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We provide a mathematical description of the imaging concept of the Spectrometer/Telescope for Imaging X-rays (STIX) onboard Solar Orbiter. Specifically, we describe the STIX indirect-imaging technique, which is based on spatial modulation of the X-ray photon flux by means of tungsten grids, and we show that each of 30 STIX imaging sub-collimators measures a Fourier component of the flaring X-ray source corresponding to a specific two-dimensional angular frequency. We also provide details about the count-distribution model, which describes the relationship between the photon flux and the measured pixel counts. The derived imaging model is the fundamental starting point both for the interpretation of STIX data and for the description of the data-calibration process. Finally, we provide an overview of the algorithms implemented for the solution of the imaging problem and a comparison of the results obtained with these different methods in the case of the SOL2022-03-31T18 flaring event. [ABSTRACT FROM AUTHOR]

The Spectrometer/Telescope for Imaging X-rays (STIX) is one of six remote sensing instruments on-board Solar Orbiter. The telescope applies an indirect imaging technique that uses the measurement of 30 visibilities, i.e., angular Fourier components of the solar flare X-ray source. Hence, the imaging problem for STIX consists of the Fourier inversion of the data measured by the instrument. In this work, we show that the visibility amplitude and phase calibration of 24 out of 30 STIX sub-collimators has reached a satisfactory level for scientific data exploitation and that a set of imaging methods is able to provide the first hard X-ray images of solar flares from Solar Orbiter. Four visibility-based image reconstruction methods and one count-based are applied to calibrated STIX observations of six events with GOES class between C4 and M4 that occurred in May 2021. The resulting reconstructions are compared to those provided by an optimization algorithm used for fitting the amplitudes of STIX visibilities. We show that the five imaging methods produce results morphologically consistent with the ones provided by the Atmospheric Imaging Assembly on board the Solar Dynamic Observatory (SDO/AIA) in UV wavelengths. The χ 2 values and the parameters of the reconstructed sources are comparable between methods, thus confirming their robustness. [ABSTRACT FROM AUTHOR]

Space telescopes for solar hard X-ray imaging provide observations made of sampled Fourier components of the incoming photon flux. The aim of this study is to design an image reconstruction method relying on enhanced visibility interpolation in the Fourier domain. The interpolation-based method is applied to synthetic visibilities generated by means of the simulation software implemented within the framework of the Spectrometer/Telescope for Imaging X-rays (STIX) mission on board Solar Orbiter. An application to experimental visibilities observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is also considered. In order to interpolate these visibility data, we have utilized an approach based on Variably Scaled Kernels (VSKs), which are able to realize feature augmentation by exploiting prior information on the flaring source and which are used here, for the first time, in the context of inverse problems. When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performance, particularly in the case of STIX imaging, which is characterized by a notably sparse sampling of the Fourier domain. In the case of RHESSI data, this novel approach is particularly reliable when the flaring sources are either characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. The use of VSKs for interpolating hard X-ray visibilities allows remarkable image reconstruction accuracy when the information on the flaring source is encoded by a small set of scattered Fourier data and when the visibility surface is affected by significant oscillations in the frequency domain. [ABSTRACT FROM AUTHOR]

Maximum Entropy is an image reconstruction method conceived to image a sparsely occupied field of view, therefore it is particularly effective at achieving super-resolution effects. Although widely used in image deconvolution, this method has been formulated in radio astronomy for the analysis of observations in the spatial frequency domain, and an Interactive Data Language code has been implemented for image reconstruction from solar X-ray Fourier data. However, this code relies on a non-convex formulation of the constrained optimization problem addressed by the Maximum Entropy approach, and this sometimes results in unreliable reconstructions characterized by unphysical shrinking effects. This paper introduces a new approach to Maximum Entropy based on the constrained minimization of a convex functional. In the case of observations recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), the resulting code provides the same super-resolution effects of the previous algorithm, while also working properly when that code produces unphysical reconstructions. We also obtain results via testing the algorithm with synthetic data simulating observations of the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter. The new code is available in the HESSI folder of the Solar SoftWare (SSW) tree. [ABSTRACT FROM AUTHOR]

Using RHESSI hard X-ray imaging spectroscopy observations, we analyze electron flux maps for a number of extended coronal loop flares. For each event, we fit a collisional model with an extended acceleration region to the observed variation of loop length with electron energy E, resulting in estimates of the plasma density in, and longitudinal extent of, the acceleration region. These quantities in turn allow inference of the number of particles within the acceleration region and hence the filling factor f—the ratio of the emitting volume to the volume that encompasses the emitting region(s). We obtain values of f that lie mostly between 0.1 and 1.0; the (geometric) mean value is f = 0.20 ×/÷ 3.9, somewhat less than, but nevertheless consistent with, unity. Further, coupling information on the number of particles in the acceleration region with information on the total rate of acceleration of particles above a certain reference energy (obtained from spatially integrated hard X-ray data) also allows inference of the specific acceleration rate (electron s–1 per ambient electron above the chosen reference energy). We obtain a (geometric) mean value of the specific acceleration rate η(20 keV) =(6.0 ×/÷ 3.4) × 10–3 electrons s–1 per ambient electron; this value has implications both for the global electrodynamics associated with replenishment of the acceleration region and for the nature of the particle acceleration process. [ABSTRACT FROM AUTHOR]