Energetics and morphology of powerful impulsive solar flares

We have studied the energetics of two impulsive solar flares of X-ray class X1.7 by assuming the electrons accelerated in several episodes of energy release to be the main source of plasma heating and reached conclusions about their morphology. The time profiles of the flare plasma temperature, emission measure, and their derivatives, and the intensity of nonthermal X-ray emission are compared; images of the X-ray sources and magnetograms of the flare region at key instants of time have been constructed. Based on a spectral analysis of the hard X-ray emission from RHESSI data and GOES observations of the soft X-ray emission, we have estimated the spatially integrated kinetic power of nonthermal electrons and the change in flare-plasma internal energy by taking into account the heat losses through thermal conduction and radiation and determined the parameters needed for thermal balance. We have established that the electrons accelerated at the beginning of the events with a relatively soft spectrum directly heat up the coronal part of the flare loops, with the increase in emission measure and hard X-ray emission from the chromosphere being negligible. The succeeding episodes of electron acceleration with a harder spectrum have virtually no effect on the temperature rise, but they lead to an increase in emission measure and hard X-ray emission from the footpoints of the flare loops.     

Observations of the December 6, 2006 solar flare: Electron acceleration and plasma heating

The flare plasma temperature calculated from GOES-11 (1.5–12.4 and 3.1–24.8 keV) data is compared with the solar nonthermal fluxes in various energy ranges in the December 6, 2006 event. Particle acceleration and plasma heating episodes took place in the pre-flare and impulsive phases; a hard (ACS SPI > 150 keV) X-ray emission was observed 5 min before the onset of the GOES X-ray flare and was not accompanied by a temperature rise. A close correlation has been found between the flare plasma temperature and the hard X-ray intensity. The temperature delayed by 0.4 min turned out to be directly proportional to the logarithm of the ACS SPI count rate within the first 3 min of the impulsive phase. This shows that the accelerated electrons responsible for the X-ray emission were the main plasma heating source in the pre-flare and impulsive phases. The correlation between the temperature and the hard X-ray intensity disappears after the observation of a resonance peak at a frequency of 245 MHz. Significant electron fluxes may no longer be able to effectively heat the expanding plasma when its density in the interaction region reaches ∼10⁹ cm⁻³. The observations of the July 23, 2002 and December 5, 2006 events confirm the trends found.     

Hard X-ray imaging evidence of nonthermal and thermal burst components

We analyze hard X-ray imaging observations of three flares, showing widely different characteristics, in order to try and discriminate the relative efficiency of heating and acceleration in the primary energy release. Using a simplified approach, we compute the hard X-ray distribution and energy deposition due to accelerated electrons, with beam and ambient plasma parameters appropriate for each of the observed events. The results are convolved with the Hard X-Ray Imaging Spectrometer (HXIS) instrumental response and compared with observations. We find that: (a) Many observations are compatible with thick target processes, and with the possibility that flares may have high (>20%) acceleration efficiency. (b) Single hard X-ray sources should be very common in the data available at present (HXIS and HINOTORI), as it is the case, as well as a transition from chromospheric footpoints to single source structures. The latter cannot then be directly interpreted as thermal sources. (c) In the particular case of a limb flare, associated with a rather weak high energy burst, we show that the spatial and spectral behavior of the hard X-ray emission is incompatible with pure nonthermal processes. We thus propose that the observed emission was principally due to the strong heating intrinsic to a reconnection process within the region of interaction between two magnetic structures which are seen in the soft X-ray data. (d) We also study the heating effect of a beam, due to Coulomb losses, during its passage through the flare loops. In some cases, rather large and localized temperature increases can be expected to appear within short timescales ( 1 s), leading to a combination of nonthermal plus thermal output in the hard X-ray spectrum, which renders virtually impossible the determination of the underlying beam parameters. We finally discuss the extent to which our conclusions are valid, considering the instrumental limitations as well as the simple physical treatment that we apply.     

Acceleration of Relativistic Protons During the 20 January 2005 Flare and CME

The origin of relativistic solar protons during large flare/CME events has not been uniquely identified so far. We perform a detailed comparative analysis of the time profiles of relativistic protons detected by the worldwide network of neutron monitors at Earth with electromagnetic signatures of particle acceleration in the solar corona during the large particle event of 20 January 2005. The intensity – time profile of the relativistic protons derived from the neutron monitor data indicates two successive peaks. We show that microwave, hard X-ray, and γ-ray emissions display several episodes of particle acceleration within the impulsive flare phase. The first relativistic protons detected at Earth are accelerated together with relativistic electrons and with protons that produce pion-decay γ rays during the second episode. The second peak in the relativistic proton profile at Earth is accompanied by new signatures of particle acceleration in the corona within ≈1R _⊙ above the photosphere, revealed by hard X-ray and microwave emissions of low intensity and by the renewed radio emission of electron beams and of a coronal shock wave. We discuss the observations in terms of different scenarios of particle acceleration in the corona.     

Hard X-ray bursts from flares behind the solar limb

The determination of the location of the region of origin of hard X-rays is important in evaluating the importance of 10–100 keV electrons in solar flares and in understanding flare particle acceleration. At present only limb-occulted events are available to give some information on the height of X-ray emission. In fifteen months of OSO-7 operation, nine major soft X-ray events had no reported correlated Hα flare. We examine the hard X-ray spectra of eight of these events with good candidate X-ray flare producing active regions making limb transit at the time of the soft X-ray bursts. All eight bursts had significant X-ray emission in the 30–44 keV range, but only one had flux at the 3σ level above 44 keV. The data are consistent with most X-ray emission occurring in the lower chromosphere, but some electron trapping at high altitudes is necessary to explain the small nonthermal fluxes observed.     

Energetics of a double flare on November 8, 1980

Here we complete an energy balance analysis of a double impulsive hard X-ray flare. From spatial observations, we deduce both flares probably occur in the same loop within the resolution of the data. For the first flare, the energy in the fast electrons (assuming a thick-target model) is comparable to the convective up-flow energy, suggesting that these are related successive modes of energy storage and transfer. The total energy lost through radiation and conduction, 2.0 × 10²⁸ erg, is comparable to the energy in fast electrons 2.5 × 10²⁸ erg. For the second flare, the energy in the fast electrons is more than one order of magnitude greater than the energy of the convective up-flow. Total energy losses are within a factor of two lower than the calculated fast electron energy. We interpret the observations as showing that the first flare occurred in a small loop with fast electrons heating the chromosphere and resulting in chromospheric evaporation increasing the density in the loop. For the second flare most of the heating occurred at the electron acceleration site. The two symmetrical components of the Ca xix resonance line and a high velocity down-flow of 115 km s ^–1 observed at the end of the second hard X-ray burst are consistent with the flare eruption (reconnection) region being high in the flare loop. The estimated altitude of the acceleration site is 5500 km above the photosphere.     

Electron Acceleration and Transport During the November 5, 1998 Solar Flare At ∼13:34 UT

This paper deals with a detailed analysis of spectral and imaging observations of the November 5, 1998 (Hα 1B, GOES M1.5) flare obtained over a large spectral range, i.e., from hard X-rays to radiometric wavelengths. These observations allowed us to probe electron acceleration and transport over a large range of altitudes that is to say within small-scale (a few 10³ km) and large-scale (a few 10⁵ km) magnetic structures. The observations combined with potential and linear force-free magnetic field extrapolations allow us to show that: (i) Flare energy release and electron acceleration are basically driven by loop–loop interactions at two independent, low lying, null points of the active region magnetic field; (ii) <300 keV hard X-ray-producing electrons are accelerated by a different process (probably DC field acceleration) than relativistic electrons that radiate the microwave emission; and (iii) although there is evidence that hard X-ray and decimetric/metric radio-emitting electrons are produced by the same accelerator, the present observations and analysis did not allow us to find a clear and direct magnetic connection between the hard X-ray emitting region and the radio-emitting sources in the middle corona.     

Imaging Observations of Quasi-Periodic Pulsatory Nonthermal Emission in Two-Ribbon Solar Flares

Using RHESSI and some auxiliary observations we examine possible connections between the spatial and temporal structure of nonthermal hard X-ray (HXR) emission sources from the two-ribbon flares of 29 May 2003 and 19 January 2005. In each of these events quasi-periodic pulsations (QPP) with time period of 1 – 3 minutes are evident in both hard X rays and microwaves. The sources of nonthermal HXR emission are situated mainly at the footpoints of the flare arcade loops observed by TRACE and the SOHO/EIT instrument in the EUV range. At least one of the sources moves systematically during and after the QPP phase in each flare. The sources move predominantly parallel to the magnetic inversion line during the 29 May flare and along flare ribbons during the QPP phase of both flares. By contrast, the sources start to show movement perpendicular to the flare ribbons with velocity comparable to that along the ribbons’ movement after the QPP phase. The sources of each pulse are localized in distinct parts of the ribbon during the QPP phase. The measured velocity of the sources and the estimated energy release rate do not correlate well with the flux of the HXR emission calculated from these sources. The sources of microwaves and thermal HXRs are situated near the apex of the flare loop arcade and are not stationary either. Almost all of the QPP as well as some pulses of nonthermal HXR emission during the post-QPP phase reveal soft – hard – soft spectral behavior, indicating separate acts of electron acceleration and injection. In our opinion at least two different flare scenarios based on the Nakariakov et al. (2006, Astron. Astrophys. 452, 343) model and on the idea of current-carrying loop coalescence are suitable for interpreting the observations. However, it is currently not possible to choose between them owing to observational limitations.     

Evolution of White-Light Flares Observed by YOHKOH

We consider in detail the evolutionary patterns of few white-light flares observed by Yohkoh. The following data have been used in the analysis: sequences of de-convolved SXT images in X-ray and optical filters, MEM reconstructed HXT images and the other supporting data. The resolution in the de-convolved images is below 1 arc sec. Working with sequences of de-convolved images makes it also possible to investigate the dynamics of these structures with high spatial accuracy. Comparison of the morphology of flare brightenings as observed in hard, soft and optical ranges reveals that these emissions are not co-spatial and are most probably related to different plasma volumes at any instant. These observations cannot be easily accommodated within standard flare scenarios. Traditionally, the hard and optical flare emissions are expected to be co-spatial and the soft X-ray emission is presumed to fill the coronal portion of flaring loop(s) during rise phase. Present observations do not easily fit to such scenario.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

Prolonged nonthermal emission from solar flares and the Neupert effect

We analyze the observations of the hard (ACS SPI, > 150 keV) and soft (GOES, 1–8 Å) X-ray emissions and the microwave (15.5 GHz) emission in the solar flares on September 7, 2005 and December 6 and 13, 2006. The time profiles of the nonthermal emission from these flares had a complex structure, suggesting that active processes in the flare region continued for a long time (more than an hour). We have verified the linear relationship between the nonthermal flux and the time derivative of the soft X-ray flux (the Neupert effect) in the events under consideration. In the first two cases, the Neupert effect held at the time of the most intense nonthermal emission peak, but not at the decay phase of the soft X-ray emission, when the intensity of the nonthermal emission was much higher than the background values. At the same time, the hard X-ray emission was suppressed compared to the main peak, while the microwave emission remained approximately at the same level. In the December 13, 2006 event, the prolonged hard X-ray emission was difficult to observe due to the fast arrival of solar protons, but the Neupert effect did not hold for its main peak either. At comparable intensities of the microwave emission on December 6 and 13, the intensity of the hard X-ray emission on December 13 at the time of the main peak was suppressed approximately by an order of magnitude. These observational facts are indicative of several particle acceleration and interaction episodes under various physical conditions during one flare. When the Neupert effect did not hold, the interaction of electrons took place mainly in a low-density medium. An effective escape of accelerated particles into interplanetary space rather than their precipitation into dense layers of the solar atmosphere may take place precisely at this time.     

X-ray imaging of three flares during the impulsive phase

The impulsive phases of three flares that occurred on April 10, May 21, and November 5, 1980 are discussed. Observations were obtained with the Hard X-ray Imaging Spectrometer (HXIS) and other instruments aboard SMM, and have been supplemented with Hα data and magnetograms. The flares show hard X-ray brightenings (16–30 keV) at widely separated locations that spatially coincide with bright Hα patches. The bulk of the soft X-ray emission (3.5–5.5 keV) originates from in between the hard X-ray brightenings. The latter are located at different sides of the neutral line and start to brighten simultaneously to within the time resolution of HXIS. Concluded is that:

1. The bright hard X-ray patches coincide with the footpoints of loops.
2. The hard X-ray emission from the footpoints is most likely thick target emission from fast electrons moving downward into the dense chromosphere.
3. The density of the loops along which the beam electrons propagate to the footpoints is restricted to a narrow range (10⁹ < n < 2 × 10¹⁰ cm^-3), determined by the instability threshold of the return current and the condition that the mean free path of the fast electrons should be larger than the length of the loop.
4. For the November 5 flare it seems likely that the acceleration source is located at the merging point of two loops near one of the footpoints.

It is found that the total flare energy is always larger than the total energy residing in the beam electrons. However, it is also estimated that at the time of the peak of the impulsive hard X-ray emission a large fraction (at least 20%) of the dissipated flare power has to go into electron acceleration. The explanation of such a high acceleration efficiency remains a major theoretical problem.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (≲1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting ∼3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to ≳100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically ∼10² kV compared to ∼10 kV for auroral substorms.

     

On the reconciliation of simultaneous microwave imaging and hard X-ray observations of a solar flare

We have compared microwave imaging data for a small flare with simultaneous hard X-ray spectral observations. The X-ray data suggest that the power-law index of the energy distribution of the radiating electrons is 5.3 (thick-target) which differs significantly from the estimate ( = 1.4) from a homogeneous optically-thin gyrosynchrotron model which fits the radio observations well. In order to reconcile these results, we explore a number of options. We investigate a double power-law energy spectrum for the energetic electrons in the flare, as assumed by other authors: the power law is steep at low energies and much flatter at the higher energies which produce the bulk of the microwaves. The deduced break energy is about 230 keV if we tentatively ignore the X-ray emission from the radio-emitting electrons: however, the emission of soft photons by the flat tail strongly contributes to the observed hard X-ray range and would flatten the spectrum there. A thin-target model for the X-ray emission is also inconsistent with radio data. An inhomogeneous gyrosynchrotron model with a number of free parameters and containing an electron distribution given by the thick-target X-ray model could be made to fit the radio data.     

Solar Impulsive Hard X-Ray Emission and Two-Stage Electron Acceleration

Heating and acceleration of electrons in solar impulsive hard X-ray (HXR) flares are studied according to the two-stage acceleration model developed by Zhang for solar 3He-rich events. It is shown that electrostatic H-cyclotron waves can be excited at a parallel phase velocity less than about the electron thermal velocity and thus can significantly heat the electrons (up to 40 MK) through Landau resonance. The preheated electrons with velocities above a threshold are further accelerated to high energies in the flare-acceleration process. The flare-produced electron spectrum is obtained and shown to be thermal at low energies and power law at high energies. In the non-thermal energy range, the spectrum can be double power law if the spectral power index is energy dependent or related. The electron energy spectrum obtained by this study agrees quantitatively with the result derived from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) HXR observations in the flare of 2002 July 23. The total flux and energy flux of electrons accelerated in the solar flare also agree with the measurements.     

High-Energy Emission from a Solar Flare in Hard X-rays and Microwaves

We investigate accelerated electron energy spectra for different sources in a large flare using simultaneous observations obtained with two instruments, the Nobeyama Radio Heliograph (NoRH) at 17 and 34 GHz, and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) at hard X-rays. This flare is one of the few in which emission up to energies exceeding 200 keV can be imaged in hard X-rays. Furthermore, we can investigate the spectra of individual sources up to this energy. We discuss and compare the HXR and microwave spectra and morphology. Although the event overall appears to correspond to the standard scenario with magnetic reconnection under an eruptive filament, several of its features do not seem to be consistent with popular flare models. In particular we find that (1) microwave emissions might be optically thick at high frequencies despite a low peak frequency in the total flux radio spectrum, presumably due to the inhomogeneity of the emitting source; (2) magnetic fields in high-frequency radio sources might be stronger than sometimes assumed; (3) sources spread over a very large volume can show matching evolution in their hard X-ray spectra that may provide a challenge to acceleration models. Our results emphasize the importance of studies of sunspot-associated flares and total flux measurements of radio bursts in the millimeter range.     

Energetics of a compact flare

We study the spatial and spectral characteristics of the 3.5 to 30.0 keV emission in a solar flare of 9 May, 1980. We find that: (a) A classical thick target interpretation of the hard X-ray burst at energies E 10 keV implies that approximately all the electrons contained within the flare loop(s) have to be accelerated per second. (b) A thermal model interpretation does not fit the data, unless its characteristics are such that it does not represent an efficient alternative to the acceleration model. We thus conclude that: (c) Acceleration does take place during the early phase of the impulsive hard X-ray event, but substantial amount of the emission at low (<20 keV) energies is of thermal origin. (d) We show the evolution of the energy content in the flare volume, and find that the energy input requirements are such that 10² erg cm^-3 s^-1 have to be released within the flare structure(s), for a period of time comparable to that of the hard X-ray burst emission. We also point out that although the main flare component ( 90% of the soft X-ray emission) was confined to a compact magnetic kernel, there are evidences of interaction of this structure with a larger field structure connecting towards the leading portion of the active region, where secondary H brightenings were observed.     

Analysis of the August 7, 1972 white light flare: Light curves and correlation with hard X-rays

Cinematic, photometric observations of the 3B flare of August 7, 1972 are described in detail. The time resolution was 2 s; the spatial resolution was 1–2″. Flare continuum emissivity at 4950 Å and at 5900 Å correlated closely in time with the 60–100 keV non-thermal X-ray burst intensity. The observed peak emissivity was 1.5 × 10¹⁰ erg cm^?2 s^?1 and the total flare energy in the 3900–6900 Å range was ～10³⁰ erg. From the close temporal correspondence and from the small distance (3″) separating the layers where the visible emission and the X-rays arose, it is argued that the hard X-ray source must have had the same silhouette as the white light flare and that the emission patches had cross-sections of 3–5″. There was also a correlation between the location of the most intense visible emissions near sunspots and the intensity and polarization of the 9.4 GHz radio emission. The flare appeared to show at least three distinct particle acceleration phases: one, occurring at a stationary source and associated with proton acceleration gave a very bluish continuum and reached peak intensity at ～ 1522 UT. At 1523 UT, a faint wave spread out at 40 km s^?1 from flare center. The spectrum of the wave was nearly flat in the range 4950–5900 Å. Association of the wave with a slow drift of the microwave emission peak to lower frequencies and with a softening of the X-ray spectrum is interpreted to mean that the particle acceleration process weakened while the region of acceleration expanded. The observations are interpreted with the aid of the flare models of Brown to mean that the same beam of non-thermal electrons that was responsible for the hard X-ray bremsstrahlung also caused the heating of the lower chromosphere that produced the white light flare.     

Electron acceleration in solar-flare magnetic traps: Model properties and their observational confirmations

Using an analytical solution of the kinetic equation, we have investigated the model properties of the coronal and chromospheric hard X-ray sources in the limb flare of July 19, 2012. We calculated the emission spectrum at the flare loop footpoints in the thick-target approximation with a reverse current and showed it to be consistent with the observed one. The spectrum of the coronal source located above the flare loop was calculated in the thin-target approximation. In this case, the slope of the hard X-ray spectrum is reproduced very accurately, but the intensity of the coronal emission is lower than the observed one by several times. Previously, we showed that this contradiction is completely removed if the additional (relative to the primary acceleration in the reconnecting current layer) electron acceleration in the coronal magnetic trap that contracts in the transverse direction and decreases in length during the impulsive flare phase is taken into account. In this paper we study in detail this effect in the context of a more realistic flare scenario, where a whole ensemble of traps existed in the hard X-ray burst time, each of which was at different stages of its evolution: formation, collapse, destruction. Our results point not only to the existence of first-order Fermi acceleration and betatron electron heating in solar flares but also to their high efficiency. Highly accurate observations of a specific flare are used as an example to show that the previously predicted theoretical features of the model find convincing confirmations.