Iain G. Hannah

Differential emission measures from the regularized inversion of Hinode and SDO data

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 ΔlogT ≈ 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.

A Trace white light and Rhessi hard X-ray study of flare energetics

In this paper we investigate the formation of the white-light (WL) continuum during solar flares and its relationship to energy deposition by electron beams inferred from hard X-ray emission. We analyze nine flares spanning GOES classifications from C4.8 to M9.1, seven of which show clear cospatial RHESSI hard X-ray and TRACE WL footpoints. We characterize the TRACE WL/UV continuum energy under two simplifying assumptions: (1) a blackbody function, or (2) a Paschen-Balmer continuum model. These set limits on the energy in the continuum, which we compare with that provided by flare electrons under the usual collisional thick-target assumptions. We find that the power required by the white-light luminosity enhancement is comparable to the electron beam power required to produce the HXR emission only if the low-energy cutoff to the spectrum is less than 25 keV. The bulk of the energy required to power the white-light flare (WLF) therefore resides at these low energies. Since such low-energy electrons cannot penetrate deep into a collisional thick target, this implies that the continuum enhancement is due to processes occurring at moderate depths in the chromosphere.

RHESSI Microflare Statistics. II. X-Ray Imaging, Spectroscopy, and Energy Distributions

We present the first statistical analysis of the thermal and nonthermal X-ray emission of all 25,705 microflares (RHESSI) observed between 2002 March and 2007 March. These events were found by searching the 6-12 keV energy range (see Paper I) and are small active region flares, from low (GOES) C class to below A class. 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 resulting wealth of information we determine about the events allows a range of the thermal and nonthermal properties to be investigated. In particular, we find that there is no correlation between the thermal loop size and the flare magnitude, indicating that microflares are not necessarily spatially small. We present the first thermal energy distribution of RHESSI flares and compare it to previous thermal energy distributions of transient events. We also present the first nonthermal power distribution of RHESSI flares and find that a few microflares have unexpectedly large nonthermal powers up to -->1028 erg s?1. The total microflare nonthermal energy, however, is still small compared to that of large flares as it occurs for shorter durations. These large energies and difficulties in analyzing the steep nonthermal spectra suggest that a sharp broken power law and thick-target bremsstrahlung model may not be appropriate for microflares.

RHESSI Microflare Statistics. I. Flare-Finding and Frequency Distributions

We present the first in-depth statistical survey of all X-ray microflares observed by RHESSI between 2002 March and 2007 March, a total of 25,705 events, an order of magnitude larger then previous studies. These microflares were found using a new flare-finding algorithm designed to search the 6-12 keV count rate when RHESSIs full sensitivity was available in order to find the smallest events. The peak and total count rate are automatically obtained along with count spectra at the peak and the microflare centroid position. Our microflare magnitudes are below GOES C class, on average GOES A class (background subtracted). They are found to occur only in active regions, not in the quiet Sun, and are similar to large flares. The monthly average microflaring rate is found to vary with the solar cycle and ranges from 90 to 5 flares a day during active and quiet times, respectively. Most flares are found to be impulsive (74%), with rise times shorter than decay times. The mean flare duration is ~6 minutes with a 1 minute minimum set by the flare-finding algorithm. The frequency distributions of the peak count rate in the energy bands, 3-6, 6-12, and 12-25 keV, can be represented by power-law distributions with a negative power-law index of -->1.50 ± 0.03, -->1.51 ± 0.03, and -->1.58 ± 0.02, respectively. We find that these power-law indices are constant as a function of time. The X-ray photon spectra for individual events can be approximated with a power-law spectrum [ -->dJ/d(hν) ~ (hν)−γ]. Using the ratio of photon fluxes between 10-15 and 15-20 keV, we find -->4 -1.7 ± 0.1. We estimate the total energy flux deposited in active regions by microflare-associated accelerated electrons (>10 keV) over the five years of observations to be, on average, below 1026 erg s−1.

HOT SPINE LOOPS AND THE NATURE OF A LATE-PHASE SOLAR FLARE

The fan-spine magnetic topology is believed to be responsible for many curious emission signatures in solar explosive events. A spine field line links topologically distinct flux domains, but direct observation of such structure has been rare. Here we report a unique event observed by the Solar Dynamic Observatory (SDO) where a set of hot coronal loops (over 10 MK) that developed during the rising phase of a flare connected to a quasi-circular ribbon at one end and a remote brightening at the other. Magnetic field extrapolation suggests these loops are partly tracers of the evolving spine field line. The sequential brightening of the ribbon, the apparent shuffling loop motion, and the increasing volume occupied by the hot loops suggest that continuous slipping- and null-point-type reconnections were at work, energizing the loop plasma and transferring magnetic flux within and across the dome-shaped, fan quasi-separatrix layer (QSL). We argue that the initial reconnection is of the “breakout” type, which then transitioned to a more violent flare reconnection nearing the flare peak with an eruption from the fan dome. Significant magnetic field changes are expected and indeed ensued, which include a change of the horizontal photospheric field, a shift of the QSL footprint, and reduction in shear of the coronal loops. This event also features an extreme-ultraviolet (EUV) late phase, i.e. a secondary emission peak observed in warm EUV lines (about 2‐7 MK) as much as 1‐2 hours after the soft X-ray peak. We show that this peak comes from the large post-reconnection loops beside and above the compact fan dome, a direct product of eruption in such topological settings. Cooling of these “late-phase arcades” naturally explains the sequential delay of the late-phase peaks in increasingly cooler EUV lines. 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 ‐ minor topological change in a sub-system may lead to explosions on a much larger scale. Subject headings: Sun: activity — Sun: corona — Sun: flares — Sun: surface magnetism — Sun: magnetic topology

Microflares and the Statistics of X-Ray Flares

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.

Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop

Aims. A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to inf er sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods. Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and ce ntroid positions of hard X-ray sources with sub-arcsecond r esolution (∼ 0.2 ′′ ) for a solar limb flare. We show that the height variations of t he chromospheric density and the magnetic flux densities can be found with unprecedented vertical resolution of∼ 150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results. Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tube in the chromosphere with height. The magnetic scale height B(z) (dB/dz) −1 is found to be of the order of 300 km and strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of∼ 900 km.

Multi-thermal dynamics and energetics of a coronal mass ejection in the low solar atmosphere

Aims. The aim of this work is to determine the multi-thermal characteristics and plasma energetics of an eruptive plasmoid and occulted flare observed by the Solar Dynamics Observatory’s Atmospheric Imaging Assembly (SDO/AIA). Methods. We study a 2010 Nov. 3 event (peaking at 12:20 UT in GOES soft X-rays) of a coronal mass ejection and occulted flare that demonstrates the morphology of a classic erupting flux rope. The high spatial and time resolution and six coronal channels of the SDO/AIA images allows the dynamics of the multi-thermal emission during the initial phases of eruption to be studied in detail. The differential emission measure is calculated, using an optimized version of a regularized inversion method, for each pixel across the six channels at different times, resulting in emission measure maps and movies in a variety of temperature ranges. Results. We find that the core of the erupting plasmoid is hot (8–11, 11–14 MK) with a similarly hot filamentary “stem” structure connecting it to the lower atmosphere, which could be interpreted as the current sheet in the flux rope model, though is wider than these models suggest. The velocity of the leading edge of the eruption is 597–664 km s-1 in the temperature range ≥3–4 MK and between 1029–1246 km s-1 for ≤2–3 MK. We estimate the density (in 11–14 MK) of the erupting core and stem during the impulsive phase to be about 3 × 109 cm-3, 6 × 109 cm-3, 9 × 108 cm-3 in the plasmoid core, stem, and surrounding envelope of material. This gives thermal energy estimates of 5 × 1029 erg, 1 × 1029 erg, and 2 × 1030 erg. The kinetic energy for the core and envelope is slightly lower. The thermal energy of the core and current sheet grows during the eruption, suggesting continuous influx of energy presumably via reconnection. Conclusions. The combination of the optimized regularized inversion method and SDO/AIA data allows the multi-thermal characteristics (i.e. velocity, density, and thermal energies) of the plasmoid eruption to be determined.

ACCELERATION, MAGNETIC FLUCTUATIONS, AND CROSS-FIELD TRANSPORT OF ENERGETIC ELECTRONS IN A SOLAR FLARE LOOP

Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration, and transport. Using RHESSI observations and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, 2002 April 14, 23:55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length ~2 × 109 cm and width ~7 × 108 cm. Energy-dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration.

The Sub-arcsecond Hard X-ray Structure of Loop Footpoints in a Solar Flare

The newly developed X-ray visibility forward fitting technique is applied to the RHESSI data of a limb flare to investigate the energy and height dependence on sizes, shapes, and position of hard X-ray (HXR) chromospheric footpoint sources. This provides information about the electron transport and chromospheric density structure. The spatial distribution of two footpoint X-ray sources is analyzed using PIXON, Maximum Entropy Method, CLEAN, and visibility forward fit algorithms at nonthermal energies from ~20 to ~200 keV. We report, for the first time, the vertical extents and widths of HXR chromospheric sources measured as a function of energy for a limb event. Our observations suggest that both the vertical and horizontal sizes of footpoints are decreasing with energy. Higher energy emission originates progressively deeper in the chromosphere, consistent with downward flare accelerated streaming electrons. The ellipticity of the footpoints grows with energy from ~0.5 at ~20 keV to ~0.9 at ~150 keV. The positions of X-ray emission are in agreement with an exponential density profile of scale height ~150 km. The characteristic size of the HXR footpoint source along the limb decreases with energy, suggesting a converging magnetic field in the footpoint. The vertical sizes of X-ray sources are inconsistent with simple collisional transport in a single density scale height but can be explained using a multi-threaded density structure in the chromosphere.