RIS: Regularized Imaging Spectroscopy for STIX on-board Solar Orbiter

TL;DR

Imaging spectroscopy with Fourier-based solar hard X-ray imagers often yields uncorrelated reconstructions across energy channels, causing spurious fluctuations in local count spectra. RIS introduces spectral regularization by using Variably Scaled Kernel (VSK) interpolation in the spatial-frequency domain to transfer information between adjacent energy channels, imposing smoothing along the count-energy direction without bremsstrahlung deconvolution. Applied to STIX visibilities from the 2022-11-11 flare, RIS starts from a triggering energy $\epsilon_0$ and propagates to a final energy $\epsilon_I$ by using the Fourier transform of the previous reconstruction as the scale function $\psi_{\epsilon_{i-1}}$ to interpolate the next channel, followed by a projected Landweber solver. Results show that RIS produces morphologies that evolve smoothly with energy and yields numerically stable, locally resolved count spectra, robust to the triggering energy and to the initial reconstruction method, thereby enabling reliable image cubes for STIX and opening avenues for spectroscopy-focused and time-dependent analyses.

Abstract

Imaging spectroscopy, i.e., the generation of spatially resolved count spectra and of cubes of count maps at different energies, is one of the main goals of solar hard X-ray missions based on Fourier imaging. For these telescopes, so far imaging spectroscopy has been realized via the generation of either count maps independently reconstructed at the different energy channels, or electron flux maps reconstructed via deconvolution of the bremsstrahlung cross-section. Our aim is to introduce the Regularized Imaging Spectroscopy method (RIS), in which regularization implemented in the count space imposes a smoothing constraint across contiguous energy channels, without the need to deconvolve the bremsstrahlung effect. STIX records imaging data computing visibilities in the spatial frequency domain. Our RIS is a sequential scheme in which part of the information coded in the image reconstructed at a specific energy channel is transferred to the reconstruction process at a contiguous channel via visibility interpolation based on Variably Scaled Kernels. In the case of STIX visibilities recorded during the November 11, 2022 flaring event, we show that RIS is able to generate hard X-ray maps whose morphology smoothly evolves from one energy channel to the contiguous one, and that from these maps it is possible to infer spatially-resolved count spectra characterized by notable numerical stability. We also show that the performances of this approach are robust with respect to both the image reconstruction method and the count energy channel utilized to trigger the sequential process. RIS is appropriate to construct image cubes from STIX visibilities that are characterized by a smooth behavior across count energies, thus allowing the generation of numerically stable (and, thus, physically reliable) local count spectra.

Figures (5)

• Figure 1: The regularized imaging spectroscopy algorithm and the outcomes corresponding to each one of its steps.
• Figure 2: Hard X-ray emission of the November 11, 2022 event in the time window between 01:30:00 and 01:32:00 UT. Left panel: STIX light-curves corresponding to three energy channels. Right panel: Level curves of the count emission provided by MEM$\_$GE and superimposed to the $1600 \AA$ emission recorded by SDO/AIA (the AIA data have been appropriately reprojected in order to account for the Solar Orbiter and SDO different vantage points). The red level curves correspond to the thermal emission in the energy range $4-6$ keV, while the green ones correspond to the non-thermal emission in the energy range $22-25$ keV.
• Figure 3: Comparison between the maps provided at contiguous energy channels by the regularized imaging spectroscopy method and the reconstructions provided by MEM$\_$GE at the same channels. Top part: reconstructions provided by RIS using the MEM$\_$GE reconstruction at the top left panel as triggering image. Bottom part: reconstructions provided by MEM$\_$GE.
• Figure 4: Local count spectra corresponding to the points highlighted by the colored crosses superimposed to the map at the top left panel. The local spectra obtained by using the maps in Figure \ref{['fig:regularized-IS']} provided by RIS are in solid line, while the ones obtained by using the maps in the same figure but provided by MEM$\_$GE when independently applied at each energy channel are in dashed line.
• Figure 5: Robustness of RIS with respect to the reconstruction method applied to generate the triggering image and on the triggering energy. Left panel: $\chi^2$ values at different energies when the triggering image is reconstrcuted by means of MEM$\_$GE (black), forward-fit with PSO (red) and CLEAN (green). The $\chi^2$ values provided by MEM$\_$GE independently at each energy channel are shown in blue. Right panel: $\chi^2$ values at different energies when the triggering energy corresponds to the lowest channel and the regularization process flows from low to high energies (black), the triggering energy corresponds to the highest channel and the regularization process flows from high to low energies (red), and the triggering energy has an intermediate value with the regularization process flowing along both directions (green).