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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.

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 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 Micro Solar-Flare Apparatus (MiSolFA) is a compact X-ray imaging spectrometer designed for a small 6U micro-satellite. As a relatively inexpensive yet capable Earth-orbiting instrument, MiSolFA is designed to image the high-energy regions of solar flares from a different perspective than that of Solar Orbiter's STIX, operating from a highly elliptical heliocentric orbit. Two instruments working together in this way would provide a 3-dimensional view of X-ray emitting regions and can bypass the dynamic range limitation preventing simultaneous coronal and chromospheric imaging. Stereoscopic X-ray observations would also contain valuable information about the anisotropy of the flare-accelerated electron distribution. To perform these types of observations, MiSolFA must be capable of imaging sources with energies between 10 and 100 keV, with 10 arcsec angular resolution. MiSolFA's Imager will be the most compact X-ray imaging spectrometer in space. Scaling down the volume by a factor of ten from previous instrument designs requires special considerations. Here we present the design principles of the MiSolFA X-ray optics, discuss the necessary compromises, and evaluate the performance of the Engineering Model., Comment: 25 pages, 10 figures, to be published in Advances in Space Research

The explanation of the coronal heating problem potentially lies in the existence of nanoflares, numerous small-scale heating events occuring across the whole solar disk. In this paper, we present the first imaging spectroscopy X-ray observations of three quiet Sun flares during the NuSTAR solar campaigns on 2016 July 26 and 2017 March 21, concurrent with SDO/AIA observations. Two of the three events showed time lags of a few minutes between peak X-ray and extreme ultraviolet (EUV) emissions. Isothermal fits with rather low temperatures in the range $3.2-4.1$ MK and emission measures of $(0.6-15)\times10^{44} \textrm{ cm}^{-3}$ describe their spectra well, resulting in thermal energies in the range $(2-6)\times10^{26}\textrm{ ergs}$. NuSTAR spectra did not show any signs of a nonthermal or higher temperature component. However, since the estimated upper limits of (hidden) nonthermal energy are comparable to the thermal energy estimates, the lack of a nonthermal component in the observed spectra is not a constraining result. The estimated GOES classes from the fitted values of temperature and emission measure fall between $1/1000 \textrm{ and } 1/100$ A class level, making them 8 orders of magnitude fainter in soft X-ray flux than the largest solar flares., Comment: Accepted for publication in ApJL

We present the first results of a search for transient hard X-ray (HXR) emission in the quiet solar corona with the \textit{Nuclear Spectroscopic Telescope Array} (\textit{NuSTAR}) satellite. While \textit{NuSTAR} was designed as an astrophysics mission, it can observe the Sun above 2~keV with unprecedented sensitivity due to its pioneering use of focusing optics. \textit{NuSTAR} first observed quiet Sun regions on 2014 November 1, although out-of-view active regions contributed a notable amount of background in the form of single-bounce (unfocused) X-rays. We conducted a search for quiet Sun transient brightenings on time scales of 100 s and set upper limits on emission in two energy bands. We set 2.5--4~keV limits on brightenings with time scales of 100 s, expressed as the temperature T and emission measure EM of a thermal plasma. We also set 10--20~keV limits on brightenings with time scales of 30, 60, and 100 s, expressed as model-independent photon fluxes. The limits in both bands are well below previous HXR microflare detections, though not low enough to detect events of equivalent T and EM as quiet Sun brightenings seen in soft X-ray observations. We expect future observations during solar minimum to increase the \textit{NuSTAR} sensitivity by over two orders of magnitude due to higher instrument livetime and reduced solar background., Comment: 11 pages, 7 figures; accepted for publication in The Astrophysical Journal

NuSTAR is a highly sensitive focusing hard X-ray (HXR) telescope and has observed several small microflares in its initial solar pointings. In this paper, we present the first joint observation of a microflare with NuSTAR and Hinode/XRT on 2015 April 29 at ~11:29 UT. This microflare shows heating of material to several million Kelvin, observed in Soft X-rays (SXRs) with Hinode/XRT, and was faintly visible in Extreme Ultraviolet (EUV) with SDO/AIA. For three of the four NuSTAR observations of this region (pre-, decay, and post phases) the spectrum is well fitted by a single thermal model of 3.2-3.5 MK, but the spectrum during the impulsive phase shows additional emission up to 10 MK, emission equivalent to A0.1 GOES class. We recover the differential emission measure (DEM) using SDO/AIA, Hinode/XRT, and NuSTAR, giving unprecedented coverage in temperature. We find the pre-flare DEM peaks at ~3 MK and falls off sharply by 5 MK; but during the microflare's impulsive phase the emission above 3 MK is brighter and extends to 10 MK, giving a heating rate of about $2.5 \times 10^{25}$ erg s$^{-1}$. As the NuSTAR spectrum is purely thermal we determined upper-limits on the possible non-thermal bremsstrahlung emission. We find that for the accelerated electrons to be the source of the heating requires a power-law spectrum of $\delta \ge 7$ with a low energy cut-off $E_{c} \lesssim 7$ keV. In summary, this first NuSTAR microflare strongly resembles much more powerful flares., Comment: Accepted for publication in ApJ. 14 pages with 12 figures and 1 table

We present observations of the occulted active region AR12222 during the third {\em NuSTAR} solar campaign on 2014 December 11, with concurrent {\em SDO/}AIA and {\em FOXSI-2} sounding rocket observations. The active region produced a medium size solar flare one day before the observations, at $\sim18$UT on 2014 December 10, with the post-flare loops still visible at the time of {\em NuSTAR} observations. The time evolution of the source emission in the {\em SDO/}AIA $335\textrm{\AA}$ channel reveals the characteristics of an extreme-ultraviolet late phase event, caused by the continuous formation of new post-flare loops that arch higher and higher in the solar corona. The spectral fitting of {\em NuSTAR} observations yields an isothermal source, with temperature $3.8-4.6$ MK, emission measure $0.3-1.8 \times 10^{46}\textrm{ cm}^{-3}$, and density estimated at $2.5-6.0 \times 10^8 \textrm{ cm}^{-3}$. The observed AIA fluxes are consistent with the derived {\em NuSTAR} temperature range, favoring temperature values in the range $4.0-4.3$ MK. By examining the post-flare loops' cooling times and energy content, we estimate that at least 12 sets of post-flare loops were formed and subsequently cooled between the onset of the flare and {\em NuSTAR} observations, with their total thermal energy content an order of magnitude larger than the energy content at flare peak time. This indicates that the standard approach of using only the flare peak time to derive the total thermal energy content of a flare can lead to a large underestimation of its value., Comment: Published in ApJ, 8 pages

We present results from the the first campaign of dedicated solar observations undertaken by the \textit{Nuclear Spectroscopic Telescope ARray} ({\em NuSTAR}) hard X-ray telescope. Designed as an astrophysics mission, {\em NuSTAR} nonetheless has the capability of directly imaging the Sun at hard X-ray energies ($>$3~keV) with an increase in sensitivity of at least two magnitude compared to current non-focusing telescopes. In this paper we describe the scientific areas where \textit{NuSTAR} will make major improvements on existing solar measurements. We report on the techniques used to observe the Sun with \textit{NuSTAR}, their limitations and complications, and the procedures developed to optimize solar data quality derived from our experience with the initial solar observations. These first observations are briefly described, including the measurement of the Fe K-shell lines in a decaying X-class flare, hard X-ray emission from high in the solar corona, and full-disk hard X-ray images of the Sun., Comment: 11 pages, accepted to ApJ

A statistical study of the correlation between hard X-ray and white light emission in solar flares is performed in order to search for a link between flare-accelerated electrons and white light formation. We analyze 43 flares spanning GOES classes M and X using observations from RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) and HMI (Helioseismic and Magnetic Imager). We calculate X-ray fluxes at 30 keV and white light fluxes at 6173 \r{A} summed over the hard X-ray flare ribbons with an integration time of 45 seconds around the peak hard-X ray time. We find a good correlation between hard X-ray fluxes and excess white light fluxes, with a highest correlation coefficient of 0.68 for photons with energy of 30 keV. Assuming the thick target model, a similar correlation is found between the deposited power by flare-accelerated electrons and the white light fluxes. The correlation coefficient is found to be largest for energy deposition by electrons above ~50 keV. At higher electron energies the correlation decreases gradually while a rapid decrease is seen if the energy provided by low-energy electrons is added. This suggests that flare-accelerated electrons of energy ~50 keV are the main source for white light production., Comment: Accepted for publication by ApJ