Nonthermal electrons accelerated in solar flares produce electromagnetic emission in two distinct, highly complementary domains - hard X-rays (HXRs) and microwaves (MWs). This paper reports MW imaging spectroscopy observations from the Expanded Owens Valley Solar Array of an M1.2 flare that occurred on 2017 September 9, from which we deduce evolving coronal parameter maps. We analyze these data jointly with the complementary Reuven Ramaty High-Energy Solar Spectroscopic Imager HXR data to reveal the spatially-resolved evolution of the nonthermal electrons in the flaring volume. We find that the high-energy portion of the nonthermal electron distribution, responsible for the MW emission, displays a much more prominent evolution (in the form of strong spectral hardening) than the low-energy portion, responsible for the HXR emission. We show that the revealed trends are consistent with a single electron population evolving according to a simplified trap-plus-precipitation model with sustained injection/acceleration of nonthermal electrons, which produces a double-powerlaw with steadily increasing break energy.
We address the problem of how particles that are accelerated by solar flares can escape promptly into the heliosphere, on time scales of an hour or less. Impulsive solar energetic particles (SEP) bursts are generally observed in association with so-called eruptive flares consisting of a coronal mass ejection (CME) and a flare. These highly prompt SEPs are believed to be accelerated directly by the flare, rather than by the CME shock, although the precise mechanism by which the particles are accelerated remains controversial. Whatever their origin, within the magnetic geometry of the standard e…
We propose a nonlinear self-consistent model of the turbulent non-resonant particle acceleration in solar flares. We simulate temporal evolution of the spectra of charged particles accelerated by strong long-wavelength MHD turbulence taking into account back reaction of the accelerated particles on the turbulence. The main finding is that the nonlinear coupling of accelerated particles and MHD turbulence result in prominent evolution of the spectra of accelerated particles, which can be either soft-hard-soft or soft-hard-harder depending on the particle injection efficiency. Such evolution pat…
Gamma-ray spectroscopy provides diagnostics of particle acceleration in solar flares, but care must be taken when interpreting the spectra due to effects of the angular distribution of the accelerated particles (such as relativistic beaming) and Compton reprocessing of the radiation in the solar atmosphere. In this paper, we use the GEANT4 Monte Carlo package to simulate the interactions of accelerated electrons and protons and study these effects on the gamma-rays resulting from electron bremsstrahlung and pion decay. We consider the ratio of the 511~keV annihilation-line flux to the continuu…
We present a unified computational framework which can be used to describe impulsive flares on the Sun and on dMe stars. The models assume that the flare impulsive phase is caused by a beam of charged particles that is accelerated in the corona and propagates downward depositing energy and momentum along the way. This rapidly heats the lower stellar atmosphere causing it to explosively expand and dramatically brighten. Our models consist of flux tubes that extend from the sub-photosphere into the corona. We simulate how flare-accelerated charged particles propagate down one-dimensional flux tu…
We investigate the relationship between the main acceleration phase of coronal mass ejections (CMEs) and the particle acceleration in the associated flares as evidenced in RHESSI non-thermal X-rays for a set of 37 impulsive flare-CME events. CME peak velocity and peak acceleration yield distinct correlations with various parameters characterizing the flare-accelerated electron spectra. The highest correlation coefficient is obtained for the relation of the CME peak velocity and the total energy in accelerated electrons (c = 0.85), supporting the idea that the acceleration of the CME and the pa…
During solar flares a large amount of electrons are accelerated within the plasma present in the solar atmosphere. Accurate measurements of the motion of these electrons start becoming available from the analysis of hard X-ray imaging-spectroscopy observations. In this paper, we discuss the linearized perturbations of the Boltzmann kinetic equation describing an ensemble of electrons accelerated by the energy release occurring during solar flares. Either in the limit of high energy or at vanishing background temperature such an equation reduces to a continuity equation equipped with an extra f…
The aim of the thesis is the study of properties of solar flares via reconstruction of energy distributions of accelerated/heated electrons, diagnostics of flare plasma based on EUV and X-ray observations, as well as the estimation of the thermal balance within the "standard" flare model. The X-ray data were obtained from the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and the Russian solar observatory KORONAS-F (IRIS experiment). The EUV data were obtained from the Solar Dynamics Observatory / Atmospheric Imaging Assembly (SDO/AIA). In the first chapter a new technique is presented…
Extending previous studies of nonthermal electron transport in solar flares which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum …
{\sl Ground Level Enhancement (GLE)} events represent the largest class of {\sl solar energetic particle (SEP)} events that require acceleration processes to produce $\gapprox 1$ GeV ions in order to produce showers of secondary particles in the Earth's atmosphere with sufficient intensity to be detected by ground-level neutron monitors, above the background of cosmics rays. Although the association of GLE events with both solar flares and coronal mass ejections (CMEs) is undisputed, the question arises about the location of the responsible acceleration site: coronal flare sites or heliospheri…
We present an analysis of the plasma parameters during the initial phase of the 12 June 2010 flare (SOL2010-06-12T00:57). A peculiarity of the flare was the detection of $γ$--emission that is unusual for such weak and short event. The analysis revealed the presence of a flare precursor detected about 5 minutes before the flare onset in 94 Å\ images which spatially coincided with the non-polarized microwave (MW) source at 17 GHz (\textit{the Nobeyama Radio Heliograph}) that is the Neutral Line associated Source (NLS). A comparison of the results obtained from MW data by \textit{the Nobeyama Rad…
The free energy that is dissipated in a magnetic reconnection process of a solar flare, generally accompanied by a coronal mass ejection (CME), has been considered as the ultimate energy source of the global energy budget of solar flares in previous statistical studies. Here we explore the effects of the aerodynamic drag force on CMEs, which supplies additional energy from the slow solar wind to a CME event, besides the magnetic energy supply. For this purpose we fit the analytical aerodynamic drag model of Cargill (2004) and Vrsnak et al.~{\bf (2013)} to the height-time profiles $r(t)$ of LAS…
The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in…
Impulsive solar energetic particle events are widely believed to be due to the prompt escape into the interplanetary medium of flare-accelerated particles produced by solar eruptive events. According to the standard model for such events, however, particles accelerated by the flare reconnection should remain trapped in the flux rope comprising the coronal mass ejection. The particles should reach the Earth only much later, along with the bulk ejecta. To resolve this paradox, we have extended our previous axisymmetric model for the escape of flare-accelerated particles to fully three-dimensiona…
In this paper, the cooling of 72 M- and X-class flares is examined using GOES/XRS and SDO/EVE. The observed cooling rates are quantified and the observed total cooling times are compared to the predictions of an analytical 0-D hydrodynamic model. It is found that the model does not fit the observations well, but does provide a well defined lower limit on a flare's total cooling time. The discrepancy between observations and the model is then assumed to be primarily due to heating during the decay phase. The decay phase heating necessary to account for the discrepancy is quantified and found be…
Sudden jets of collimated plasma arise from many locations on the Sun, including active regions. The magnetic field along which a jet emerges is often open to interplanetary space, offering a clear "escape route" for any flare-accelerated electrons and making jets lucrative targets for studying particle acceleration and the solar sources of transient heliospheric events. Bremsstrahlung hard X-rays (HXRs) could, in principle, trace the accelerated electrons that escape along the paths of the jets, but measurements of the escaping electron beams are customarily difficult due to the low densities…
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 Å 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 betwe…
Solar flare hard X-ray spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spectrum, and hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here we develop and apply a physically self-consistent warm-target approach which involves the use of both hard X-ray spectroscopy and imaging data. The approach allows an accurate determination of the electro…
We investigate the type III radio bursts and X-ray signatures of accelerated electrons in a well observed solar flare in order to find the spatial properties of the acceleration region. Combining simultaneous RHESSI hard X-ray flare data and radio data from Phoenix-2 and the Nançay radioheliograph, the outward transport of flare accelerated electrons is analyzed. The observations show that the starting frequencies of type III bursts are anti-correlated with the HXR spectral index of solar flare accelerated electrons. We demonstrate both analytically and numerically that the type III burst star…
Solar flares are driven by the release of magnetic energy from reconnection events in the solar corona, whereafter energy is transported to the chromosphere, heating the plasma and causing the characteristic radiative losses. In the collisional thick-target model, electrons accelerated to energies exceeding 10 keV traverse the corona and impact the chromosphere, where they deposit their energy through collisions with the much denser plasma in the lower atmosphere. While there are undoubtedly high energy non-thermal electrons accelerated in flares, it is unclear whether these electron beams are…
We have evaluated the energetics of 38 solar eruptive events observed by a variety of spacecraft instruments between February 2002 and December 2006, as accurately as the observations allow. The measured energetic components include: (1) the radiated energy in the GOES 1 - 8 A band; (2) the total energy radiated from the soft X-ray (SXR) emitting plasma; (3) the peak energy in the SXR-emitting plasma; (4) the bolometric radiated energy over the full duration of the event; (5) the energy in flare-accelerated electrons above 20 keV and in flare-accelerated ions above 1 MeV; (6) the kinetic and p…
In this paper, we investigate the energy partition of two homologous M1.1 circular-ribbon flares (CRFs) in active region (AR) 12434. They were observed by \textit{SDO}, \textit{GOES}, and \textit{RHESSI} on 2015 October 15 and 16, respectively. The peak thermal energy, nonthermal energy of flare-accelerated electrons, total radiative loss of hot plasma, and radiant energies in 1$-$8 Å and 1$-$70 Å of the flares are calculated. The two flares have similar energetics. The peak thermal energies are (1.94$\pm$0.13)$\times$10$^{30}$ erg. The nonthermal energies in flare-accelerated electrons are (3…
X-ray observations are a direct diagnostic of fast electrons produced in solar flares, energized during the energy release process and directed towards the Sun. Since the properties of accelerated electrons can be substantially changed during their transport and interaction with the background plasma, a model must ultimately be applied to X-ray observations in order to understand the mechanism responsible for their acceleration. A cold thick target model is ubiquitously used for this task, since it provides a simple analytic relationship between the accelerated electron spectrum and the emitti…
One of the most important products of solar flares are nonthermal energetic particles which may carry up to 50\% energy releasing in the flaring processes. In radio observations, nonthermal particles generally manifest as spectral fine structures with fast frequency drifting rates, named as solar fast drifting radio bursts (FDRBs). This work demonstrated three types of FDRBs, including type III pair bursts, narrow band stochastic spike bursts following the type III bursts and spike-like bursts superimposed on type II burst in an X1.3 flare on 2014 April 25. We find that although all of them ha…
We describe a new approach for modeling the transport of high energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically solves the Fokker-Planck equation and includes forces corresponding to Coulomb collisions in a flux loop with nonuniform ionization, synchrotron emission reaction, magnetic mirroring and a return current electric field. Our solution to the Fokker-Planck equation includes second-order pitch angle and momentum diffusion. It is applicable to particles of arbitr…
Solar energetic particles (SEPs), including protons and heavy ions, are believed to be accelerated either by CME shock or by magnetic reconnection. The latter also produces solar flares, in which the white light flares (WLFs) are among the most energetic ones. Magnetic reconnections occur in the corona and the accelerated particles propagate both downward and upward along the magnetic loops. The former is the source of flare emission and the latter is thought to be SEPs. Therefore, a comparison between flare emission and SEP events provides valuable constraint in determining the acceleration s…
Sunquakes are enhanced seismic waves excited in some energetic solar flares. Up to now, their origin has still been controversial. In this Letter, we select and study 20 strong flares in Solar Cycle 24, whose impulse phase is fully captured by the \emph{Reuven Ramaty High Energy Solar Spectroscopic Imager} (\emph{RHESSI}). For 11 out of 12 sunquake-active flares in our sample, the hard X-ray (HXR) emission shows a good temporal and spatial correlation with the white-light (WL) enhancement and the sunquake. Spectral analysis also reveals a harder photon spectrum that extends to several hundred …
In some flares the thermal component appears much earlier than the nonthermal component in X-ray range. Using sensitive microwave observations we revisit this finding made by Battaglia et al. (2009) based on RHESSI data analysis. We have found that nonthermal microwave emission produced by accelerated electrons with energy of at least several hundred keV, appears as early as the thermal soft X-ray emission indicative that the electron acceleration takes place at the very early flare phase. The non-detection of the hard X-rays at that early stage of the flares is, thus, an artifact of a limited…
The properties of solar flare plasma can be determined from the observation of optically thin lines. The emitting ion distribution determines the shape of the line, with an isothermal Maxwellian ion distribution producing a Gaussian profile. Non-Gaussian lines may indicate more complex ion distributions. We investigate the possibility of determining flare-accelerated non-thermal ion or plasma velocity distributions. We study EUV spectral lines during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer (EIS). The flare is located close to the eastern solar limb with an extende…
We report on G-band emission observed by the Solar Optical Telescope onboard the Hinode satellite in association with the X1.5-class flare on 2006 December 14. The G-band enhancements originate from the footpoints of flaring coronal magnetic loops, coinciding with non-thermal hard X-ray bremsstrahlung sources observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager. At the available 2 minute cadence, the G-band and hard X-ray intensities are furthermore well correlated in time. Assuming that the G-band enhancements are continuum emission from a blackbody, we derived the total radia…
Hinode's observations revealed a very dynamic and complex chromosphere. This require revisiting the assumption that the chromospheric footpoints of solar flares are areas where accelerated particles only lose energy due to collisions. Traditionally electrons are thought to be accelerated in the coronal part of the loop, then travel to the footpoints where they lose their energy and radiate the observed Hard X-ray. Increasing observational evidence challenges this assumption. We review the evidence against this assumption and present the new Local Re-acceleration Thick Target Model (LRTTM) wher…
The unusually large NOAA active region 2192, observed in October 2014, was outstanding in its productivity of major two-ribbon flares without coronal mass ejections. On a large scale, a predominantly north-south oriented magnetic system of arcade fields served as a strong, also lateral, confinement for a series of large two-ribbon flares originating from the core of the active region. The large initial separation of the flare ribbons, together with an almost absent growth in ribbon separation, suggests a confined reconnection site high up in the corona. Based on a detailed analysis of the conf…
Energetic electrons accelerated by solar flares often give rise to type III radio bursts at a broad waveband and even interplanetary type III bursts (IT3) if the wavelength extends to decameter-kilometer. In this Letter, we investigate the probability of the flares that produce IT3, based on the sample of 2272 flares above M-class observed from 1996 to 2016. It is found that only 49.6% of the flares are detected to be accompanied with IT3. The duration, peak flux, and fluence of the flares with and without IT3 both present power-law distributions in the frequency domain, but the corresponding …
The model of stochastic acceleration of particles by turbulence has been successful in explaining many observed features of solar flares. Here we demonstrate a new method to obtain the accelerated electron spectrum and important acceleration model parameters from the high resolution hard X-ray observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In our model, electrons accelerated at or very near the loop top produce thin target bremsstrahlung emission there and then escape downward producing thick target emission at the loop footpoints. Based on the elec…
Solar flare electron acceleration is an extremely efficient process, but the method of acceleration is not well constrained. Two of the essential diagnostics: electron anisotropy (velocity angle to the guiding magnetic field) and the high energy cutoff (highest energy electrons produced by the acceleration conditions: mechanism, spatial extent, time), are important quantities that can help to constrain electron acceleration at the Sun but both are poorly determined. Here, using electron and X-ray transport simulations that account for both collisional and non-collisional transport processes su…
We present a detailed examination on the coronal nonthermal emissions during the preflare phase of the X4.8 flare that occurred on 2002 July 23. The microwave (17 GHz and 34 GHz) data obtained with Nobeyama Radioheliograph, at Nobeyama Solar Radio Observatory and the hard X-ray (HXR) data taken with {\it Reuven Ramaty High Energy Solar Spectroscopic Imager} obviously showed nonthermal sources that are located above the flare loops during the preflare phase. We performed imaging spectroscopic analyses on the nonthermal emission sources both in microwaves and in HXRs, and confirmed that electron…
In this note, we consider radio characteristics of three proton flares that caused discrete enhancements of solar energetic particles (SEPs) near Earth. The analysis confirmed that the flux density and frequency spectrum of microwave bursts, although the latter are generated by electrons propagating to the photosphere, reflect the number and energy spectrum of accelerated particles, including the 10-100 MeV protons coming to Earth.
The aim of the present paper is to use quasi-periodic oscillations in hard X-rays (HXRs) of solar flares as a diagnostic tool for investigation of impulsive electron acceleration. We have selected a number of flares which showed quasi-periodic oscillations in hard X-rays and their loop-top sources could be easily recognized in HXR images. We have considered MHD standing waves to explain the observed HXR oscillations. We interpret these HXR oscillations as being due to oscillations of magnetic traps within cusp-like magnetic structures. This is confirmed by a good correlation between periods of…
In our recent paper (Solar Physics 261, 233) we investigated quasi-periodic oscillations of hard X-rays during impulsive phase of solar flares. We have come to conclusion that they are caused by magnetosonic oscillations of magnetic traps within the volume of hard-X-ray (HXR) loop-top sources. In the present paper we investigate four flares which show clear quasi-periodic sequences of HXR pulses. We also describe our phenomenological model of oscillating magnetic traps to show that it can explain observed properties of HXR oscillations. Main results are the following: 1. We have found that low…
X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHE…
Driven by recent RHESSI observations of confined loop-top hard X-ray sources in solar flares, we consider stochastic acceleration of electrons in the presence of Coulomb collisions. If electron escape from the acceleration region can be neglected, the electron distribution function is determined by a balance between diffusive acceleration and collisions. Such a scenario admits a stationary solution for the electron distribution function that takes the form of a kappa distribution. We show that the evolution toward this kappa distribution involves a "wave front" propagating forwards in velocity…
We report on a large stellar flare from the nearby dMe flare star EV Lac observed by the Swift and Konus-Wind satellites and the Liverpool Telescope. It is the first large stellar flare from a dMe flare star to result in a Swift trigger based on its hard X-ray intensity. Its peak f_X from 0.3--100 keV of 5.3x10^-8 erg/cm2/s is nearly 7000 times larger than the star's quiescent coronal flux, and the change in magnitude in the white filter is >4.7. This flare also caused a transient increase in EV Lac's bolometric luminosity (L_bol) during the early stages of the flare, with a peak estimated L_X…
Solar flares involve the sudden release of magnetic energy in the solar corona. Accelerated nonthermal electrons have often been invoked as the primary means for transporting the bulk of the released energy to the lower solar atmosphere. However, significant challenges remain for this scenario, especially in accounting for the large number of accelerated electrons inferred from observations. Propagating magnetohydrodynamics (MHD) waves, particularly those with subsecond/second-scale periods, have been proposed as an alternative means for transporting the released flare energy, likely alongside…
Quasi-periodic oscillations of the hard X-ray (HXR) emission of the large flare of 2 November 1991 have been investigated using HXR light curves and soft X-ray and HXR images recorded by the {\sl Yohkoh} X-ray telescopes. The results of the analysis of these observations are the following: i) The observations confirm that electrons are accelerated in oscillating magnetic traps which are contained within the cusp magnetic structure. ii) The amplitude of the HXR pulses increase due to the increase in the amplitude of the magnetic trap oscillations and the increase in the density within the traps…
Most theoretical descriptions of the production of solar flare bremsstrahlung radiation assume the collision of dilute accelerated particles with a cold, dense target plasma, neglecting interactions of the fast particles with each other. This is inadequate for situations where collisions with this background plasma are not completely dominant, as may be the case in, for example, low-density coronal sources. We aim to formulate a model of a self-interacting, entirely fast electron population in the absence of a dense background plasma, to investigate its implications for observed bremsstrahlung…
We report the detection of emission from a non-thermal electron distribution in a small solar microflare (GOES class A5.7) observed by the Nuclear Spectroscopic Telescope Array (NuSTAR), 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 non-thermal hard X-rays from the Sun using a direct image…
We compare four different methods of calculating uncertainty estimates in fitting parameterized models to RHESSI X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra ar…
A large arcade flare of 2 March 1993 has been investigated using X-ray observations recorded by the {\sl Yohkoh} and GOES satellites and the {\sl Compton Gamma Ray Observatory}. We analyzed quasi-periodicity of the hard-X-ray (HXR) pulses in the flare impulsive phase and found close similarity between the quasi-periodic sequence of the pulses with that observed in another large arcade flare of 2 November 1991. This similarity helped to explain the strong HXR pulses which were recorded at the end of the impulsive phase, as due to an inflow of dense plasma (coming from the chromospheric evaporat…
Emission of solar flares across the electromagnetic spectrum is often observed in the form of two expanding ribbons. The standard flare model explains the flare ribbons as footpoints of magnetic arcades, emitting due to interaction of energetic particles with the chromospheric plasma. However, the physics of this interaction and properties of the accelerated particles are still unknown. We present results of multiwavelength observations of C2.1 flare of August 15, 2013, observed with New Solar Telescope (NST) of Big Bear Solar Observatory, Solar Dynamics Observatory (SDO), GOES and FERMI space…
Particle acceleration is one of the most significant features that are ubiquitous among space and cosmic plasmas. It is most prominent during flares in the case of the Sun, with which huge amount of electromagnetic radiation and high-energy particles are expelled into the interplanetary space through acceleration of plasma particles in the corona. Though it has been well understood that energies of flares are supplied by the mechanism called magnetic reconnection based on the observations in X-rays and EUV with space telescopes, where and how in the flaring magnetic field plasmas are accelerat…
Flaring release of magnetic energy in solar corona is only possible if the magnetic field deviates from a potential one. We show that the linear MHD modes excited on top of the non-potential magnetic field possess a nonzero kinetic helicity. Accordingly, this necessarily results in a noticeable kinetic helicity of the turbulence, composed of these linear modes with various scales and random phases, generated at the flare site by the primary energy release, which may be important for many applications. In particular, a nonzero turbulence helicity has a potentially strong effect on the particle …
