Aims. To demonstrate the capabilities of regularized inversion to recover differential emission measures (DEMs) from multiwavelength observations provided by telescopes such as Hinode and SDO. Methods. We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions.Results. The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is Δ log T ≈ 0.1−0.5 and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time. Conclusions. Regularized inversion quickly determines the DEM from solar observations and provides reliable error estimates (both horizontal and vertical) which allows the temperature spread of coronal plasma to be robustly quantified.

We present X-ray imaging and spectral analysis of all microflares the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observed between March 2002 and March 2007, a total of 25,705 events. These microflares are small flares, from low GOES C Class to below A Class (background subtracted) and are associated with active regions. They were found by searching the 6-12 keV energy range during periods when the full sensitivity of RHESSI's detectors was available (see paper I). Each microflare is automatically analyzed at the peak time of the 6-12 keV emission: the thermal source size is found by forward-fitting the complex visibilities for 4-8 keV, and the spectral parameters (temperature, emission measure, power-law index) are found by forward fitting a thermal plus nonthermal model. The combination of these parameters allows us to present the first statistical analysis of the thermal and non-thermal energy at the peak times of microflares. On average a RHESSI microflare has a fitted thermal loop width 8 Mm (11 ′′ ), length 23 Mm (32 ′′ ) and volume 1×10 27 cm 3 , temperature 13 MK, emission measure 3 × 10 46 cm −3 and density of 6 × 10 9 cm −3 . There is no correlation between the loop size and the flare magnitude, either flux in the loop or GOES class, indicating that microflares are not necessarily spatially small. There is also no clear correlation between the thermal parameters except between the RHESSI and GOES emission measures, the GOES values are generally twice the RHESSI emission measures. The microflare thermal energy at the time of peak emission in 6-12 keV ranges over 10 26 to 10 30 erg and has a median value of 10 28 erg. The frequency distribution of the thermal energy deviates from a power-law at low and high energies arising from a deficiency of events due to instrumental and selection effects. It is difficult to compare this energy distribution to previous thermal energy distributions of transient events, as the work sought nanoflares through imaging in EUV or soft X-rays and covered just a few hours. There are large uncertainties in the majority of the non-thermal parameters, due to the steep spectra down to low energies. We typically find a power-law index of 7 above a break energy of 9 keV, which corresponds to a low-energy cut-off in the electron distribution as low as 12 keV. The resulting non-thermal power estimates, covering 10 25 to 10 28 erg s −1 with median value of 10 26 erg s −1 , therefore have large uncertainties as well. The few microflares with unexpectedly large non-thermal powers 10 28 erg s −1 have the smallest uncertainties, of about 10%. The total non-thermal energy however is still small compared to that of large flares as it occurs for shorter durations.

The fan-spine magnetic topology is believed to be responsible for many curious features in solar explosive events. A spine field line links distinct flux domains, but direct observation of such feature has been rare. Here we report a unique event observed by the Solar Dynamic Observatory where a set of hot coronal loops (over 10 MK) connected to a quasi-circular chromospheric ribbon at one end and a remote brightening at the other. Magnetic field extrapolation suggests these loops are partly tracer of the evolving spine field line. Continuous slipping-and null-point-type reconnections were likely at work, energizing the loop plasma and transferring magnetic flux within and across the fan quasi-separatrix layer. We argue that the initial reconnection is of the "breakout" type, which then transitioned to a more violent flare reconnection with an eruption from the fan dome. Significant magnetic field changes are expected and indeed ensued. This event also features an extreme-ultraviolet (EUV) late phase, i.e. a delayed secondary emission peak in warm EUV lines (about 2-7 MK). We show that this peak comes from the cooling of large post-reconnection loops beside and above the compact fan, a direct product of eruption in such topological settings. The long cooling time of the large arcades contributes to the long delay; additional heating may also be required. Our result demonstrates the critical nature of cross-scale magnetic coupling -topological change in a sub-system may lead to explosions on a much larger scale.

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This review surveys the statistics of solar X-ray flares, emphasising the new views that RHESSI has given us of the weaker events (the microflares). The new data reveal that these microflares strongly resemble more energetic events in most respects; they occur solely within active regions and exhibit high-temperature/nonthermal emissions in approximately the same proportion as major events. We discuss the distributions of flare parameters (e.g., peak flux) and how these parameters correlate, for instance via the Neupert effect. We also highlight the systematic biases involved in intercomparing data representing many decades of event magnitude. The intermittency of the flare/microflare occurrence, both in space and in time, argues that these discrete events do not explain general coronal heating, either in active regions or in the quiet Sun.