On Analysis of Dual Spacecraft Stereoscopic Observations to Determine the Three-Dimensional Morphology and Plasma Properties of Solar Coronal Flux Tubes
By using two spacecraft equipped with multi-bandpass X-ray telescopes, it is possible to obtain direct 3-dimensional morphology of coronal structures which is essential for understanding the energetics and dynamics of the solar atmosphere. X-ray observations taken only in orbit about the Earth are inadequate to fully resolve the 3-dimensional nature of the solar corona. These Earth-orbit observations produce 2-dimensional images and an appropriate model must be included to derive the 3-dimensional structures from the line-of-sight information. Stereoscopic observations from space will remove this limitation and are needed if we are to improve our knowledge of the 3-dimensional morphology of the corona. Several important points regarding a stereoscopic mission are investigated and illustrated using model coronal flux tubes and image-rendering techniques. Synthesized images are formed by integrating the emission from volume elements along the line-of-sight path through a 3-dimensional volume in which a set of model flux tubes are located. The flux tubes are defined by (1) a plasma model defining the emissivity for a specific density, temperature, and pressure distribution, and (2) a magnetic field model from which a set of field lines are selected to define the geometry of the flux tubes. The field lines are used to define the flux-tube volume by assuming an initial base radius and conservation of flux. An effective instrumental spectral-response function is folded into the integration. Analysis of pairs of these synthesized images with various angular perspectives are used to investigate the effect of angular separation on mission objectives. The resulting images and analysis provide guidelines for developing a stereoscopic mission. Our study produced four important results, namely: (1) An angular separation of ~30 degrees maximizes the scientific return by direct triangulation analysis because of the tradeoff between increased line-of-sight resolution of position and decreased recognition of individual loop structures arising from the overlapping of multiple loops with increasing angular separation. (2) The analysis benefits from the use of time-differential images to select flux tubes from the collection of numerous overlapping systems by selecting only recently heated or cooled flux tubes. (3) An analysis needs to be developed for algebraic reconstruction techniques applying a priori information, specific to the solar coronal structures, i.e., flux-tube continuity, maximum emission strength, non-negative emission, previous history, and maximum gradients of emission. (4) An analysis strategy combining triangulation, modeling techniques, and algebraic restoration is necessary to derive a complete understanding of the 3-dimensional morphology of the magnetic field. In the same way that helioseismology is classical viewing of the Sun with a tailored set of analysis tools for probing the interior of the Sun, heliostereoscopy is classical viewing of the X-ray emitting corona and requires a tailored set of analysis tools to deduce the true 3-dimensional structure of the corona.