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 i s possible to obtain direct 3-dimensional morphology of coronal structures which is essential for understanding the energetics and dynamics of the sol ar atmosphere. X-ray observations taken only in orbit about the Earth are i nadequate to fully resolve the 3-dimensional nature of the solar corona. Th ese Earth-orbit observations produce 2-dimensional images and an appropriat e model must be included to derive the 3-dimensional structures from the li ne-of-sight information. Stereoscopic observations from space will remove t his limitation and are needed if we are to improve our knowledge of the 3-d imensional morphology of the corona. Several important points regarding a stereoscopic mission are investigated and illustrated using model coronal flux tubes and image-rendering techniqu es. Synthesized images are formed by integrating the emission from volume e lements along the line-of-sight path through a 3-dimensional volume in whic h a set of model flux tubes are located. The flux tubes are defined by (I) 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 held lines are selected to define the geometry of the flux tubes. The f ield lines are used to define the flux-tube volume by assuming an initial b ase radius and conservation of flux. An effective instrumental spectral-res ponse function is folded into the integration. Analysis of pairs of these s ynthesized images with various angular perspectives are used to investigate the effect of angular separation on mission objectives. The resulting imag es and analysis provide guidelines for developing a stereoscopic mission. Our study produced four important results, namely: (1) An angular separatio n of similar to 30 degrees maximizes the scientific return by direct triang ulation analysis because of the tradeoff between increased line-of-sight re solution of position and decreased recognition of individual loop structure s arising from the overlapping of multiple loops with increasing angular se paration. (2) The analysis benefits from the use of time-differential image s to select flux tubes from the collection of numerous overlapping systems by selecting only recently heated or cooled flux tubes. (3) An analysis nee ds to be developed for algebraic reconstruction techniques applying a prior i information, specific to the solar coronal structures, i.e., flux-tube co ntinuity, maximum emission strength, non-negative emission, previous histor y, and maximum gradients of emission. (4) An analysis strategy combining tr iangulation, modeling techniques, and algebraic restoration is necessary to derive a complete understanding of the 3-dimensional morphology of the mag netic held. In the same way that helioseismology is classical viewing of th e 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 an d requires a tailored set of analysis tools to deduce the true 3-dimensiona l structure of the corona.