NuSTAR Observation of Energy Release in 11 Solar Microflares.

Solar flares are explosive releases of magnetic energy. Hard X-ray (HXR) flare emission originates from both hot (millions of Kelvin) plasma and nonthermal accelerated particles, giving insight into flare energy release. The Nuclear Spectroscopic Telescope ARray (NuSTAR) utilizes direct-focusing optics to attain much higher sensitivity in the HXR range than that of previous indirect imagers. This paper presents 11 NuSTAR microflares from two active regions (AR 12671 on 2017 August 21 and AR 12712 on 2018 May 29). The temporal, spatial, and energetic properties of each are discussed in context with previously published HXR brightenings. They are seen to display several "large flare" properties, such as impulsive time profiles and earlier peak times in higher-energy HXRs. For two events where the active region background could be removed, microflare emission did not display spatial complexity; differing NuSTAR energy ranges had equivalent emission centroids. Finally, spectral fitting showed a high-energy excess over a single thermal model in all events. This excess was consistent with additional higher-temperature plasma volumes in 10/11 microflares and only with an accelerated particle distribution in the last. Previous NuSTAR studies focused on one or a few microflares at a time, making this the first to collectively examine a sizable number of events. Additionally, this paper introduces an observed variation in the NuSTAR gain unique to the extremely low livetime (<1%) regime and establishes a correction method to be used in future NuSTAR solar spectral analysis.

NuSTAR observations of a repeatedly microflaring active region.

We investigate the spatial, temporal, and spectral properties of 10 microflares from AR12721 on 2018 September 9 and 10 observed in X-rays using the Nuclear Spectroscopic Telescope ARray and the Solar Dynamic Observatory's Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager. We find GOES sub-A class equivalent microflare energies of 1026-1028 erg reaching temperatures up to 10 MK with consistent quiescent or hot active region (AR) core plasma temperatures of 3-4 MK. One microflare (SOL2018-09-09T10:33), with an equivalent GOES class of A0.1, has non-thermal hard X-ray emission during its impulsive phase (of non-thermal power ~7 × 1024 erg s-1) making it one of the faintest X-ray microflares to have direct evidence for accelerated electrons. In 4 of the 10 microflares, we find that the X-ray time profile matches fainter and more transient sources in the extreme-ultraviolet, highlighting the need for observations sensitive to only the hottest material that reaches temperatures higher than those of the AR core (>5 MK). Evidence for corresponding photospheric magnetic flux cancellation/emergence present at the footpoints of eight microflares is also observed.

Accelerated Electrons Observed Down to <7 keV in a NuSTAR Solar Microflare.

We report the detection of emission from a nonthermal electron distribution in a small solar microflare (GOES class A5.7) observed by the Nuclear Spectroscopic Telescope Array, with supporting observation by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The flaring plasma is well accounted for by a thick-target model of accelerated electrons collisionally thermalizing within the loop, akin to the "coronal thick-target" behavior occasionally observed in larger flares. This is the first positive detection of nonthermal hard X-rays from the Sun using a direct imager (as opposed to indirectly imaging instruments). The accelerated electron distribution has a spectral index of 6.3 ± 0.7, extends down to at least 6.5 keV, and deposits energy at a rate of ~2 × 1027 erg s-1, heating the flare loop to at least 10 MK. The existence of dominant nonthermal emission in X-rays down to <5 keV means that RHESSI emission is almost entirely nonthermal, contrary to what is usually assumed in RHESSI spectroscopy. The ratio of nonthermal to thermal energies is similar to that of large flares, in contrast to what has been found in previous studies of small RHESSI flares. We suggest that a coronal thick target may be a common property of many small microflares based on the average electron energy and collisional mean free path. Future observations of this kind will enable understanding of how flare particle acceleration changes across energy scales, and will aid the push toward the observational regime of nanoflares, which are a possible source of significant coronal heating.

NuSTAR Observation of a Minuscule Microflare in a Solar Active Region.

We present X-ray imaging spectroscopy of one of the weakest active region (AR) microflares ever studied. The microflare occurred at ~11:04 UT on 2018 September 9 and we studied it using the Nuclear Spectroscopic Telescope ARray (NuSTAR) and the Solar Dynamic Observatory's Atmospheric Imaging Assembly (SDO/AIA). The microflare is observed clearly in 2.5-7 keV with NuSTAR and in Fe XVIII emission derived from the hotter component of the 94 Å SDO/AIA channel. We estimate the event to be three orders of magnitude lower than a GOES A class microflare with an energy of 1.1 × 1026 erg. It reaches temperatures of 6.7 MK with an emission measure of 8.0 × 1043 cm-3. Non-thermal emission is not detected but we instead determine upper limits to such emission. We present the lowest thermal energy estimate for an AR microflare in literature, which is at the lower limits of what is still considered an X-ray microflare.

Sensitivity of a juvenile subject-specific musculoskeletal model of the ankle joint to the variability of operator-dependent input.

Subject-specific musculoskeletal modelling is especially useful in the study of juvenile and pathological subjects. However, such methodologies typically require a human operator to identify key landmarks from medical imaging data and are thus affected by unavoidable variability in the parameters defined and subsequent model predictions. The aim of this study was to thus quantify the inter- and intra-operator repeatability of a subject-specific modelling methodology developed for the analysis of subjects with juvenile idiopathic arthritis. Three operators each created subject-specific musculoskeletal foot and ankle models via palpation of bony landmarks, adjustment of geometrical muscle points and definition of joint coordinate systems. These models were then fused to a generic Arnold lower limb model for each of three modelled patients. The repeatability of each modelling operation was found to be comparable to those previously reported for the modelling of healthy, adult subjects. However, the inter-operator repeatability of muscle point definition was significantly greater than intra-operator repeatability ( p < 0.05) and predicted ankle joint contact forces ranged by up to 24% and 10% of the peak force for the inter- and intra-operator analyses, respectively. Similarly, the maximum inter- and intra-operator variations in muscle force output were 64% and 23% of peak force, respectively. Our results suggest that subject-specific modelling is operator dependent at the foot and ankle, with the definition of muscle geometry the most significant source of output uncertainty. The development of automated procedures to prevent the misplacement of crucial muscle points should therefore be considered a particular priority for those developing subject-specific models.

A Patient-Specific Foot Model for the Estimate of Ankle Joint Forces in Patients with Juvenile Idiopathic Arthritis.

Juvenile idiopathic arthritis (JIA) is the leading cause of childhood disability from a musculoskeletal disorder. It generally affects large joints such as the knee and the ankle, often causing structural damage. Different factors contribute to the damage onset, including altered joint loading and other mechanical factors, associated with pain and inflammation. The prediction of patients' joint loading can hence be a valuable tool in understanding the disease mechanisms involved in structural damage progression. A number of lower-limb musculoskeletal models have been proposed to analyse the hip and knee joints, but juvenile models of the foot are still lacking. This paper presents a modelling pipeline that allows the creation of juvenile patient-specific models starting from lower limb kinematics and foot and ankle MRI data. This pipeline has been applied to data from three children with JIA and the importance of patient-specific parameters and modelling assumptions has been tested in a sensitivity analysis focused on the variation of the joint reaction forces. This analysis highlighted the criticality of patient-specific definition of the ankle joint axes and location of the Achilles tendon insertions. Patient-specific detection of the Tibialis Anterior, Tibialis Posterior, and Peroneus Longus origins and insertions were also shown to be important.

Evaluation of a Kinematically-Driven Finite Element Footstrike Model.

A dynamic finite element model of a shod running footstrike was developed and driven with 6 degree of freedom foot segment kinematics determined from a motion capture running trial. Quadratic tetrahedral elements were used to mesh the footwear components with material models determined from appropriate mechanical tests. Model outputs were compared with experimental high-speed video (HSV) footage, vertical ground reaction force (GRF), and center of pressure (COP) excursion to determine whether such an approach is appropriate for the development of athletic footwear. Although unquantified, good visual agreement to the HSV footage was observed but significant discrepancies were found between the model and experimental GRF and COP readings (9% and 61% of model readings outside of the mean experimental reading ± 2 standard deviations, respectively). Model output was also found to be highly sensitive to input kinematics with a 120% increase in maximum GRF observed when translating the force platform 2 mm vertically. While representing an alternative approach to existing dynamic finite element footstrike models, loading highly representative of an experimental trial was not found to be achievable when employing exclusively kinematic boundary conditions. This significantly limits the usefulness of employing such an approach in the footwear development process.

A new method of observing weak extended x-ray sources with the Reuven Ramaty high-energy solar spectroscopic imager.

We present a new method, fan-beam modulation, for observing weak extended x-ray sources with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). This space-based solar x-ray and gamma-ray telescope has much greater sensitivity than previous experiments in the 3-25 keV range, but is normally not well suited to detecting extended sources since their signal is not modulated by RHESSI's rotating grids. When the spacecraft is offpointed from the target source, however, the fan-beam modulation time-modulates the transmission by shadowing resulting from exploiting the finite thickness of the grids. In this article we detail how the technique is implemented and verify its consistency with sources with clear known signals that have occurred during RHESSI offpointing: microflares and the Crab Nebula. In both cases the results are consistent with previous and complementary measurements. Preliminary work indicates that this new technique allows RHESSI to observe the integrated hard x-ray spectrum of weak extended sources on the quiet Sun.