Maximum flux density of the gyrosynchrotron spectrum in a nonuniform source

The maximum flux density of a gyrosynchrotron radiation spectrum in a mag- netic dip|oe model with self absorption and gyroresonance is calculated. Our calculations show that the maximum flux density of the gyrosynchrotron spectrum increases with in- creasing low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle, and with decreasing energy spectral index of energetic electrons, number density and temperature of thermal electrons. It is found that there are linear correlations between the logarithms of the maximum flux density and the above eight parameters with correlation coefficients higher than 0.91 and fit accuracies better than 10%. The maximum flux density could be a good indicator of the changes of these source parameters. In addition, we find that there are very good positive linear correla- tions between the logarithms of the maximum flux density and peak frequency when the above former five parameters vary respectively. Their linear correlation coefficients are higher than 0.90 and the fit accuracies are better than 0.5%.     

Variable synchrotron emission from BL Lacertae objects. I. Shock-in-jet scenario

This paper presents a modeling of the variable synchrotron emission in the BL Lacertae sources (BLLs). Flux variability is assumed to be a result of the interaction between a relativistic shock wave with a magnetized jet material. Long-term flares (of months to years durations) are modeled via the propagation of a plane relativistic shock wave though the emission zone of a cylindrical form with the radius R and length H. As for short-term bursts (lasting from days to weeks), they may result from shock passage through the jet inhomogeneities such as a shell of enhanced density downstream to a Mach disc, originated due to pressure imbalance between the jet and its ambient medium. Emitting particles (electrons) gain the energies, sufficient to produce synchrotron photons at optical—X-ray frequencies, via the first-order Fermi mechanism. Observation’s frequency is the main parameter determining a rate of the increase/ decay of the emission via the characteristic decay time of emitting electrons. The magnetic field, assumed to be turbulent with an average field constant throughout the entire emission zone, is another key parameter determining the slope of a lightcurve corresponding to the flare—the higher strength the magnetic field has, the steeper the lightcurve is. The rest input parameters (shock speed, jet viewing angle, maximum/minimum energies of the electrons, particles’ density etc.), as well the strength of average magnetic field, influence the energy output from a flare.     

Electrostatic instability excited by an electron beam trapped in the magnetic mirror of the magnetosphere

A dispersion relation which takes into account the nonuniformity of the magnetic field as well as the plasma density along the field lines is obtained for an electrostatic wave propagating parallel to the magnetic field. This dispersion relation is solved for a particular case in which a group of electrons with a monochromatic distribution in magnetic moment is mixed with a low energy plasma. Such electrons are shown to excite ion acoustic waves carried by the low-energy plasma component near multiples of the bounce frequency of these electrons. The theoretical results are applied to explain electrostatic oscillations with a period of approximately fifty seconds observed in the high energy electron fluxes at synchronous altitude.     

The source and structure of the jovian radiation belt

The radio emission from Jupiter at 10, 21 cm wavelength has been measured with a spatial resolution of the order of 1 Jupiter radius. This may be analytically reduced to the emission per cubic centimeter of source at each measured frequency. The theoretically predicted synchrotron emission of electrons as a function of frequency, magnetic field and electron energy can then be compared to the observed source emissivity to obtain the number density and ‘temperature’ of the electrons. Present observations taken at different epochs are not sufficiently reliable to infer peak energies within an order of magnitude. Nevertheless the present results indicate that electrons diffuse in rapidly (in a time of the order of months) conserving the first adiabatic invariant and reach a peak energy at about 2 Jupiter radii. The electron energy decreases rapidly nearer the planet because of energy lost to radiation in the large magnetic field close to the planet.     

Interpretation of the Radiation of Coronal Suprathermal Streams. I.

This is the first part of a series of two articles aimed at revealing the role of the Compton effect in scattering of the solar photospheric radiation by coronal suprathermal streams. The simplest situation of a single beam of electrons gyrating around the strength lines of magnetic field is considered. Attention is focused on the height-independent problem, in which the role of the spatial angle of incident radiation is ignored. Analytical expressions for the frequency change of interacting photons and for the proper cross-section of the scattering process are derived. The results of numerical calculations show that the effect may by significant even for moderate energies of fast electrons and will be observable only if the fractional density of fast electrons is not too small.     

Energy Cutoff,Energy Index,and Density of Nonthermal Electrons Responsible for Solar Microwave and HXR Bursts

The purpose of this paper is to investigate the crossing point of the power-law distribution lines calculated during different times of microwave and hard X-ray bursts. A linear correlation between the logarithm of the total density and the energy index of nonthermal electrons described by a power-law is proven to be a necessary condition for the crossing of a group of power-law distribution lines corresponding to the time evolution of the nonthermal electrons during a solar microwave and HXR burst. The common crossing point of these lines may be considered as evidence of a common cutoff energy of the nonthermal electrons responsible for gyrosynchrotron or bremsstrahlung radiation. When the common crossing point is close to the low-energy cutoff, the correlation coefficient is negative, and vice versa. The result may be useful for estimating the cutoff energy as well as the particle acceleration mechanism.     

The magnetic field strength and energy flux of energetic electrons in a microwave burst source region

The observations of a microwave burst with multiple impulses on 1993 Oct 2, 073940–074100 UT are analysed. This event consists of multiple impulses superimposed on a slowly varying burst background. Our formula for coronal magnetic field diagnostics was used here for the first time to derive the field strength and information on the energetic electrons. The results are: 1) The mean spectral index of the impulsive component in the optically thin part is less than that of the slow background by 1 (a harder spectrum). The mean brightness temperature at 19.6 GHz of the former is 6 times that of the latter. 2) The mean magnetic strengths of the impulse and slow burst regions are 158 G and 531 G, respectively. The time variation in the slow burst region is saddle-shaped, being 50% lower in the middle than at the beginning and end. 3) The column density NL and number density N of energetic electrons in the impulsive component are 4% and 8% of those of the slow component, but the energy flux and emission coefficient are 100% and 800% greater. The two components appear to be produced by two different electron groups with different energy distributions in two different regions.     

Magnetic field strength estimation in synchrotron radiation sources

In this paper a method of estimating the magnetic field strength,B, in a homogeneous microwave burst source with simplified expressions for the synchrotron radiation is presented. An approximate formula of the magnetic field is obtained using the method. Once the magnetic field is estimated the total number of energetic electrons along the line of sightN L can be estimated also. The errors ofB andN L have been given. It is found that this method is useful for semiquantitative investigations of models of radio burst sources.     

Location and parameters of a microwave millisecond spike event

A typical microwave millisecond spike event on November 2, 1997 was observed by the radio spectrograph of National Astronomical Observatories (NAOs) at 2.6–3.8 GHz with high time and frequency resolution. This event was also recorded by Nobeyama Radio Polarimeters (NoRP) at 1–35 GHz and Radio Heliograph (NoRH) at 17 GHz. The source at 17 GHz is located in one foot-point of a small bright coronal loop of YOHKOH SXT and SOHO EIT images with strong photospheric magnetic field in SOHO MDI magnetograph. It is assumed that the electron cyclotron maser instability and gyro-resonance absorption dominate, respectively, the rising and decay phase of the spike event. For different harmonic number of gyro-frequency or magnetic field strength, a fitting program with free plasma parameters is used to minimize the difference between the observational and theoretical values of the exponential growth and decay rates for a given spike. The plasma parameters at third harmonic number are more comparable to their typical values in solar corona. Hence, it is able to provide a diagnosis for the source parameters (magnetic field, density, and temperature), the properties of radiations (wave vector and propagation angle), and the properties of non-thermal electrons (density, pitch angle, and energy). The results are also comparable with the diagnosis of the gyro-synchrotron radiation model, the frequency drift rates and a dipole magnetic field model, as well as the YOHKOH SXT and SOHO MDI data. This study is supported by the NFSC project nos. 10333030 and 10273025, and “973” program with no. G2000078403.     

Energetic Electrons in Loop Top and Footpoint Microwave Sources

We have studied two microwave events with one-loop top (LT) and two-footpoint (FP) sources observed at 17 and 34 GHz by the Nobeyama Radioheliograph (NoRH). The microwave brightness peak is located near the FPs of the flare loop for one event, but near the LT for the other event. The microwave spectra of the FP sources are considerably softer (by 2.0) than that of the LTs for both events. We assume that the microwave emission is gyro-synchrotron radiation from energetic electrons trapped in a magnetic dipole field and the energetic electron distribution is isotropic in pitch angle and power law. In the gyro-synchrotron calculations, the self-absorption and gyro-resonance absorption are taken into account simultaneously. The numerical calculations based on the general equation of radiative transfer show that the distributions of energetic electrons along a flare loop are highly inhomogeneous: accelerated electrons are concentrated in the FPs for both events. Even for the event with brightness maximum near the LT the electron number density of the LT source is still an order of magnitude lower than that of the FP sources. The emission peak near LT results mainly from the much harder spectral index of the energetic electrons in the LT source.     

The dependence of solar hard X-ray burst intensity on magnetic field strength

The measurements of peak intensities of hard X-ray bursts from hot flare plasma electrons as a function of peak frequency of associated microwave radio bursts are discussed. The latter is proportional to the magnetic field strength. The results suggest that the flare hard X-rays are emitted when the electron plasma frequency is comparable to the electron gyrofrequency. Thus, the hard X-ray peak intensity varies as B ^4.2, where B is the magnetic field strength.On leave from the Geophysical Institute, Slovak Academy of Sciences, 947 01 Hurbanovo, Czechoslovakia.Deceased 22 July, 1986.     

Electron-acoustic instability driven by a crossfield hot electron-beam

On the basis of kinetic theory, the electron-acoustic instability is studied in a three component plasma consisting of a hot electron-beam and stationary cool electrons and ions. The transformation of the instability into the modified two-stream instability for wave propagation oblique to the confining magnetic field is also investigated. In our model both the electrons and ions are magnetized, with the beam drifting across the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is examined. In addition, we investigate the effect of anisotropies in the velocity distributions of the hot electron-beam and the cool electrons on the instability growth rate.     

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.     

Determination of the coronal magnetic field and the radio-emitting electron energy from a Type IV solar radio burst

The intensity and frequency spectrum of gyro-synchrotron emission from energetic solar electrons radiating in coronal magnetic fields are calculated. These calculations, based on a recent study of the generation of gyro-synchrotron emission in a magnetoactive plasma, are applied to a Type IV radio burst originating at a high altitude in the solar corona. It is shown that the observed frequency spectrum of the burst, which exhibits very sharp low and high frequency cutoffs, can be best understood in terms of gyro-synchrotron emission in an ionized medium and that from the observed frequency spectrum and the ambient coronal density it is possible to deduce both the magnetic field at the site of the emission and the range of electron energies responsible for the burst.NAS-NASA Post-Doctoral Resident Research Associate.Research supported by the National Research Foundation under grant GP-849.     

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.     

Acoustic Mode Frequencies of the Sun During the Minimum Phase Between Solar Cycles 23 and 24

We investigate the spatial and temporal variations of the high-degree mode frequencies calculated over localized regions of the Sun during the extended minimum phase between solar cycles 23 and 24. The frequency shifts measured relative to the spatial average over the solar disk indicate that the correlation between the frequency shift and magnetic field strength during the low-activity phase is weak. The disk-averaged frequency shifts computed relative to a minimal activity period also reveal a moderate correlation with different activity indices, with a maximum linear correlation of about 72?%. From the investigation of the frequency shifts at different latitudinal bands, we do not find a consensus period for the onset of solar cycle 24. The frequency shifts corresponding to most of the latitudes in the northern hemisphere and 30° south of the equator indicate the minimum epoch to be February 2008, which is earlier than inferred from solar activity indices.     

On the role of reverse current on the hard X-ray production in solar flares and time-lags between high- and low-energy photons

The evolution of energy and angular distributions of electrons has been studied accounting for the reverse current effect by combining analytically treated small angle multiple scatterings with large angle Monte-Carlo calculations. Reverse current and potential variations as function of column density have been computed. It is found that the reverse current decreases steeply with increase in electron energy. However, it becomes significant for low-energy electrons. By use of these distributions and bremsstrahlung crosssection, the X-ray energy spectrum has been calculated. The nature of the resulting X-ray spectrum integrated over all column depths is similar to the one without reverse current. The time-lag between high-and low-energy photon production has been calculated. It is found that there is a small difference between time-lags as function of observation angles. This fact can be used to test the validity of the beamed thick target model.     

一个微波爆发的源区磁场和高能电子的能流估计

本文分析了１９９３年１０月２日０７：３９：４０－０７：４１：００ＵＴ时段太阳产生的一个多脉冲微波暴的观测，认为它是由多个脉冲爆发叠加在一个慢变爆发背景上组成的．根据谱分析和利用我们的日冕磁场诊断公式［１］，第一次获得了一个爆发源区的磁场强度和高能电子的信息，其主要结果是：（１）脉冲爆发分量在光薄部分的射电谱指数的平均值比慢变爆发背景的值小１，即前者的谱比后者的硬．在１９．６ＧＨｚ上的亮度温度前者比后者高６倍．（２）从脉冲爆发分量和慢变爆发背景分量推断的源区磁场平均值分别为１５８和５３１高斯，且发现在爆发期间，慢变暴源区磁场强度随时间圣马鞍形变化，在极大相的值比脉冲相和下降相低约５０％（３）产生脉冲暴分量的高能电子的柱密度ＮＬ和数密度Ｎ（＞Ｅ０）分别为慢变暴分量的４％和８％，但它们所携带的能流和发射系数要比慢变爆发分量的值高１倍和８倍！表明这两种爆发成份可能分别来自能谱不同的两群电子在不同爆发源区的辐射．     

Cutoff frequency and the reflection of vertically propagating magnetoacoustic gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere stratified in the field of gravity, we investigate the main patterns of vertical propagation of magnetoacoustic gravity waves (MAGWs) in the approximation of a horizontal potential magnetic field. We have established that the cutoff frequency for MAGWs below which they cannot propagate does not depend on the magnetic field strength and is equal to that for acoustic gravity waves, the Lamb frequency. The cutoff frequency is shown to be unaffected by the linear interaction between counterpropagating MAGWs that results from a nonuniform height distribution of the Alfvén velocity and that causes the reflection of propagating waves at relatively large heights.