corona in a central magnetic field

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona.Comment: Accepted for publication in Astrophysics & Space Scienc

Comment on "Resolving the 180-deg Ambiguity in Solar Vector Magnetic Field Data: Evaluating the Effects of Noise, Spatial Resolution, and Method Assumptions"

In a recent paper, Leka at al. (Solar Phys. 260, 83, 2009)constructed a synthetic vector magnetogram representing a three-dimensional magnetic structure defined only within a fraction of an arcsec in height. They rebinned the magnetogram to simulate conditions of limited spatial resolution and then compared the results of various azimuth disambiguation methods on the resampled data. Methods relying on the physical calculation of potential and/or non-potential magnetic fields failed in nearly the same, extended parts of the field of view and Leka et al. (2009) attributed these failures to the limited spatial resolution. This study shows that the failure of these methods is not due to the limited spatial resolution but due to the narrowly defined test data. Such narrow magnetic structures are not realistic in the real Sun. Physics-based disambiguation methods, adapted for solar magnetic fields extending to infinity, are not designed to handle such data; hence, they could only fail this test. I demonstrate how an appropriate limited-resolution disambiguation test can be performed by constructing a synthetic vector magnetogram very similar to that of Leka et al. (2009) but representing a structure defined in the semi-infinite space above the solar photosphere. For this magnetogram I find that even a simple potential-field disambiguation method manages to resolve the ambiguity very successfully, regardless of limited spatial resolution. Therefore, despite the conclusions of Leka et al. (2009), a proper limited-spatial-resolution test of azimuth disambiguation methods is yet to be performed in order to identify the best ideas and algorithms.Comment: Solar Physics, in press (19 pp., 5 figures, 2 tables

Nonlinear force-free reconstruction of the global solar magnetic field: methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday's equation, give rise to a respective normal field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modelled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition - the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic

Flat galaxies with dark matter halos - existence and stability

We consider a model for a flat, disk-like galaxy surrounded by a halo of dark matter, namely a Vlasov-Poisson type system with two particle species, the stars which are restricted to the galactic plane and the dark matter particles. These constituents interact only through the gravitational potential which stars and dark matter create collectively. Using a variational approach we prove the existence of steady state solutions and their nonlinear stability under suitably restricted perturbations.Comment: 39 page

Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?

The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field upward from underlying vector boundary data. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere, and unfortunately these data do not fulfill the force-free condition. We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be self-consistently applied. To this end, we have developed a minimization procedure that yields a more chromosphere-like field, using the measured photospheric field vectors as input. The procedure includes force-free consistency integrals, spatial smoothing, and -- newly included in the version presented here -- an improved match to the field direction as inferred from fibrils as can be observed in, e.g., chromospheric H$\alpha$ images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. The proposed preprocessing method allows us to approximate the chromospheric vector field to within a few degrees and the free energy in the coronal field to within one percent.Comment: 22 pages, 6 Figur

Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features

Locating current sheets in the solar corona

Current sheets are essential for energy dissipation in the solar corona, in particular by enabling magnetic reconnection. Unfortunately, sufficiently thin current sheets cannot be resolved observationally and the theory of their formation is an unresolved issue as well. We consider two predictors of coronal current concentrations, both based on geometrical or even topological properties of a force free coronal magnetic field. First, there are separatrices related to magnetic nulls. Through separatrices the magnetic connectivity changes discontinuously. Coronal magnetic nulls are, however, very rare. At second, inspired by the concept of generalized magnetic reconnection without nulls, quasi-separatrix layers (QSL) were suggested. Through QSL the magnetic connectivity changes continuously, though strongly. The strength of the connectivity change can be quantified by measuring the squashing of the flux tubes which connect the magnetically conjugated photospheres. We verify the QSL and separatrix concepts by comparing the sites of magnetic nulls and enhanced squashing with the location of current concentrations in the corona. Due to the known difficulties of their direct observation we simulated the coronal current sheets by numerically calculating the response of the corona to energy input from the photosphere heating a simultaneously observed EUV Bright Point. We did not find coronal current sheets not at the separatrices but at several QSL locations. The reason is that although the geometrical properties of force free extrapolated magnetic fields can indeed, hint at possible current concentrations, a necessary condition for current sheet formation is the local energy input into the corona

Self-gravitating Brownian particles in two dimensions: the case of N=2 particles

We study the motion of N=2 overdamped Brownian particles in gravitational interaction in a space of dimension d=2. This is equivalent to the simplified motion of two biological entities interacting via chemotaxis when time delay and degradation of the chemical are ignored. This problem also bears some similarities with the stochastic motion of two point vortices in viscous hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We analytically obtain the density probability of finding the particles at a distance r from each other at time t. We also determine the probability that the particles have coalesced and formed a Dirac peak at time t (i.e. the probability that the reduced particle has reached r=0 at time t). Finally, we investigate the variance of the distribution and discuss the proper form of the virial theorem for this system. The reduced particle has a normal diffusion behaviour for small times with a gravity-modified diffusion coefficient =r_0^2+(4k_B/\xi\mu)(T-T_*)t, where k_BT_{*}=Gm_1m_2/2 is a critical temperature, and an anomalous diffusion for large times ~t^(1-T_*/T). As a by-product, our solution also describes the growth of the Dirac peak (condensate) that forms in the post-collapse regime of the Smoluchowski-Poisson system (or Keller-Segel model) for T<T_c=GMm/(4k_B). We find that the saturation of the mass of the condensate to the total mass is algebraic in an infinite domain and exponential in a bounded domain.Comment: Revised version (20/5/2010) accepted for publication in EPJ

Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics

Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy $S_{1/2}$ for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.Comment: 15 pages, RevTe