A Study of the Peak Frequency of the Geosynchronous Spectrum in a Nonuniform Source

This paper investigates in detail the peak frequency of gyrosynchrotron radiation spectrum with self and gyroresonance absorption for a model of nonuniform magnetic field. It is found that the peak frequency shifts from lower frequency to higher frequency with increases in the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle. When the number density and temperature of thermal electrons increase, the peak frequency also shifts to a slightly higher frequency. However, the peak frequency is independent of the energy spectral index, high-energy cutoff of energetic electrons and the height of the radio source’s upper boundary. It is also found for the first time that there is a good linear correlation between the logarithms of the peak frequency and the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength, and viewing angle, respectively. Their correlation coefficients are higher than 0.95 and the standard errors are less than 0.06.     

Temporal and spatial distribution of the magnetic field and density of nonthermal electrons in the source of solar microwave bursts

The temporal and spatial distribution of the magnetic field and density of non-thermal electrons in the source of solar microwave bursts are studied by the gyrosynchrotron model, using the observations of the high-resolution spectrometer at the Owens Valley solar interferometer. The general results are consistent with the previous knowledge about these parameters. For example, the magnetic field decreases with increasing radio flux, and the distribution gradually flattens, so that the non-uniformity of the magnetic field decreases gradually, meanwhile the density increases, and the nonthermal electrons propagate from lower to higher levels. It is interesting that the oscillation of the density is detected at lower frequencies, and there is a correlation between the density and the energy index. The main purpose of this paper is to develop a diagnostic method for the basic plasma parameters in solar flares.     

Relation between X-ray flux and radio flux from cosmic objects

The relationship between the X-ray flux and the radio flux from cosmic objects is investigated. We consider the emission from energetic electrons on the condition in which a plasma and a magnetic field exist. As energetic electrons under the circumstances emit both X-rays by the bremsstrahlung mechanism and radio waves by the gyrosynchrotron mechanism simultaneously, it is shown that the radio flux density is closely related to the X-ray flux density. Solving an integral equation describing the X-ray flux density at Earth, we obtain the energy spectrum of electrons in the emitting region. Inserting the result into equation of the radio flux density at Earth, we obtain the direct formula between the X-ray flux density and the radio flux density. The relation is independent of the distance between Earth and cosmic sources. Assuming a power-law X-ray spectrum, we evaluate the numerical relation between two flux densities.     

Resonant Transition Radiation and Solar Radio Bursts

This paper presents general relations for the intensity of the resonant transition radiation (RTR) and their detailed analysis. This analysis shows that the spectrum amplitude of the x-mode at some frequencies for high-energy electrons can grow with the magnetic field increase in some interval from zero value; it can even dominate over that for the o-mode. With further magnetic field increase, the intensity of the RTR x-mode decreases in comparison with the intensity of the o-mode and this decrease is higher for higher velocities of energetic electrons. The polarization of the RTR depends on the velocity of energetic electrons, too. For velocities lower than some velocity limit v<v _i the RTR emission is unpolarized in a broad interval of magnetic field intensities in the radio source. For reasonable values of indices of the power-law distribution functions of energetic electrons, the RTR is broadband in frequencies (df/f≈0.2−0.4). Furthermore, we show various dependencies of the RTR and its spectral characteristics. Assuming the same radio flux of the transition radiation and the gyro-synchrotron one at the Razin frequency, we estimate the limit magnetic field in the radio source of the transition radiation. Then, we analyze possible sources of small-scale inhomogeneities (thermal density fluctuations, Langmuir and ion-sound waves), which are necessary for the transition radiation. Although the small-scale inhomogeneities connected with the Langmuir waves lead to the plasma radiation, which is essentially stronger than RTR, the inhomogeneities of the ion-sound waves are suitable for the RTR without any other radiation. We present the relations describing the RTR for anisotropic distribution functions of fast electrons. We consider the distribution functions of fast electrons in the form of the Legendre polynomials which depend on the pitch-angle. We analyze the influence of the degree of the anisotropy (an increase of the number of terms in the Legendre polynomial) on spectral characteristics of the RTR. A comparison with previous studies is made. As an example of the use of the derived formulas for the RTR, the 24 December 1991 event is studied. It is shown that the observed decimetric burst can be generated by the RTR in the plasma with the density inhomogeneities at the level 〈ΔN ²〉/N ²=2.5⋅10⁻⁵.     

Evidence that Synchrotron Emission from Nonthermal Electrons Produces the Increasing Submillimeter Spectral Component in Solar Flares

We investigate the origin of the increasing spectra observed at submillimeter wavelengths detected in the flare on 2 November 2003 starting at 17:17 UT. This flare, classified as an X8.3 and 2B event, was simultaneously detected by RHESSI and the Solar Submillimeter Telescope (SST) at 212 and 405 GHz. Comparison of the time profiles at various wavelengths shows that the submillimeter emission resembles that of the high-energy X rays observed by RHESSI whereas the microwaves observed by the Owens Valley Solar Array (OVSA) resemble that of ∼50 keV X rays. Moreover, the centroid position of the submillimeter radiation is seen to originate within the same flaring loops of the ultraviolet and X-ray sources. Nevertheless, the submillimeter spectra are distinct from the usual microwave spectra, appearing to be a distinct spectral component with peak frequency in the THz range. Three possibilities to explain this increasing radio spectra are discussed: (1) gyrosynchrotron radiation from accelerated electrons, (2) bremsstrahlung from thermal electrons, and (3) gyrosynchrotron emission from the positrons produced by pion or radioactive decay after nuclear interactions. The latter possibility is ruled out on the grounds that to explain the submillimeter observations requires 3000 to 2×10⁵ more positrons than what is inferred from X-ray and γ-ray observations. It is possible to model the emission as thermal; however, such sources would produce too much flux in the ultraviolet and soft X-ray wavelengths. Nevertheless we are able to explain both spectral components at microwave and submillimeter wavelengths by gyrosynchrotron emission from the same population of accelerated electrons that emit hard X rays and γ rays. We find that the same 5×10³⁵ electrons inferred from RHESSI observations are responsible for the compact submillimeter source (0.5 arcsec in radius) in a region of 4500 G low in the atmosphere, and for the traditional microwave spectral component by a more extended source (50 arcsec) in a 480 G magnetic field located higher up in the loops. The extreme values in magnetic field and source size required to account for the submillimeter emission can be relaxed if anisotropy and transport of the electrons are taken into account.     

Diagnostics of the Low-Cutoff Energy of Nonthermal Electrons in Solar Microwave and Hard X-Ray Bursts

The low-cutoff energy has a strong effect on the relationship between the radiation and electron spectral indices in both nonthermal gyrosynchrotron and bremsstrahlung theories. Hence, we have to calculate or fit the low-cutoff energy together with the electron spectral index as two independent parameters. Theoretical calculations of nonthermal gyrosynchrotron and bremsstrahlung radiations suggest a new method to obtain the exact solutions of the low-cutoff energy and the electron spectral index from the observable photon spectral indices at two adjacent energy or frequency bands (double power law). One flare on 10 June 2000 was studied as an example of the hard X-ray and microwave diagnostics for the low-cutoff energy and the electron spectral index. The results showed some differences between hard X-ray and microwave diagnostics.     

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.     

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.     

SOURCE PARAMETERS FOR IMPULSIVE BURSTS OBSERVED IN THE RANGE 18–23 GHz

Here, we report on impulsive solar radio bursts observed for the first time with high time/spectral resolution in the range 18 to 23 GHz. Using observational parameters and assuming nonthermal gyrosynchrotron emission from energetic electrons in a loop structure, we have estimated the density of nonthermal electrons, magnetic field, and dimension of the source along the line of sight.     

Radial oscillations of coronal loops and microwave radiation from solar flares

We consider the damping mechanisms for the radial oscillations of solar coronal loops in the approximation of a thin magnetic flux tube. We show that the free tube oscillations can have a high Q if the plasma density inside the magnetic flux tube is much higher than the density outside. We analyze the effect of radial coronal-loop magnetic-field oscillations on the modulation of the microwave radiation from solar flares. In the case of a nonthermal gyrosynchrotron mechanism, the fluxes from optically thin and optically thick sources are modulated in antiphase. Based on our model, we diagnose the flare plasma. For the event of May 23, 1990, we estimate the spectral index for accelerated electrons, α≈4.4, and the magnetic-field strength in the region of energy release, B≈190 G.     

The Number of Magnetic Null Points in the Quiet Sun Corona

The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points. These points can be found directly in a potential field extrapolation or their density can be estimated from the Fourier spectrum of the magnetogram. The spectral estimate, in which the extrapolated field is assumed to be random and homogeneous with Gaussian statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO’s MDI. The majority of null points occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null point, with altitude greater than 1.5 Mm, above every 322 Mm² patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minima shows that the null point density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete elements with mean flux 〈|φ|〉=1.0×10¹⁹ Mx distributed randomly with density n=0.007 Mm⁻².     

Gamma-ray and microwave evidence for two phases of acceleration in solar flares

Relativistic electrons in large solar flares produce gamma-ray continuum by bremsstrahlung and microwave emission by gyrosynchrotron radiation. Using observations of the 1972, August 4 flare, we evaluate in detail the electron spectrum and the physical properties (density, magnetic field, size, and temperature) of the common emitting region of these radiations. We also obtain information on energetic protons in this flare by using gamma-ray lines. From the electron spectrum, the proton-to-electron ratio, and the time dependences of the microwave emission, the 2.2 MeV line and the gamma-ray continuum, we conclude that in large solar flares relativistic electrons and energetic nuclei are accelerated by a mechanism which is different from the mechanism which accelerates 100 keV electrons in flares.Research supported by NASA Grant 21-002-316 at the University of Maryland, College Park.     

How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes

A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 10⁵ G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 10⁵-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the “Ω effect” in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 10⁵-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of “convective collapse” for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed.     

Historical Dataset Reconstruction and a Prediction Method of Solar 10.7 cm Radio Flux

We reconstruct the developing history of solar 10.7 cm radio flux (F10.7) since 1848, based on the yearly sunspot number and the variations. A relationship between the maximum and the linear regression slope of the first 3 years starting from minimum of the solar cycle is considered. We put forward a method of predicting the maximum of F10.7 by means of the slope-maximum relationship. Running tests for cycles 19 to 23 indicate that the method can properly predict the peak of F10.7.     

Parameters of the intense X-ray and gamma-ray radiation from the solar flare of May 20, 2002, as observed from the Coronas-F spacecraft

We consider temporal, spectral, and polarization parameters of the hard X-ray and gamma-ray radiation observed during the solar flare of May 20, 2002, in the course of experiments with the SONG and SPR-N instruments onboard the Coronas-F spacecraft. This flare is one of the most intense gamma-ray events among all of the bursts of solar hard electromagnetic radiation detected since the beginning of the Coronas-F operation (since July 31, 2001) and one of the few gamma-ray events observed during solar cycle 23. A simultaneous analysis of the Coronas-F and GOES data on solar thermal X-ray radiation suggests that, apart from heating due to currents of matter in the the flare region, impulsive heating due to the injection of energetic electrons took place during the near-limb flare S21E65 of May 20, 2002. These electrons produced intense hard X-ray and gamma-ray radiation. The spectrum of this radiation extends up to energies ≥7 MeV. Intense gamma-ray lines are virtually unobservable against the background of the nonthermal continuum. The polarization of the hard X-ray (20–100 keV) radiation was estimated to be ≤15–20%. No significant increase in the flux of energetic protons from the flare under consideration was found. At the same time, according to ACE data, the fluxes of energetic electrons in interplanetary space increased shortly (～25 min) after the flare.     

Solar coronal heating by magnetic cancellation – II. Disconnected and unequal bipoles

Two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature (CMF) and the associated coronal X-ray bright point (XBP) are presented. Coronal magnetic reconnection is found to produce the Ohmic heating required for a coronal XBP. During the BP phase where reconnection occurs above the base, about 90–95 per cent of the magnetic flux of the converging magnetic bipole cancels at the base. The last ≈5 to 10 per cent of the base magnetic flux is cancelled when reconnection occurs at the base. Reconnection happens in a time-dependent way in response to the imposed converging footpoint motions. A potential field model gives a good first approximation to the qualitative behaviour of the system, but the magnetohydrodynamics (MHD) experiments reveal several quantitative differences: for example, the effects of plasma inertia and a pressure build-up in-between the converging bipole are to delay the onset of coronal reconnection above the base and to lower the maximum X -point height.     

On model predictions of the power spectral density of radial solar p modes

We investigate the frequency dependence of the power spectral density of low-degree solar p modes by comparing measurements with the results of a stochastic-excitation model. In the past it was common practice to use the total power in such investigations. Using the maximum of the power spectral density instead provides a direct comparison with the measured mode heights in the observed power spectrum. This method permits a more careful calibration of the adjustable parameters in the excitation model, a model which we present here, for the first time, in a format that precisely and unambiguously relates the amplitudes of the modes of oscillation to the Reynolds stress in the equilibrium model. We find that errors in the theory of the linear mode damping rates, particularly at low frequency, have a dramatic impact on the predictions of the mode heights in the spectral density, whereas parameter changes in the stochastic excitation model, within a plausible domain of parameter space, have a comparatively small effect.     

Measurements of the ambient photoelectron spectrum from atmosphere explorer: II. AE-E measurements from 300 to 1000 km during solar minimum conditions

The ambient photoelectron spectrum above 300 km has been measured for a sample of 500 AE-E orbits during the period 13 December 1975 to 24 February 1976 corresponding to solar minimum conditions. The 24 h average and maximum ΣK_p were 19 and 35, respectively. The photoelectron flux above 300 km was found to have an intensity and energy spectrum characteristic of the 250–300 km production region only when there was a low plasma density at the satellite altitude. Data taken at local times up to 3 h after sunrise were of this type and the escaping flux was observed to extend to altitudes above 900 km with very little modification, as predicted by several theoretical calculations. The flux at high altitudes was found to be extremely variable throughout the rest of the day, probably as a result of attenuation and energy loss to thermal plasma along the path of the escaping photoelectrons. This attenuation was most pronounced where the photoelectrons passed through regions of high plasma density associated with the equatorial anomaly. At altitudes of 600 km, the photoelectron fluxes ranged from severely attenuated to essentially unaltered—depending on the specific conditions, Photoelectron fluxes from conjugate regions were often less attenuated than those observed arriving from the high density regions immediately below. Comparison of the observed attenuations, photoelectron line broadening, and energy loss due to coulomb scattering from the thermal plasma with rough calculations based on stopping power and transmission coefficients of thermal plasma for fast electrons yielded order of magnitude agreement—satisfactory in view of the large number of assumptions necessary for the calculations. Overall, the impression of the high altitude photoelectron flux which emerges from this work is that the fluxes are extremely variable as a consequence of interactions with the thermal plasma whose density is in turn affected by electrodynamic and neutral wind processes in the underlying F region.     

太阳射电爆发现象中的电子回旋脉泽辐射

太阳射电爆发(Solar Radio Burst, SRB)是太阳高能电子与背景等离子体相互作用产生的感应辐射现象,其多样的动力学谱类型及其复杂的精细结构反映了辐射源区磁等离子体结构状态丰富的物理信息,而相关辐射机制则是解读相关物理信息的关键工具.长期以来,在SRB辐射机制的研究中一直存在着争议不决的两种主要机制,即等离子体辐射机制和电子回旋脉泽(Electron Cyclotron Maser, ECM)辐射机制.近年来,针对传统的ECM辐射机制应用到SRB现象时遇到的一些主要困难,发展了由幂律谱电子低能截止驱动和包含快电子束自生阿尔文波效应的新型ECM驱动模型,并成功应用于解释各类不同SRB动力学谱的形成机制.基于这些新型的ECM辐射模型,系统地总结了ECM辐射机制在各种不同类型SRB现象中的应用,并对它们不同动力学谱结构的形成给出了一致统一的物理解释.