A Time-Evolving 3D Method Dedicated to the Reconstruction of Solar plumes and Results Using Extreme Ultra-Violet Data

arXiv:0802.0113v1 [astro-ph] 1 Feb 2008 Solar Physics DOI: 10.1007/•••••-•••-•••-••••-• A Time-Evolving 3D Method Dedicated to the Reconstruction of Solar Plumes and Results Using Extreme Ultra-Violet Data Nicolas Barbey∗† · Frédéric Auchère∗· Thomas Rodet† · Jean -Claude Vial∗ Received: 9 May 2007 / Accepted: 24 January 2008 c⃝Springer •••• Abstract An important issue in the tomographic reconstruction of the solar poles is the relatively rapid evolution of the polar plumes. We demonstrate that it is possible to take into account this temporal evolution in the reconstruction. The difficulty of this problem comes from the fact that we want a 4D reconstruction (three spatial dimensions plus time) while we only have 3D data (2D images plus time). To overcome this difficulty, we introduce a model that describes polar plumes as stationary objects whose intensity varies homogeneously with time. This assumption can be physically justified if one accepts the stability of the magnetic structure. This model leads to a bilinear inverse problem. We describe how to extend linear inversion methods to these kinds of problems. Studies of simulations show the reliability of our method. Results for SOHO/EIT data show that we are able to estimate the temporal evolution of polar plumes in order to improve the reconstruction of the solar poles from only one point of view. We expect further improvements from STEREO/EUVI data when the two probes will be separated by about 60◦. 1. Introduction A method known as solar rotational tomography has been used to retrieve the 3D geometry of the solar corona (Frazin 2000; Frazin and Janzen 2002). This method assumes the stability of the structures during the time necessary to acquire the data. Since we generally have only one point of view at our disposal, about 15 days are required to have data for half a solar rotation at the poles. Here, we focus our study on solar polar plumes. They are bright, radial, coronal ray structures located at the solar poles in regions of open magnetic field. The study of plumes is of great interest since it may be the key to the understanding of the acceleration of the fast component of the solar wind (Teriaca et al., 2003). However the three- dimensional shape of these structures is poorly known and different assumptions have ∗Institut d’Astrophysique Spatiale, Université Paris-Sud, Orsay, France email: nicolas.barbey@ias.u-psud.fr, frederic.auchere@ias.u-psud.fr, jean-claude.vial@ias.u-psud.fr †Laboratoire des Signaux et Syst`emes, Supéléc, Gif-sur-Yvette, France email: nicolas.barbey@lss.supelec.fr, thomas.rodet@lss.supelec.fr N. Barbey et al. been made, e.g. Gabriel et al., 2005; Llebaria, Saez, and Lamy, 2002. The plumes are known to evolve with a characteristic time of approximately 24 hours on spatial scales typical of Extreme ultra-violet Imaging Telescope (SOHO/EIT) data (2400 km) (DeForest, Lamy, and Llebaria, 2001). Consequently the stability assumption made in rotational tomography fails. Fortunately, the Solar TErestrial RElations Observatory (STEREO) mission consists of two identical spacecraft STEREOA and STEREOB which take pictures of the Sun from two different points of view. With the SOHO mission still operating, this results in three,simultaneous points of view. Three viewpoints help to improve the reconstruction of the plumes, but they are still not enough to use standard tomographic algorithms. The problem is underdetermined and consequently one has to add a priori information in order to overcome the lack of information. This leads to challenging and innovative signal analysis problems. There are different ways to deal with underdetermination depending on the kind of object to be reconstructed. Interestingly the field of medical imaging faces the same kind of issues. In cardiac reconstruction, authors make use of the motion periodicity in association with a high redundancy of the data (Grass et al., 2003; Kachelriess, Ulzheimer, and Kalender, 2000). If one can model the motion as an affine transfor- mation, and if one assumes that we know this transformation, one can obtain an analytic solution (Ritchie et al., 1996; Roux et al., 2004). In solar tomography, the proposed innovative approaches involve the use of ad- ditional data such as magnetic-field measurements in the photosphere (Wiegelmann and Inhester, 2003) or data fusion (Frazin and Kamalabadi, 2005). Attempts have been made by Frazin et al. (2005) to treat temporal evolution using Kalman filtering. Since polar plumes have apparently a local, rapid, and aperiodic temporal evo- lution, we developed as in the previously referenced work, a model based on the specifics of the object we intend to reconstruct (preliminary results can be found in Barbey et al., (2007). Plumes have an intensity which evolves rapidly with time, but their position can be considered as constant. This hypothesis is confirmed by previous studies of the plumes such as DeForest, Lamy, and Llebaria (2001). The model is made u

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