Three-dimensional reconstruction of the streamer belt and other large-scale structures of the solar corona. I. Method

International audienceContext: The high spatial resolution, white-light images obtained by the LASCO coronagraphs provide a detailed record of the solar corona over almost a full solar cycle. Their analysis and interpretation poses a formidable challenge for ultimately retrieving the 3-dimensional distribution of electrons in the corona. Aims: Our goal is to implement an efficient forward modeling method capable of generating high-resolution synthetic images of large-scale coronal structures (the streamer belt, isolated streamers, coronal mass ejections) over any time scales (as long as a solar cycle) to be directly compared, both qualitatively and quantitatively, to coronographic images of the corona. Methods: Our model assumes a 3-dimensional distribution of electrons described by analytic functions and represented using the octree compression's techniques. The radiance of the synthetic images is calculated with a ray-tracing algorithm that incorporates the Thomson scattering. A multi-octree generalization of the method allows simulation of the temporal evolution of the structures. We first concentrate on the coronal streamer belt. Starting from photospheric magnetograms, we calculate the position of the neutral line at the source surface (2.5 R_sun) using the potential field source surface model. The plasma sheet forming the belt is centered on the current sheet represented as the radial extension of the neutral line. Its electron density is represented by a parametric function of both the distances to the Sun center and to the current sheet. The parameters are optimized by adjusting the synthetic images to the observations, using either the coronal images or synoptic maps of the corona. The method is then extended to other large-scale coronal structures, polar plumes, and coronal mass ejections. Results: As examples, we present results for the streamer belt observed by LASCO-C2 during two Carrington rotations, CR 1910 and CR 1913, as well as illustrations of future coronographic observations expected from the STEREO and Solar Orbiter missions. The results suggest that our method is sufficient for qualitatively and quantitatively simulating the structures of the solar corona even if some discrepancies can be noticed. A systematic analysis of the LASCO data over almost a full solar cycle will be developed in forthcoming articles