3D evolution of a solar flare thermal X-ray loop-top source

Context. The recent launch of Solar Orbiter has placed a solar X-ray imager (Spectrometer/Telescope for Imaging X-rays; STIX) beyond Earth orbit for the first time. This introduces the possibility of deriving the 3D locations and volumes of solar X-ray sources by combining STIX observations with those of Earth-orbiting instruments such as the Hinode X-ray Telescope (XRT). These measurements promise to improve our understanding of the evolution and energetics of solar flares. However, substantial design differences between STIX and XRT present important challenges that must first be overcome.Aims. We aim to: 1) explore the validity of combining STIX and XRT for 3D analysis given their different designs, 2) understand uncertainties associated with 3D reconstruction and their impact on the derived volume and thermodynamic properties, 3) determine the validity of the scaling law that is traditionally used to estimate source volumes from single-viewpoint observations, 4) chart the temporal evolution of the location, volume, and thermodynamic properties of a thermal X-ray loop-top source of a flare based on a 3D reconstruction for the first time.Methods. The SOL2021-05-07T18:43 M3.9-class flare is analysed using co-temporal observations from STIX and XRT, which, at the time, were separated by an angle of 95.4 degrees relative to the flare site. The 3D reconstruction is performed via elliptical tie-pointing and the visualisation by JHelioviewer, which is enabled by new features developed for this project. Uncertainties associated with the 3D reconstruction are derived from an examination of projection effects given the observer separation angle and the source orientation and elongation.Results. Firstly, we show that it is valid to combine STIX 6-10 keV and XRT Be-thick observations for 3D analysis for the flare examined in this study. However, the validity of doing so in other cases may depend on the nature of the observed source. Therefore, careful consideration should be given on a case-by-case basis. Secondly, the optimal observer separation angle for 3D reconstruction is 90 degrees +/- 5 degrees, but the uncertainties are still relatively small in the range 90 degrees +/- 20 degrees. Other angles are viable, but are associated with higher uncertainties, which can be quantified. Thirdly, the traditional area-to-volume scaling law may overestimate the 3D-derived volume of the thermal X-ray loop-top source studied here by over a factor of 2. This is beyond the uncertainty of the 3D reconstruction. The X-ray source was not very asymmetric, and so the overestimation may be greater for more elongated sources. In addition, the degree of overestimation can vary with time and viewing angle, demonstrating that the true source geometry can evolve differently in different dimensions. 3D reconstruction is therefore necessary to derive more reliable volumes. Simply applying a modified scaling law to single-viewpoint observations is not sufficient. Finally, the vertical motion of the X-ray source is consistent with previous observations of limb flares. This indicates that 3D reconstruction by elliptical tie-pointing provides reliable 3D locations. The uncertainties of thermodynamic properties derived from volume, temperature, and/or emission measure are dominated by those of the volume. In contrast to single-viewpoint studies, observationally constrained volume uncertainties can be assigned via 3D reconstruction, which lends quantifiable credibility to scientific conclusions drawn from the derived thermodynamic properties.