3D reconstruction of thermal hard X-ray sources in solar flares from combined STIX and HXI visibilities

¹ MIDA, Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, I-16146, Genova, Italy
² University of Applied Sciences and Arts Northwestern Switzerland (FHNW), School of Computer Science, Bahnhofstrasse 6, Windisch, 5210, Switzerland
³ Swiss Federal Institute of Technology in Zurich (ETHZ), Rämistrasse 1, 8001, Zürich, Switzerland
⁴ University College London, Mullard Space Science Labratory, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK
⁵ Division of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences (CAS), Nanjing, 210023, China
⁶ School of Astronomy and Space Science, University of Science and Technology of China, Hefei, 230026, China
⁷ Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025, Pino Torinese, Italy
⁸ Space Sciences Laboratory, University of California, 7 Gauss Way, 94720, Berkeley, USA

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Received: 19 December 2025
Accepted: 29 April 2026

Abstract

Context. The Spectrometer/Telescope for Imaging X-rays (STIX) on board the ESA Solar Orbiter mission and the Hard X-ray Imager (HXI) aboard the Advanced Space-based Solar Observatory (ASO-S) satellite provide for the first time systematic coverage of solar flare hard X-ray sources from different vantage points. This unprecedented configuration enables the reconstruction of the three-dimensional (3D) hard X-ray intensity distribution of the thermal emission in solar flares.

Aims. The main objectives of this study are twofold: (1) to perform 3D reconstructions of the thermal hard X-ray source of a solar flare using stereoscopic Fourier data (visibilities) provided by STIX and HXI; and (2) to investigate the evolution in time of the reconstructed 3D source morphology.

Methods. The sets of 2D visibilities measured by STIX and HXI represent a sampling of the 3D Fourier transform of the flaring hard X-ray source on two planes orthogonal to the instruments’ lines of sight. Therefore, the 3D reconstruction problem is analogous to the standard 2D imaging problem and can be addressed with similar techniques. In this case, we performed 3D reconstructions by means of the iterative space reconstruction algorithm (ISRA).

Results. We consider the SOL2024-10-03T12:12 event observed by STIX and HXI from largely different vantage points separated by 85.7°. We performed 3D reconstructions of the flaring thermal emission at a 10 s cadence, and we determined the X-ray source height and radial velocity over time. As a consistency test, we show that the morphology and location of our 3D reconstructions are consistent with the corresponding 2D images independently obtained from STIX and HXI data.

Conclusions. The proposed 3D reconstruction methodology provides reliable results for events with a separation angle close to 90°. However, the dynamic range of the 3D reconstructions is limited by the low number of observed visibilities (as in the 2D case) and by the limited number of vantage points on the flaring events.