Photospheric Stereoscopy: Direct Estimation of Solar Surface-Height Variations

Abstract

The orbit of the Solar Orbiter mission carries it and the Polarimetric and Helioseismic Imager (PHI), which is onboard, away from the Sun–Earth line, opening up the first ever possibility of doing stereoscopy of solar photospheric structures. We present a method for a stereoscopic analysis of the height variations in the solar photosphere. This method enables the estimation of relevant quantities, such as the Wilson depression of sunspots and pores. We demonstrate the feasibility of the method using simulated Stokes-I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$I$\\end{document} continuum observations of an MHD simulation of the solar-surface layers. Our method estimates the large-scale variations in the solar surface by shifting and correlating two virtual images, mapped from the same surface feature observed from two different vantage points. The resulting vector is then introduced as an initial height estimate in the least-squares Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm to reproduce smaller scale structures. The height estimates from the simulated images reproduce well the overall height variations of the MHD simulation. We studied which viewing angles give the best results and found the optimal separation of the view points to be between 10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$10^{\\circ }$\\end{document} and 40∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$40^{\\circ }$\\end{document}; but neither viewing direction should be inclined by more than 30∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$30^{\\circ }$\\end{document} from the vertical to the solar surface. The method yields reliable results if the data have a signal-to-noise ratio of 50 or higher. The influence of the spatial resolution of the observed images is considered and discussed.