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The solar wind drag-based model is a widely used framework for predicting the propagation of Coronal Mass Ejections (CMEs) through interplanetary space. This model primarily considers the aerodynamic drag exerted by the solar wind on CMEs. However, factors like magnetic forces, pressure gradients, and the internal dynamics within CMEs justify the need of introducing an additional small-scale acceleration term in the game. Indeed, by accounting for this extra acceleration, the extended drag-based model is shown to offer improved accuracy in describing the evolution of CMEs through the heliosphere and, in turn, in forecasting CME trajectories and arrival times at Earth. This enhancement is crucial for better predicting Space Weather events and mitigating their potential impacts on space-based and terrestrial technologies.

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.

This study addresses the prediction of geomagnetic disturbances by exploiting machine learning techniques. Specifically, the Long-Short Term Memory recurrent neural network, which is particularly suited for application over long time series, is employed in the analysis of in-situ measurements of solar wind plasma and magnetic field acquired over more than one solar cycle, from $2005$ to $2019$, at the Lagrangian point L$1$. The problem is approached as a binary classification aiming to predict one hour in advance a decrease in the SYM-H geomagnetic activity index below the threshold of $-50$ nT, which is generally regarded as indicative of magnetospheric perturbations. The strong class imbalance issue is tackled by using an appropriate loss function tailored to optimize appropriate skill scores in the training phase of the neural network. Beside classical skill scores, value-weighted skill scores are then employed to evaluate predictions, suitable in the study of problems, such as the one faced here, characterized by strong temporal variability. For the first time, the content of magnetic helicity and energy carried by solar transients, associated with their detection and likelihood of geo-effectiveness, were considered as input features of the network architecture. Their predictive capabilities are demonstrated through a correlation-driven feature selection method to rank the most relevant characteristics involved in the neural network prediction model. The optimal performance of the adopted neural network in properly forecasting the onset of geomagnetic storms, which is a crucial point for giving real warnings in an operational setting, is finally showed.

AI-FLARES (Artificial Intelligence for the Analysis of Solar Flares Data) is a research project funded by the Agenzia Spaziale Italiana and by the Istituto Nazionale di Astrofisica within the framework of the ``Attivit\`a di Studio per la Comunit\`a Scientifica Nazionale Sole, Sistema Solare ed Esopianeti'' program. The topic addressed by this project was the development and use of computational methods for the analysis of remote sensing space data associated to solar flare emission. This paper overviews the main results obtained by the project, with specific focus on solar flare forecasting, reconstruction of morphologies of the flaring sources, and interpretation of acceleration mechanisms triggered by solar flares.

Regularized imaging spectroscopy was introduced for the construction of electron flux images at different energies from count visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In this work we seek to extend this approach to data from the Spectrometer/Telescope for Imaging X-rays (STIX) on-board the Solar Orbiter mission. Our aims are to demonstrate the feasibility of regularized imaging spectroscopy as a method for analysis of STIX data, and also to show how such analysis can lead to insights into the physical processes affecting the nonthermal electrons responsible for the hard X-ray emission observed by STIX. STIX records imaging data in an intrinsically different manner from RHESSI. Rather than sweeping the angular frequency plane in a set of concentric circles (one circle per detector), STIX uses $30$ collimators, each corresponding to a specific angular frequency. In this paper we derive an appropriate modification of the previous computational approach for the analysis of the visibilities observed by STIX. This approach also allows for the observed count data to be placed into non-uniformly-spaced energy bins. We show that the regularized imaging spectroscopy approach is not only feasible for analysis of the visibilities observed by STIX, but also more reliable. Application of the regularized imaging spectroscopy technique to several well-observed flares reveals details of the variation of the electron flux spectrum throughout the flare sources. We conclude that the visibility-based regularized imaging spectroscopy approach is well-suited to analysis of STIX data. We also use STIX electron flux spectral images to track, for the first time, the behavior of the accelerated electrons during their path from the acceleration site in the solar corona toward the chromosphere

Aims: To formulate, implement, and validate a user-independent release of CLEAN for Fourier-based image reconstruction of hard X-rays flaring sources. Methods: CLEAN is an iterative deconvolution method for radio and hard X-ray solar imaging. In a specific step of its pipeline, CLEAN requires the convolution between an idealized version of the instrumental Point Spread Function (PSF), and a map collecting point sources located at positions on the solar disk from where most of the flaring radiation is emitted. This convolution step has highly heuristic motivations and the shape of the idealized PSF, which depends on the user's choice, impacts the shape of the overall reconstruction. Here we propose the use of an interpolation/extrapolation process to avoid this user-dependent step, and to realize a completely unbiased version of CLEAN. Results: Applications to observations recorded by the Spectrometer/Telescope for Imaging X-rays (STIX) on-board Solar Orbiter show that this unbiased release of CLEAN outperforms the standard version of the algorithm in terms of both automation and reconstruction reliability, with reconstructions whose accuracy is in line with the one offered by other imaging methods developed in the STIX framework. Conclusions: This unbiased version of CLEAN proposes a feasible solution to a well-known open issue concerning CLEAN, i.e., its low degree of automation. Further, this study provided the first application of an interpolation/extrapolation approach to image reconstruction from STIX experimental visibilities.

FOXSI is a direct-imaging, hard X-ray (HXR) telescope optimized for solar flare observations. It detects hot plasma and energetic electrons in and near energy release sites in the solar corona via bremsstrahlung emission, measuring both spatial structure and particle energy distributions. It provides two orders of magnitude faster imaging spectroscopy than previously available, probing physically relevant timescales (<1s) never before accessible to address fundamental questions of energy release and efficient particle acceleration that have importance far beyond their solar application (e.g., planetary magnetospheres, flaring stars, accretion disks). FOXSI measures not only the bright chromospheric X-ray emission where electrons lose most of their energy, but also simultaneous emission from electrons as they are accelerated in the corona and propagate along magnetic field lines. FOXSI detects emission from high in the tenuous corona, where previous instruments have been blinded by nearby bright features and will fully characterizes the accelerated electrons and hottest plasmas as they evolve in energy, space, and time to solve the mystery of how impulsive energy release leads to solar eruptions, the primary drivers of space weather at Earth, and how those eruptions are energized and evolve., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 14 pages, 4 figures, 1 table

This Letter reports the first observational estimate of the heating rate in the slowly expanding solar corona. The analysis exploits the simultaneous remote and local observations of the same coronal plasma volume with the Solar Orbiter/Metis and the Parker Solar Probe instruments, respectively, and relies on the basic solar wind magnetohydrodynamic equations. As expected, energy losses are a minor fraction of the solar wind energy flux, since most of the energy dissipation that feeds the heating and acceleration of the coronal flow occurs much closer to the Sun than the heights probed in the present study, which range from 6.3 to 13.3 solar radii. The energy deposited to the supersonic wind is then used to explain the observed slight residual wind acceleration and to maintain the plasma in a non-adiabatic state. As derived in the Wentzel-Kramers-Brillouin limit, the present energy transfer rate estimates provide a lower limit, which can be very useful in refining the turbulence-based modeling of coronal heating and subsequent solar wind acceleration.

Coronal Mass Ejections (CMEs) correspond to dramatic expulsions of plasma and magnetic field from the solar corona into the heliosphere. CMEs are scientifically relevant because they are involved in the physical mechanisms characterizing the active Sun. However, more recently CMEs have attracted attention for their impact on space weather, as they are correlated to geomagnetic storms and may induce the generation of Solar Energetic Particles streams. In this space weather framework, the present paper introduces a physics-driven artificial intelligence (AI) approach to the prediction of CMEs travel time, in which the deterministic drag-based model is exploited to improve the training phase of a cascade of two neural networks fed with both remote sensing and in-situ data. This study shows that the use of physical information in the AI architecture significantly improves both the accuracy and the robustness of the travel time prediction.

Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we present what we call mapped variably scaled kernels, which take advantage of both strategies. We present some theoretical analysis and then we show their efficacy via numerical experiments. Moreover, we test such a new basis for image reconstruction tasks in the framework of hard X-ray astronomical imaging.

Multi-scale deconvolution is an ill-posed inverse problem in imaging, with applications ranging from microscopy, through medical imaging, to astronomical remote sensing. In the case of high-energy space telescopes, multi-scale deconvolution algorithms need to account for the peculiar property of native measurements, which are sparse samples of the Fourier transform of the incoming radiation. The present paper proposes a multi-scale version of CLEAN, which is the most popular iterative deconvolution method in Fourier space imaging. Using synthetic data generated according to a simulated but realistic source configuration, we show that this multi-scale version of CLEAN performs better than the original one in terms of accuracy, photometry, and regularization. Further, the application to a data set measured by the NASA Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) shows the ability of multi-scale CLEAN to reconstruct rather complex topographies, characteristic of a real flaring event.

Aims. To provide a schematic mathematical description of the imaging concept of the Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter. The derived model is the fundamental starting point for both the interpretation of STIX data and the description of the data calibration process. Methods. We describe the STIX indirect imaging technique which is based on spatial modulation of the X-ray photon flux by means of tungsten grids. We show that each of 30 STIX imaging sub-collimators measures a complex Fourier component of the flaring X-ray source corresponding to a specific angular frequency. We also provide details about the count distribution model, which describes the relationship between the photon flux and the measured pixel counts. Results. We define the image reconstruction problem for STIX from both visibilities and photon counts. 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.

Aima. To determine to what extent the problem of forward fitting visibilities measured by the Spectrometer/Telescope Imaging X-rays (STIX) on-board Solar Orbiter is more challenging with respect to the same problem in the case of previous hard X-ray solar imaging missions; to identify an effective optimization scheme for parametric imaging for STIX. Methods. This paper introduces a Particle Swarm Optimization (PSO) algorithm for forward fitting STIX visibilities and compares its effectiveness with respect to the standard simplex-based optimization algorithm used so far for the analysis of visibilities measured by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). This comparison is made by considering experimental visibilities measured by both RHESSI and STIX, and synthetic visibilities generated by accounting for the STIX signal formation model. Results. We found out that the parametric imaging approach based on PSO is as reliable as the one based on the simplex method in the case of RHESSI visibilities. However, PSO is significantly more robust when applied to STIX simulated and experimental visibilities. Conclusions. Standard deterministic optimization is not effective enough for forward-fitting the few visibilities sampled by STIX in the angular frequency plane. Therefore a more sofisticated optimization scheme must be introduced for parametric imaging in the case of the Solar Orbiter X-ray telescope. The forward-fitting routine based on PSO we introduced in this paper proved to be significantly robust and reliable, and could be considered as an effective candidate tool for parametric imaging in the STIX context.

Context. The Spectrometer/Telescope for Imaging X-rays (STIX) is one of 6 remote sensing instruments on-board Solar Orbiter. It provides hard X-ray imaging spectroscopy of solar flares by sampling the Fourier transform of the incoming flux. Aims. To show that the visibility amplitude and phase calibration of 24 out of 30 STIX sub-collimators is well advanced and that a set of imaging methods is able to provide the first hard X-ray images of the flaring Sun from Solar Orbiter. Methods. We applied four visibility-based image reconstruction methods and a count-based one to calibrated STIX observations. The resulting reconstructions are compared to those provided by an optimization algorithm used for fitting the amplitudes of STIX visibilities. Results. When applied to six flares with GOES class between C4 and M4 which occurred in May 2021, 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 $\chi^2$ values and the parameters of the reconstructed sources are comparable between methods, thus confirming their robustness. Conclusions. This paper shows that the current calibration of the main part of STIX sub-collimators has reached a satisfactory level for scientific data exploitation, and that the imaging algorithms already available in the STIX data analysis software provide reliable and robust reconstructions of the morphology of solar flares.

The evaluation of sky characteristics plays a fundamental role for many astrophysical experiments and ground-based observations. In solar physics, the main requirement for such observations is a very low sky brightness value, that is, less than one-millionth of the solar disk brightness. Few places match such requirement for ground-based, out-of-eclipse coronagraphic measurements. A candidate coronagraphic site is the Dome C plateau in Antarctica. In this paper, we show the first results of the sky brightness measurements at Dome C with the Extreme Solar Coronagraphy Antarctic Program Experiment (ESCAPE) at Italian-French Concordia Station, on Dome C, Antarctica (3300 m) during the summer XXXIV and XXXV Expeditions of the "Italian Piano Nazionale Ricerche Antartiche" (PNRA). The sky brightness measurements were carried out with the internally-occulted Antarctic coronagraph - AntarctiCor. In optimal atmospheric conditions, the sky brightness of Dome C has reached values of the order of 1.0 to 0.7 millionth of of the solar disk brightness.

This Letter addresses the first Solar Orbiter (SO) -- Parker Solar Probe (PSP) quadrature, occurring on January 18, 2021, to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic field and the bulk kinetic energy flux density can be empirically inferred along the coronal current sheet with an unprecedented accuracy, allowing in particular estimation of the Alfv\'en radius at 8.7 solar radii during the time of this event. This is thus the very first study of the same solar wind plasma as it expands from the sub-Alfv\'enic solar corona to just above the Alfv\'en surface., Comment: 10 pages, 4 figures

The investigation of the wind in the solar corona initiated with the observations of the resonantly scattered UV emission of the coronal plasma obtained with UVCS-SOHO, designed to measure the wind outflow speed by applying the Doppler dimming diagnostics. Metis on Solar Orbiter complements the UVCS spectroscopic observations, performed during solar activity cycle 23, by simultaneously imaging the polarized visible light and the HI Ly-alpha corona in order to obtain high-spatial and temporal resolution maps of the outward velocity of the continuously expanding solar atmosphere. The Metis observations, on May 15, 2020, provide the first HI Ly-alpha images of the extended corona and the first instantaneous map of the speed of the coronal plasma outflows during the minimum of solar activity and allow us to identify the layer where the slow wind flow is observed. The polarized visible light (580-640 nm), and the UV HI Ly-alpha (121.6 nm) coronal emissions, obtained with the two Metis channels, are combined in order to measure the dimming of the UV emission relative to a static corona. This effect is caused by the outward motion of the coronal plasma along the direction of incidence of the chromospheric photons on the coronal neutral hydrogen. The plasma outflow velocity is then derived as a function of the measured Doppler dimming. The static corona UV emission is simulated on the basis of the plasma electron density inferred from the polarized visible light. This study leads to the identification, in the velocity maps of the solar corona, of the high-density layer about +/-10 deg wide, centered on the extension of a quiet equatorial streamer present at the East limb where the slowest wind flows at about (160 +/- 18) km/s from 4 Rs to 6 Rs. Beyond the boundaries of the high-density layer, the wind velocity rapidly increases, marking the transition between slow and fast wind in the corona.

The Spectrometer/Telescope for Imaging X-rays (STIX) is the HXR instrument onboard Solar Orbiter designed to observe solar flares over a broad range of flare sizes, between 4-150 keV. We report the first STIX observations of microflares recorded during the instrument commissioning phase in order to investigate the STIX performance at its detection limit. This first result paper focuses on the temporal and spectral evolution of STIX microflares occuring in the AR12765 in June 2020, and compares the STIX measurements with GOES/XRS, SDO/AIA, and Hinode/XRT. For the observed microflares of the GOES A and B class, the STIX peak time at lowest energies is located in the impulsive phase of the flares, well before the GOES peak time. Such a behavior can either be explained by the higher sensitivity of STIX to higher temperatures compared to GOES, or due to the existence of a nonthermal component reaching down to low energies. The interpretation is inconclusive due to limited counting statistics for all but the largest flare in our sample. For this largest flare, the low-energy peak time is clearly due to thermal emission, and the nonthermal component seen at higher energies occurs even earlier. This suggests that the classic thermal explanation might also be favored for the majority of the smaller flares. In combination with EUV and SXR observations, STIX corroborates earlier findings that an isothermal assumption is of limited validity. Future diagnostic efforts should focus on multi-wavelength studies to derive differential emission measure distributions over a wide range of temperatures to accurately describe the energetics of solar flares. Commissioning observations confirm that STIX is working as designed. As a rule of thumb, STIX detects flares as small as the GOES A class. For flares above the GOES B class, detailed spectral and imaging analyses can be performed., Comment: 19 pages, 11 figures

The EU funded the FLARECAST project, that ran from Jan 2015 until Feb 2018. FLARECAST had a R2O focus, and introduced several innovations into the discipline of solar flare forecasting. FLARECAST innovations were: first, the treatment of hundreds of physical properties viewed as promising flare predictors on equal footing, extending multiple previous works; second, the use of fourteen (14) different ML techniques, also on equal footing, to optimize the immense Big Data parameter space created by these many predictors; third, the establishment of a robust, three-pronged communication effort oriented toward policy makers, space-weather stakeholders and the wider public. FLARECAST pledged to make all its data, codes and infrastructure openly available worldwide. The combined use of 170+ properties (a total of 209 predictors are now available) in multiple ML algorithms, some of which were designed exclusively for the project, gave rise to changing sets of best-performing predictors for the forecasting of different flaring levels. At the same time, FLARECAST reaffirmed the importance of rigorous training and testing practices to avoid overly optimistic pre-operational prediction performance. In addition, the project has (a) tested new and revisited physically intuitive flare predictors and (b) provided meaningful clues toward the transition from flares to eruptive flares, namely, events associated with coronal mass ejections (CMEs). These leads, along with the FLARECAST data, algorithms and infrastructure, could help facilitate integrated space-weather forecasting efforts that take steps to avoid effort duplication. In spite of being one of the most intensive and systematic flare forecasting efforts to-date, FLARECAST has not managed to convincingly lift the barrier of stochasticity in solar flare occurrence and forecasting: solar flare prediction thus remains inherently probabilistic., Comment: 67 pages, 14 figures; submitted

We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven interpolation based on Variably Scaled Kernels (VSKs), whose implementation is here tailored for inverse problems. The so-constructed interpolants are used as inputs for a standard iterative inversion scheme. After providing theoretical results concerning the spectrum of the VSK collocation matrix, we test the method on astrophysical imaging benchmarks.

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. % methods heading (mandatory) The interpolation-based method is applied on 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, for image reconstruction purposes.} % results heading (mandatory) When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performances, 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 either the flaring sources are characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. % conclusions heading (optional), leave it empty if necessary The use of VSKs for interpolating hard X-ray visibilities allows a notable 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.

Machine learning is nowadays the methodology of choice for flare forecasting and supervised techniques, in both their traditional and deep versions, are becoming the most frequently used ones for prediction in this area of space weather. Yet, machine learning has not been able so far to realize an operating warning system for flaring storms and the scientific literature of the last decade suggests that its performances in the prediction of intense solar flares are not optimal. The main difficulties related to forecasting solar flaring storms are probably two. First, most methods are conceived to provide probabilistic predictions and not to send binary yes/no indications on the consecutive occurrence of flares along an extended time range. Second, flaring storms are typically characterized by the explosion of high energy events, which are seldom recorded in the databases of space missions; as a consequence, supervised methods are trained on very imbalanced historical sets, which makes them particularly ineffective for the forecasting of intense flares. Yet, in this study we show that supervised machine learning could be utilized in a way to send timely warnings about the most violent and most unexpected flaring event of the last decade, and even to predict with some accuracy the energy budget daily released by magnetic reconnection during the whole time course of the storm. Further, we show that the combination of sparsity-enhancing machine learning and feature ranking could allow the identification of the prominent role that energy played as an Active Region property in the forecasting process.

Maximum Entropy is an image reconstruction method conceived to image a sparsely occupied field of view and therefore particularly appropriate to achieve 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 (IDL) 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 working properly also when that code produces unphysical reconstructions. Results are also provided of 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 {\em{HESSI}} folder of the Solar SoftWare (SSW)tree.

Multiple Myeloma (MM) is a blood cancer implying bone marrow involvement, renal damages and osteolytic lesions. The skeleton involvement of MM is at the core of the present paper, exploiting radiomics and artificial intelligence to identify image-based biomarkers for MM. Preliminary results show that MM is associated to an extension of the intrabone volume for the whole body and that machine learning can identify CT image features mostly correlating with the disease evolution. This computational approach allows an automatic stratification of MM patients relying of these biomarkers and the formulation of a prognostic procedure for determining the disease follow-up.

Metis is the first solar coronagraph designed for a space mission capable of performing simultaneous imaging of the off-limb solar corona in both visible and UV light. The observations obtained with Metis aboard the Solar Orbiter ESA-NASA observatory will enable us to diagnose, with unprecedented temporal coverage and spatial resolution, the structures and dynamics of the full corona from 1.7 $R_\odot$ to about 9 $R_\odot$. Due to the uniqueness of the Solar Orbiter mission profile, Metis will be able to observe the solar corona from a close vantage point (down to 0.28 AU), achieving out-of-ecliptic views with the increase of the orbit inclination over time. Moreover, observations near perihelion, during the phase of lower rotational velocity of the solar surface relative to the spacecraft, will allow longer-term studies of the coronal features. Thanks to a novel occultation design and a combination of a UV interference coating of the mirrors and a spectral bandpass filter, Metis images the solar corona simultaneously in the visible light band, between 580 and 640 nm, and in the UV H I Lyman-{\alpha} line at 121.6 nm. The coronal images in both the UV Lyman-{\alpha} and polarised visible light are obtained at high spatial resolution with a spatial scale down to about 2000 km and 15000 km at perihelion, in the cases of the visible and UV light, respectively. A temporal resolution down to 1 second can be achieved when observing coronal fluctuations in visible light. The Metis measurements will allow for complete characterisation of the main physical parameters and dynamics of the electron and neutral hydrogen/proton plasma components of the corona in the region where the solar wind undergoes acceleration and where the onset and initial propagation of coronal mass ejections take place, thus significantly improving our understanding of the region connecting the Sun to the heliosphere.

Solar flares originate from magnetically active regions but not all solar active regions give rise to a flare. Therefore, the challenge of solar flare prediction benefits by an intelligent computational analysis of physics-based properties extracted from active region observables, most commonly line-of-sight or vector magnetograms of the active-region photosphere. For the purpose of flare forecasting, this study utilizes an unprecedented 171 flare-predictive active region properties, mainly inferred by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) in the course of the European Union Horizon 2020 FLARECAST project. Using two different supervised machine learning methods that allow feature ranking as a function of predictive capability, we show that: i) an objective training and testing process is paramount for the performance of every supervised machine learning method; ii) most properties include overlapping information and are therefore highly redundant for flare prediction; iii) solar flare prediction is still - and will likely remain - a predominantly probabilistic challenge.

Image saturation has been an issue for several instruments in solar astronomy, mainly at EUV wavelengths. However, with the launch of the Atmospheric Imaging Assembly (AIA) as part of the payload of the Solar Dynamic Observatory (SDO) image saturation has become a big data issue, involving around 10^$ frames of the impressive dataset this beautiful telescope has been providing every year since February 2010. This paper introduces a novel desaturation method, which is able to recover the signal in the saturated region of any AIA image by exploiting no other information but the one contained in the image itself. This peculiar methodological property, jointly with the unprecedented statistical reliability of the desaturated images, could make this algorithm the perfect tool for the realization of a reconstruction pipeline for AIA data, able to work properly even in the case of long-lasting, very energetic flaring events.

In the framework of the Hough transform technique to detect curves in images, we provide a bound for the number of Hough transforms to be considered for a successful optimization of the accumulator function in the recognition algorithm. Such a bound is consequence of geometrical arguments. We also show the robustness of the results when applied to synthetic datasets strongly perturbed by noise. An algebraic approach, discussed in the appendix, leads to a better bound of theoretical interest in the exact case.

The Spectrometer/Telescope for Imaging X-rays (STIX) will look at solar flares across the hard X-ray window provided by the Solar Orbiter cluster. Similarly to the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), STIX is a visibility-based imaging instrument, which will ask for Fourier-based image reconstruction methods. However, in this paper we show that, as for RHESSI, also for STIX count-based imaging is possible. Specifically, here we introduce and illustrate a mathematical model that mimics the STIX data formation process as a projection from the incoming photon flux into a vector made of 120 count components. Then we test the reliability of Expectation Maximization for image reconstruction in the case of several simulated configurations typical of flare morphology., Comment: submitted to A&A

We describe two inversion methods for the reconstruction of hard X-ray solar images. The methods are tested against experimental visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and synthetic visibilities based on the design of the Spectrometer/Telescope for Imaging X-rays (STIX)., Comment: submitted to 'Nuovo Cimento' as proceeding SOHE3

We describe here the application of a machine learning method for flare forecasting using vectors of properties extracted from images provided by the Helioseismic and Magnetic Imager in the Solar Dynamics Observatory (SDO/HMI). We also discuss how the method can be used to quantitatively assess the impact of such properties on the prediction process., Comment: submitted to 'Nuovo Cimento' as proceeding of SOHE3

'Flare Likelihood and Region Eruption Forecasting (FLARECAST)' is a Horizon 2020 project, which realized a technological platform for machine learning algorithms, with the objective of providing the space weather community with a prediction service for solar flares. This paper describes the FLARECAST service and shows how the methods implemented in the platform allow both flare prediction and a quantitative assessment of how the information contained in the space data utilized in the analysis may impact the forecasting process., Comment: IEEE Italy Session - 4th International Forum on Research and Technologies for Society and Industry

The hard X-ray emission in a solar flare is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship amongst these sources is critical to determine the role of each in the energy release and transport processes that occur within the flare. In this paper we present a novel method to identify and characterize each source of hard X-ray emission. The method permits a quantitative determination of the most likely number of subsources present, and of the relative probabilities that the hard X-ray emission in a given subregion of the flare is represented by a complicated multiple source structure or by a simpler single source. We apply the method to a well-studied flare on 2002~February~20 in order to assess competing claims as to the number of chromospheric footpoint sources present, and hence to the complexity of the underlying magnetic geometry/toplogy. Contrary to previous claims of the need for multiple sources to account for the chromospheric hard X-ray emission at different locations and times, we find that a simple two-footpoint-plus-coronal-source model is the most probable explanation for the data. We also find that one of the footpoint sources moves quite rapidly throughout the event, a factor that presumably complicated previous analyses. The inferred velocity of the footpoint corresponds to a very high induced electric field, compatible with those in thin reconnecting current sheets., Comment: accepted in ApJ

This paper shows that compressed sensing realized by means of regularized deconvolution and the Finite Isotropic Wavelet Transform is effective and reliable in hard X-ray solar imaging. The method utilizes the Finite Isotropic Wavelet Transform with Meyer function as the mother wavelet. Further, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. The method is applied against both synthetic data mimicking the Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are compared with the results provided by standard visibility-based reconstruction methods. The results show that the application of the sparsity constraint and the use of a continuous, isotropic framework for the wavelet transform provide a notable spatial accuracy and significantly reduce the ringing effects due to the instrument point spread functions.

We introduce a hybrid approach to solar flare prediction, whereby a supervised regularization method is used to realize feature importance and an unsupervised clustering method is used to realize the binary flare/no-flare decision. The approach is validated against NOAA SWPC data.

How impulsive magnetic energy release leads to solar eruptions and how those eruptions are energized and evolve are vital unsolved problems in Heliophysics. The standard model for solar eruptions summarizes our current understanding of these events. Magnetic energy in the corona is released through drastic restructuring of the magnetic field via reconnection. Electrons and ions are then accelerated by poorly understood processes. Theories include contracting loops, merging magnetic islands, stochastic acceleration, and turbulence at shocks, among others. Although this basic model is well established, the fundamental physics is poorly understood. HXR observations using grazing-incidence focusing optics can now probe all of the key regions of the standard model. These include two above-the-looptop (ALT) sources which bookend the reconnection region and are likely the sites of particle acceleration and direct heating. The science achievable by a direct HXR imaging instrument can be summarized by the following science questions and objectives which are some of the most outstanding issues in solar physics (1) How are particles accelerated at the Sun? (1a) Where are electrons accelerated and on what time scales? (1b) What fraction of electrons is accelerated out of the ambient medium? (2) How does magnetic energy release on the Sun lead to flares and eruptions? A Focusing Optics X-ray Solar Imager (FOXSI) instrument, which can be built now using proven technology and at modest cost, would enable revolutionary advancements in our understanding of impulsive magnetic energy release and particle acceleration, a process which is known to occur at the Sun but also throughout the Universe., Comment: Next Generation Solar Physics Mission white paper, 2 figures

We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill--posed inverse problem that needs regularization, and we propose to use the Expectation--Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation., Comment: 14 pages, 6 figures, currently under revision

The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition technique, which is mainly used to detect straight lines in digital images and which has been recently extended to the automatic recognition of algebraic plane curves. Although defined in very different ways, in numerical applications both transforms ultimately take an image as an input and provide, as an output, a function defined on a parameter space. The parameters in this space describe a family of curves, which represent either the integration domains considered in the (generalized) Radon transform, or the curves to be detected by means of the Hough transform. In both cases, the 2D plot of the intensity values of the output function is the so-called (Radon or Hough) sinogram. While the Hough sinogram is produced by an algorithm whose implementation requires that the parameter space be discretized in cells, the Radon sinogram is mathematically defined on a continuous parameter space, which in turn may need to be discretized just for physical or numerical reasons. In this paper, by considering a more general and n-dimensional setting, we prove that, whether the input image is described as a set of points (possibly with different intensity values) or as a piecewise constant function, its (rescaled) Hough sinogram converges to the corresponding Radon sinogram as the discretization step in the parameter space tends to zero. We also show that this result may have a notable impact on the image reconstruction problem of inverting the Radon sinogram recorded by a medical imaging scanner, and that the description of the Hough transform problem within the framework of regularization theory for inverse problems is worth investigating.

Saturation affects a significant rate of images recorded by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory. This paper describes a computational method and a technological pipeline for the de-saturation of such images, based on several mathematical ingredients like Expectation Maximization, image correlation and interpolation. An analysis of the computational properties and demands of the pipeline, together with an assessment of its reliability are performed against a set of data recorded from the Feburary 25 2014 flaring event.

The Atmospheric Imaging Assembly in the Solar Dynamics Observatory provides full Sun images every 1 seconds in each of 7 Extreme Ultraviolet passbands. However, for a significant amount of these images, saturation affects their most intense core, preventing scientists from a full exploitation of their physical meaning. In this paper we describe a mathematical and automatic procedure for the recovery of information in the primary saturation region based on a correlation/inversion analysis of the diffraction pattern associated to the telescope observations. Further, we suggest an interpolation-based method for determining the image background that allows the recovery of information also in the region of secondary saturation (blooming).

The Spectrometer/Telescope for Imaging X-rays (STIX) is a hard X-ray imaging spectroscopy device to be mounted in the Solar Orbiter cluster with the aim of providing images and spectra of solar flaring regions at different photon energies in the range from a few keV to around 150 keV. The imaging modality of this telescope is based on the Moire pattern concept and utilizes 30 sub-collimators, each one containing a pair of co-axial grids. This paper applies Fourier analysis to provide the first rigorous description of the data formation process in STIX. Specifically, we show that, under first harmonic approximation, the integrated counts measured by STIX sub-collimators can be interpreted as specific spatial Fourier components of the incoming photon flux, named visibilities. Fourier analysis also allows the quantitative assessment of the reliability of such interpretation. The description of STIX data in terms of visibilities has a notable impact on the image reconstruction process, since it fosters the application of Fourier-based imaging algorithms., Comment: submitted to SIAM Journal on Imaging Sciences

Many bone shapes in the human skeleton are characterized by profiles that can be associated to equations of algebraic curves. Fixing the parameters in the curve equation, by means of a classical pattern recognition procedure like the Hough transform technique, it is then possible to associate an equation to a specific bone profile. However, most skeleton districts are more accurately described by piecewise defined curves. This paper utilizes an iterative approach of the Hough transform without re-voting, to provide an efficient procedure for describing the profile of a bone in the human skeleton as a collection of different but continuously attached curves.

This paper is concerned with the image reconstruction problem when the measured data are solar hard X-ray modulation profiles obtained from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)} instrument. Our goal is to demonstrate that a statistical iterative method classically applied to the image deconvolution problem is very effective when utilized for the analysis of count modulation profiles in solar hard X-ray imaging based on Rotating Modulation Collimators. The algorithm described in this paper solves the maximum likelihood problem iteratively and encoding a positivity constraint into the iterative optimization scheme. The result is therefore a classical Expectation Maximization method this time applied not to an image deconvolution problem but to image reconstruction from count modulation profiles. The technical reason that makes our implementation particularly effective in this application is the use of a very reliable stopping rule which is able to regularize the solution providing, at the same time, a very satisfactory Cash-statistic (C-statistic). The method is applied to both reproduce synthetic flaring configurations and reconstruct images from experimental data corresponding to three real events. In this second case, the performance of Expectation Maximization, when compared to Pixon image reconstruction, shows a comparable accuracy and a notably reduced computational burden; when compared to CLEAN, shows a better fidelity with respect to the measurements with a comparable computational effectiveness. If optimally stopped, Expectation Maximization represents a very reliable method for image reconstruction in the RHESSI context when count modulation profiles are used as input data.

Using {\em 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 $f = 0.20 \times \div 3.9$, 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 $\eta(20$ keV) $ = (6.0 \times / \div 3.4) \times 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.

In order to study the acceleration and propagation of bremsstrahlung-producing electrons in solar flares, we analyze the evolution of the flare loop size with respect to energy at a variety of times. A GOES M3.7 loop-structured flare starting around 23:55 on 2002 April 14 is studied in detail using \textit{Ramaty High Energy Solar Spectroscopic Imager} (\textit{RHESSI}) observations. We construct photon and mean-electron-flux maps in 2-keV energy bins by processing observationally-deduced photon and electron visibilities, respectively, through several image-processing methods: a visibility-based forward-fit (FWD) algorithm, a maximum entropy (MEM) procedure and the uv-smooth (UVS) approach. We estimate the sizes of elongated flares (i.e., the length and width of flaring loops) by calculating the second normalized moments of the intensity in any given map. Employing a collisional model with an extended acceleration region, we fit the loop lengths as a function of energy in both the photon and electron domains. The resulting fitting parameters allow us to estimate the extent of the acceleration region which is between $\sim 13 \rm{arcsec}$ and $\sim 19 \rm{arcsec}$. Both forward-fit and uv-smooth algorithms provide substantially similar results with a systematically better fit in the electron domain.The consistency of the estimates from these methods provides strong support that the model can reliably determine geometric parameters of the acceleration region. The acceleration region is estimated to be a substantial fraction ($\sim 1/2$) of the loop extent, indicating that this dense flaring loop incorporates both acceleration and transport of electrons, with concurrent thick-target bremsstrahlung emission., Comment: 8 pages, 5 figures, accepted to Astronomy and Astrophysics journal

X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion bremsstrahlung, photoelectric absorption and Compton back-scatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons using albedo, improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data., Comment: This is an article for a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011); 10.1007/s11214-011-9804-x

Hard X-Ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs. We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading and consider how to improve fitting procedures. We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the Bethe-Heitler cases. We show that above a low-energy cutoff the Kramers and Bethe-Heitler results match reasonably well with results for exact cross-sections up to energies around 100 keV; that below the low-energy cutoff, Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results; but that our analytical forms are a very good match. Analytical forms of the Bethe-Heitler photon spectra from general power-law electron spectra are an excellent match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations., Comment: 7 pages, 4 figures, submitted to Astronomy and Astrophysics

Although both electron-ion and electron-electron bremsstrahlung contribute to the hard X-ray emission from solar flares, the latter is normally ignored. Such an omission is not justified at electron (and photon) energies above $\sim 300$ keV, and inclusion of the additional electron-electron bremsstrahlung in general makes the electron spectrum required to produce a given hard X-ray spectrum steeper at high energies. Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot produce photons of all energies up to the maximum electron energy involved. The maximum possible photon energy depends on the angle between the direction of the emitting electron and the emitted photon, and this suggests a diagnostic for an upper cutoff energy and/or for the degree of beaming of the accelerated electrons. We analyze the large event of January 17, 2005 observed by RHESSI and show that the upward break around 400 keV in the observed hard X-ray spectrum is naturally accounted for by the inclusion of electron-electron bremsstrahlung. Indeed, the mean source electron spectrum recovered through a regularized inversion of the hard X-ray spectrum, using a cross-section that includes both electron-ion and electron-electron terms, has a relatively constant spectral index $\delta$ over the range from electron kinetic energy $E = 200$ keV to $E = 1$ MeV. However, the level of detail discernible in the recovered electron spectrum is not sufficient to determine whether or not any upper cutoff energy exists., Comment: 7 pages, 5 figures, submitted to Astrophysical Journal

Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here we develop and apply an enhanced regularization algorithm for this process making use of physical constraints on the form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context: Generalized Singular Value Decomposition (GSVD) to deal with different orders of constraints; rectangular form of the cross-section matrix to extend the solution energy range; regularization with various forms of the smoothing operator; and "preconditioning" of the problem. We show by simulations that this technique yields electron spectra with considerably more information and higher quality than previous algorithms., Comment: 21 pages, 8 fugures, accepted to Solar Physics

Kontar et al. (2004) have shown how to recover mean source electron spectra in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate ${overline F}(E)$ forms with certain desirable properties (e.g., higher order derivatives). They further note that such analyses may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the injected (accelerated) electron spectrum $F_0(E_0)$ (assuming that Coulomb collisions in a cold target dominate the electron energetics) is facilitated by the use of higher-order regularization methods., Comment: 10 pages, 7 figures, accepted to Solar Physics