3D electron density distributions in the solar corona during solar minima: assessment for more realistic solar wind modeling

Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996-1997 and 2008-2010), devoid of coronal mass ejections. The goals are to derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method and to compare the results between the two solar minima and with two magnetohydrodynamic models. First, we confirm that the values of the density distribution in thermodynamic models are more realistic than in polytropic ones. The tomography provides more accurate distributions in the polar regions, and we find that the density in tomographic and thermodynamic solutions varies with the solar cycle in both polar and equatorial regions. Second, we find that the highest-density structures do not always correspond to the predicted large-scale heliospheric current sheet or its helmet streamer but can follow the locations of pseudo-streamers. We deduce that tomography offers reliable density distributions in the corona, reproducing the slow time evolution of coronal structures, without prior knowledge of the coronal magnetic field over a full rotation. Finally, we suggest that the highest-density structures show a differential rotation well above the surface depending on how they are magnetically connected to the surface. Such valuable information on the rotation of large-scale structures could help to connect the sources of the solar wind to their in situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus.Comment: 23 pages, 9 figure

Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

The Discrete radon transform: A more efficient approach to image reconstruction

The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,π). In practice, however, we pre-filter discrete projections take

3D Coronal Density Reconstruction and Retrieving the Magnetic Field Structure during Solar Minimum

Measurement of the coronal magnetic field is a crucial ingredient in understanding the nature of solar coronal phenomena at all scales. We employed STEREO/COR1 data obtained during a deep minimum of solar activity in February 2008 (Carrington rotation CR 2066) to retrieve and analyze the three-dimensional (3D) coronal electron density in the range of heights from 1.5 to 4 Rsun using a tomography method. With this, we qualitatively deduced structures of the coronal magnetic field. The 3D electron density analysis is complemented by the 3D STEREO/EUVI emissivity in the 195 A band obtained by tomography for the same CR. A global 3D MHD model of the solar corona was used to relate the reconstructed 3D density and emissivity to open/closed magnetic field structures. We show that the density maximum locations can serve as an indicator of current sheet position, while the locations of the density gradient maximum can be a reliable indicator of coronal hole boundaries. We find that the magnetic field configuration during CR 2066 has a tendency to become radially open at heliocentric distances greater than 2.5 Rsun. We also find that the potential field model with a fixed source surface (PFSS) is inconsistent with the boundaries between the regions with open and closed magnetic field structures. This indicates that the assumption of the potential nature of the coronal global magnetic field is not satisfied even during the deep solar minimum. Results of our 3D density reconstruction will help to constrain solar coronal field models and test the accuracy of the magnetic field approximations for coronal modeling.Comment: Published in "Solar Physics

A range description for the planar circular Radon transform

The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. Range conditions include the recently found set of moment type conditions, which happens to be incomplete, as well as the rest of conditions that have less standard form. In order to explain the procedure better, a similar (non-standard) treatment of the range conditions is described first for the usual Radon transform on the plane.Comment: submitted for publicatio