Gregory D. Fleishman

GYROSYNCHROTRON EMISSION FROM ANISOTROPIC ELECTRON DISTRIBUTIONS

We present numerical calculations of the intensity, degree of polarization, and spectral index of gyrosynchrotron emission produced by fast electrons with anisotropic pitch-angle distributions. The anisotropy is found to affect the emission substantially. The emission intensity can change up to a few orders of magnitude at the optically thin region compared with the isotropic case. The local value of spectral index changes considerably with the anisotropy. X-mode polarization increases for loss cone distributions and decreases for beamlike distributions. Moreover, the sense of polarization can correspond to the ordinary wave mode at the optically thin region for a certain range of view angles for beamlike distributions. We discuss possible applications and observability of the effects obtained.

FAST GYROSYNCHROTRON CODES

Radiation produced by charged particles gyrating in a magnetic field is highly significant in the astrophysics context. Persistently increasing resolution of astrophysical observations calls for corresponding three-dimensional modeling of the radiation. However, available exact equations are prohibitively slow in computing a comprehensive table of high-resolution models required for many practical applications. To remedy this situation, we develop approximate gyrosynchrotron (GS) codes capable of quickly calculating the GS emission (in non-quantum regime) from both isotropic and anisotropic electron distributions in non-relativistic, mildly relativistic, and ultrarelativistic energy domains applicable throughout a broad range of source parameters including dense or tenuous plasmas and weak or strong magnetic fields. The computation time is reduced by several orders of magnitude compared with the exact GS algorithm. The new algorithm performance can gradually be adjusted to the users needs depending on whether precision or computation speed is to be optimized for a given model. The codes are made available for users as a supplement to this paper.

Three-dimensional Radio and X-Ray Modeling and Data Analysis Software: Revealing Flare Complexity

Many problems in solar physics require analysis of imaging data obtained in multiple wavelength domains with differing spatial resolution in a framework supplied by advanced three-dimensional (3D) physical models. To facilitate this goal, we have undertaken a major enhancement of our IDL-based simulation tools developed earlier for modeling microwave and X-ray emission. The enhanced software architecture allows the user to (1) import photospheric magnetic field maps and perform magnetic field extrapolations to generate 3D magnetic field models; (2) investigate the magnetic topology by interactively creating field lines and associated flux tubes; (3) populate the flux tubes with user-defined nonuniform thermal plasma and anisotropic, nonuniform, nonthermal electron distributions; (4) investigate the spatial and spectral properties of radio and X-ray emission calculated from the model; and (5) compare the model-derived images and spectra with observational data. The package integrates shared-object libraries containing fast gyrosynchrotron emission codes, IDL-based soft and hard X-ray codes, and potential and linear force-free field extrapolation routines. The package accepts user-defined radiation and magnetic field extrapolation plug-ins. We use this tool to analyze a relatively simple single-loop flare and use the model to constrain the magnetic 3D structure and spatial distribution of the fast electrons inside this loop. We iteratively compute multi-frequency microwave and multi-energy X-ray images from realistic magnetic flux tubes obtained from pre-flare extrapolations, and compare them with imaging data obtained by SDO, NoRH, and RHESSI. We use this event to illustrate the tools use for the general interpretation of solar flares to address disparate problems in solar physics.

A Broadband Microwave Burst Produced by Electron Beams

The theoretical and experimental study of fast electron beams attracts much attention in astrophysics and the laboratory. In the case of solar flares, the problem of reliable beam detection and diagnostics is of exceptional importance. This paper explores the fact that electron beams moving obliquely to the magnetic field or along the field with some angular scatter around the beams propagation direction can generate microwave continuum bursts through the gyrosynchrotron mechanism. The characteristics of the microwave bursts produced by beams differ from those in the case of isotropic or loss-cone distributions, which suggests a new quantitative diagnostic for beams in the solar corona. To demonstrate the potential of this tool, we analyze a radio burst that occurred during an impulsive class 1B/M6.7 flare on 2001 March 10 (NOAA AR 9368; N27 degrees, W42 degrees). Based on detailed analysis of the spectral, temporal, and spatial relationships, we obtain firm evidence that the microwave continuum burst was produced by electron beams. We develop and apply a new forward-fitting algorithm based on the exact gyrosynchrotron formulae and employing both total-power and polarization measurements to solve the inverse problem of the beam diagnostics. The burst is found to have been generated by an oblique beam in a region of reasonably strong magnetic field (similar to 200-300 G) and observed at a quasi-transverse viewing angle. We find that the lifetime of the emitting electrons in the radio source was relatively short, tau(l) approximate to 0.5 s, consistent with a single reflection of the electrons from a magnetic mirror at the footpoint with the stronger magnetic field. We discuss the implications of these findings for electron acceleration in flares and beam diagnostics.

SUB-THZ RADIATION MECHANISMS IN SOLAR FLARES

Observations in the sub-THz range of large solar flares have revealed a mysterious spectral component increasing with frequency and hence distinct from the microwave component commonly accepted to be produced by gyrosynchrotron (GS) emission from accelerated electrons. Evidently, having a distinct sub-THz component requires either a distinct emission mechanism (compared to the GS one), or different properties of electrons and location, or both. We find, however, that the list of possible emission mechanisms is incomplete. This Letter proposes a more complete list of emission mechanisms, capable of producing a sub-THz component, both well known and new in this context, and calculates a representative set of their spectra produced by (1) free-free emission, (2) GS emission, (3) synchrotron emission from relativistic positrons/electrons, (4) diffusive radiation, and (5) Cherenkov emission. We discuss the possible role of the mechanisms in forming the sub-THz emission and emphasize their diagnostics potential for flares.

Broadband Quasi-periodic Radio and X-Ray Pulsations in a Solar Flare

We describe microwave and hard X-ray observations of strong quasi-periodic pulsations from the GOES X1.3 solar flare on 2003 June 15. The radio observations were made jointly by the Owens Valley Solar Array (OVSA), the Nobeyama Polarimeter (NoRP), and the Nobeyama Radioheliograph (NoRH). Hard X-ray observations were made by RHESSI. Using Fourier analysis, we study the frequency- and energy-dependent oscillation periods, differential phase, and modulation amplitudes of the radio and X-ray pulsations. Focusing on the more complete radio observations, we also examine the modulation of the degree of circular polarization and of the radio spectral index. The observed properties of the oscillations are compared with those derived from two simple models for the radio emission. In particular, we explicitly fit the observed modulation amplitude data to the two competing models. The first model considers the effects of MHD oscillations on the radio emission. The second model considers the quasi-periodic injection of fast electrons. We demonstrate that quasi-periodic acceleration and injection of fast electrons is the more likely cause of the quasi-periodic oscillations observed in the radio and hard X-ray emission, which has important implications for particle acceleration and transport in the flaring sources.

Radio spectral evolution of an X-ray-poor impulsive solar flare : Implications for plasma heating and electron acceleration

We present radio and X-ray observations of an impulsive solar flare that was moderately intense in microwaves, yet showed very meager EUV and X-ray emission. The flare occurred on 2001 October 24 and was well observed at radio wavelengths by the Nobeyama Radioheliograph (NoRH), the Nobeyama Radio Polarimeters (NoRP), and the Owens Valley Solar Array (OVSA). It was also observed in EUV and X-ray wavelength bands by the TRACE, GOES, and Yohkoh satellites. We find that the impulsive onset of the radio emission is progressively delayed with increasing frequency relative to the onset of hard X-ray emission. In contrast, the time of flux density maximum is progressively delayed with decreasing frequency. The decay phase is independent of radio frequency. The simple source morphology and the excellent spectral coverage at radio wavelengths allowed us to employ a nonlinear χ2-minimization scheme to fit the time series of radio spectra to a source model that accounts for the observed radio emission in terms of gyrosynchrotron radiation from MeV-energy electrons in a relatively dense thermal plasma. We discuss plasma heating and electron acceleration in view of the parametric trends implied by the model fitting. We suggest that stochastic acceleration likely plays a role in accelerating the radio-emitting electrons.

Decimetric Spike Bursts versus Microwave Continuum

We analyze properties of decimetric spike bursts occurring simultaneously with microwave gyrosynchrotron continuum bursts. We found that all of the accompanying microwave bursts were highly polarized in the optically thin range. The sense of polarization of the spike clusters is typically the same as that of the optically thin gyrosynchrotron emission, implying preferential extraordinary wave-mode spike polarization. Optically thick spectral indices of the continuum in spike-producing events were not observed to be larger than 2.5, suggesting low or absent Razin suppression. This implies that the plasma frequency-to-gyrofrequency ratio is systematically lower in the spike-producing bursts than in other bursts. The spike cluster flux density is found to be tightly correlated with the high-frequency spectral index of the microwave continuum for each event, while the flux-to-flux correlation may not be present. We discovered strong evidence that the trapped fast electrons producing the microwave gyrosynchrotron continuum have an anisotropic pitch-angle distribution of the loss cone type in the spike-producing bursts. The spike clusters are mainly generated when the trapped electrons have the hardest and the most anisotropic distributions. The new properties are discussed against the currently available ideas about emission processes and models for spike generation. We conclude that the findings strongly support the electron cyclotron maser mechanism of spike emission, with characteristics agreeing with expectations from the local-trap model.

A COLD, TENUOUS SOLAR FLARE: ACCELERATION WITHOUT HEATING

We report the observation of an unusual cold, tenuous solar flare, which reveals itself via numerous and prominent non-thermal manifestations, while lacking any noticeable thermal emission signature. RHESSI hard X-rays and 0.1-18 GHz radio data from OVSA and Phoenix-2 show copious electron acceleration (1035 electrons s-1 above 10 keV) typical for GOES M-class flares with electrons energies up to 100 keV, but GOES temperatures not exceeding 6.1 MK. The imaging, temporal, and spectral characteristics of the flare have led us to a firm conclusion that the bulk of the microwave continuum emission from this flare was produced directly in the acceleration region. The implications of this finding for the flaring energy release and particle acceleration are discussed.

Three-dimensional Simulations of Gyrosynchrotron Emission from Mildly Anisotropic Nonuniform Electron Distributions in Symmetric Magnetic Loops

Microwave emission of solar flares is formed primarily by incoherent gyrosynchrotron radiation generated by accelerated electrons in coronal magnetic loops. The resulting emission depends on many factors, including pitch-angle distribution of the emitting electrons and the source geometry. In this work, we perform systematic simulations of solar microwave emission using recently developed tools (GS Simulator and fast gyrosynchrotron codes) capable of simulating maps of radio brightness and polarization as well as spatially resolved emission spectra. A three-dimensional model of a symmetric dipole magnetic loop is used. We compare the emission from isotropic and anisotropic (of loss-cone type) electron distributions. We also investigate effects caused by inhomogeneous distribution of the emitting particles along the loop. It is found that the effect of the adopted moderate electron anisotropy is the most pronounced near the footpoints and it also depends strongly on the loop orientation. Concentration of the emitting particles at the looptop results in a corresponding spatial shift of the radio brightness peak, thus reducing effects of the anisotropy. The high-frequency ( 50 GHz) emission spectral index is specified mainly by the energy spectrum of the emitting electrons; however, at intermediate frequencies (around 10-20 GHz), the spectrum shape is strongly dependent on the electron anisotropy, spatial distribution, and magnetic field nonuniformity. The implications of the obtained results for the diagnostics of the energetic electrons in solar flares are discussed.