Multi-Spacecraft Solar Surface Stereoscopy: a Method for Direct Estimates of the Wilson Depression from Combined Observations of SO/PHI and SDO/HMI

The Wilson depression is the largest height variation in the solar photosphere. Quantifying it is key in the understanding of sunspots. In this work we present a method for a stereoscopic analysis of the height variations in the solar photosphere and to produce the first direct estimates of the Wilson depression. This stereoscopic method allows for the first time to directly compute height variations on the solar surface. The method presented in this work yields variations in altitude of the solar surface by shifting and correlating two images, mapped along the same epipolar surface profile observed from two different vantage points. This method relies on epipolar geometry and requires a precise camera calibration to resolve the altitude variations of a few hundred kilometers. The performance and constraints of our method are tested using simulated Stokes-I continuum observations of an MHD simulation of the solar surface layers. The resulting height estimate is then introduced as an initial height estimate in an optimization algorithm in order to reproduce smaller scale structures. The height estimates from our method reproduce well the overall height variations of the MHD simulation. When applied to test data, our method yields reliable results for a separation of the viewing points between 10° and 40°; and a signal to noise ratio (SNR) of at least 50. We also test the effect that the resolution of the data has on the performance of the method. We also apply our method to simultaneous continuum intensity observations of a sunspot from Solar Orbiter’s Polarimetric and Helioseismic Imager (SO/PHI) and Solar Dynamic Observatory’s Helioseismic Magnetic Imager (SDO/HMI) observed on October 29th of 2022. The process of the calibration and rectification of the data as well as the necessary corrections to the data in order to apply the method to the observations are presented. The results of the stereoscopic analysis of the sunspot, yield a Wilson depression of roughly 800 km. The resolution of the data is the most limiting factor of the performance of the method. A discussion of the method and its limitations, its performance and the obtained results are presented, and possible extensions of the method as well as possible applications of it are discussed.