Nonlinear treatment for solar radio spikes

We emphasize that a nonlinear treatment is required to realize the diagnostic potentiality of solar spiky emission. The observational constraints including the latest data on the harmonic structure, degree, and sense of polarization are discussed. A set of coupled equations for energy density of high-frequency normal modes of a magneto-active plasma involving the most important nonlinear effects within the three-wave approximation is deduced. The equations include both previously known and new effects. The qualitative evaluations of the equations obtained have provided a few new findings: (i) quasi-linear relaxation of fast electrons on quasi-potential waves (_) occurs in a characteristic time scale of the order of 10 ms if the frequency,f, is about 1 GHz; (ii) the stimulated scattering of the transverse waves on the background plasma particles is shown to be important if the brightness temperature of the spiky emission exceeds 10¹⁵–10¹⁶ K; (iii) the Raman scattering of the transverse waves on background plasma density inhomogeneities may suppress the electron cyclotron maser instability if n _e ² /n _e ² 3 × (10^–4–10^–5).     

On the harmonic structure of solar radio spikes

This paper analyzes the frequency structure of the bands of electron-cyclotron maser instability. The calculations show that each term of the series describing the growth rate provides a double-peak structure, if we accept a nonthermal electron distribution with a two-side loss-cone. The ratio of central frequencies is found to be non-integer in general case. We conclude that the harmonic structure of solar radio spikes observed in a number of events can be imitated by electron-cyclotron maser emission of mildly relativistic electrons with a power-law momentum distribution.     

Nonlinear parametric instability and millisecond solar radio spikes

A model of nonlinear parametric instability (NLPI) modulation is suggested to explain the millisecond spikes in solar decimetric radio emission. The radio emission energy will periodically transfer to two other waves, and the intensity of the radio emission will be modified by NLPI processes in the corona, when the matching conditions of three-wave coupling are satisfied. This model can simultaneously explain the duration of spikes, why the millisecond spikes have not been observed in other solar radio emission, and the relation between the duration of the spikes and the intensity and the frequency of the radio emission as well.     

Millisecond spikes in a short decimetric solar radio burst

The characteristics of the millisecond spikes with short duration and weak flux density which were observed with high time resolution (1 ms) at 1420, 2000 and 2840 MHz during the great type IV solar radio burst of 30 July 1990 are introduced in detail in this article. The time profiles of the spikes are statistically analyzed and the parameters of the spike source are also estimated.     

Millisecond radio spikes

Millisecond spikes of the solar radio emission are known for more than two decades. They have recently seen a surge in interest of theoreticians who are fascinated by their high brightness temperature of up to 10¹⁵ K, their association with hard X-ray bursts, and a possibly very intimate relation to electron acceleration. This review is intended to bridge the gap that presently seems to separate theory and observations. The wide range of spike observations is summarized and brought into the perspective of recent models. It is concluded that spikes yield a considerable potential for the diagnostics of energetic particles, their origin, and history in astrophysical plasmas.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Thermodiffusional small-scale irregularities in the plasma turbulence region and solar radio spikes

Magnetic field-aligned irregularities of the background plasma are assumed to be responsible for a strong conversion of upper hybrid plasma wave turbulence (PT) into the radio emission. It is shown that small-scale stratification (induced by PT interference and thermodiffusion) leads to the random occurrence of spike-type radio bursts.     

Thermal cyclotron radio emission of neutral current sheets in the solar corona

Cyclotron radiation (its frequency spectrum and polarization) of thermal electrons in a neutral current sheet is considered. It is shown that cyclotron radiation is able to escape only from a thin edge of the sheet where the magnetic field is practically homogeneous. Due to this, the frequency spectrum has the form of comparatively narrow lines with integer ratio of frequencies. This fact enables one to recognize neutral current sheets in the solar corona by their radio emission.     

Effects of the distribution function of non-thermal electrons and of cyclotron resonant absorption on millisecond radio spikes

A theoretical analysis of electron-cyclotron maser instabilities indicates that the distribution function of non-thermal electrons influences millisecond radio spikes in solar flares, and that a hollow beam distribution is more likely than a loss-cone distribution. The restrictions of classical theories of cyclotron resonant absorption are discussed and a formula is derived for the absorption coefficient near the resonant frequency. Finally, the computations show that for typical coronal parameters, the growth rates of the fundamental of fast extraordinary modes are much faster than those of their second harmonics; and because the directional angle of the fundamental is smaller, its resonant absorption may be neglected. Moreover, the band-width of the fundamental is consistent with observation of radio spikes; therefore, we claim that the millisecond radio spikes in the decimetric range are composed mainly of fundamentals of the fast extraordinary modes. The second harmonics of fast extraordinary modes may be generated for directions near to the vertical to the magnetic field, but it is impossible to observe both fundamental and second harmonics in the same direction.     

Emission of cyclotron radiation by interstellar planets

In the solar system all planets that have significant magnetic fields also emit electron cyclotron radiation, usually near the auroral regions around the magnetic poles. In this study we use scaling laws based on solar system data to estimate the power and frequency of the auroral cyclotron emissions from interstellar planets (or sub-brown dwarfs). The emission can be powered either by motion of the planet through the interstellar plasma or by unipolar induction due to a moon. According to our results, in interstellar space the unipolar induction mechanism is potentially more effective than the motional emission mechanism. Typical emission power is around 10¹⁰-10¹² W, but significantly stronger emissions are obtained in the most optimistic estimates. We have to conclude that detection of a rogue Jupiter would be very difficult, if not impossible with the radio telescopes available now or in the near future, but in very favorable conditions a much more massive and rapidly rotating (or otherwise strongly magnetized) gas giant with a large nearby moon could be detected up to ∼57 pc distance with the square kilometer array. There may be a few thousand large enough interstellar planets this close to the solar system. For reference, we point out that according to previous studies some known hot Jupiters are expected to emit up to 10¹⁴-10¹⁶ W of cyclotron radiation, orders of magnitude more than the typical interstellar planets discussed here. However, these emissions have not yet been detected.     

Harmonic emission and polarization of millisecond radio spikes

The spectral distribution of millisecond radio spikes observed by the Zürich spectrometers in the 200–1100 MHz range has been studied. In one event out of a total of 36 we have found clearly developed harmonic structure. The ratio between the two bands of emission was 1:1.39 ± 0.01. We have also determined the sense of circular polarization of the spike events and compared it to the magnetic polarity of the leading spot of the flaring active region. According to the Leading Spot Rule the majority of the events (10 out of 13) were emitted in the ordinary mode.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

The microwave spectrum of solar millisecond spikes

The microwave radiation from solar flares sometimes shows short and intensive spikes which are superimposed on the burst continuum. In order to determine the upper frequency limit of their occurrence and the circular polarization, a statistical analysis has been performed on our digital microwave observations from 3.2 to 92.5 GHz. Additionally, fine structures have been investigated with a fast (5 ms) 32-channel spectrometer at 3.47 GHz. We found that 10% of the bursts show fine structures at 3.2 and 5.2 GHz, whereas none occurred above 8.4 GHz. Most of the observed spikes were very short ( 10 ms) and their bandwidth varied from below 0.5 MHz to more than 200 MHz. Simultaneous observations at two further frequencies showed no coincident spikes at the second and third harmonic. The observations can be explained by the theory of electron cyclotron masering if the observed bandwidths are determined by magnetic field inhomogeneities or if the rise times are independent of the source diameters. The latter would imply source sizes between 50 and 100 km.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Trajectories followed by U-like solar radio bursts

Radiospectrographic observations of some U-like bursts have been employed in combination with a model coronal condensation due to Waldmeier to derive trajectories along which the disturbing agency, which excites the radio emission, may have travelled. Such trajectories as connect regions of opposite magnetic polarity within one centre of activity should have a parachute-like shape in order to account for the observations. Travelling velocities are of the order of 35000 to 55000 km/sec. Moreover, the distribution of U-like bursts in heliographic longitude is investigated and an attempt is made to explain the fact that the second branches of U-like bursts are less developed than the first branches.     

Theory of solar radio pulsation

We show that the observed modulation of some coronal microwave, X-ray and Type III emission into pulses of 10 sec intervals is a consequence of the stimulation of electron cyclotron waves propagated in the whistler mode in dipole-like bipolar regions of dimension 0.2 R . Assuming that a power law spectrum of 10 keV electrons with a slope similar to solar flare protons can be trapped in a bipolar region, we show that whistlers can be generated by pitch angle instability. The resultant 10 sec bounce motion of whistler wave trains leads to enhanced, modulated emission in microwave and X-ray frequencies by pitch angle scattering of MeV electrons, and to modulated Type III emission by scattering with coherent plasma waves. A direct prediction of the theory is the existence of sympathetic pulsations at two sources a fraction of a solar radius apart. A second test of the theory is that modulated Type III emission should show strong polarization.This work was conducted under U.S. Air Force Space and Missile Systems Organization (SAMSO) Contract No. F04701-69-C-0066.     

Ion cyclotron instability in the solar wind

An ion cyclotron instability, arising because of the relative drift between the beam and the main components of the proton distribution function in the solar wind at 1 AU, is studied. The instability is excited in a bounded range of wave numbers provided the relative drift exceeds a certain minimum value called instability threshold. For 1, the instability threshold is smaller than or equal to the threshold of magnetosonic and Alfvén instabilities. The growth rates are enhanced by increasing relative drift and ratio of beam to main proton number density and by decreasing the wave numbers.     

Electron cyclotron maser emission from solar flares

Energetic electrons, with energies 10–100 keV, accelerated during the impulsive phase of solar flares, sometimes encounter increasing magnetic fields as they stream towards the chromosphere. A consequence of the conservation of their magnetic moment is that the electrons with large initial pitch angle will be reflected at different heights from the atmosphere. Energetic electrons reflected below the transition zone will lose most of their energy to collisions and will never return to the corona. Thus, electrons reflected above the transition zone form a loss-cone velocity distribution which can be unstable to Electron Cyclotron Maser (ECM). The interaction of quasi-perpendicular shocks with the ambient coronal plasma will form a ‘ring’ or ‘hollow beam’ velocity distribution upstream of the shock. ‘Ring’ velocity distributions are also unstable to the ECM instability. A review of the recent results on the theory of ECM will be presented. We will focus our discussion on the questions: (a) What are the characteristics of the linear growth rate of the ECM during solar flares? (b) How does the ECM saturate and what is its efficiency? (c) How does the ECM generated radiation modify the flare environment? Finally we will review the outstanding questions in the theory of ECM and we will relate the theoretical predictions to current observations.     

Satellite information system malfunctions caused by broadband solar radio emission during solar flares

The paper briefly discusses the impairment of normal functioning of the global positioning system (GPS) and the global navigation satellite system (GLONASS) caused by broadband solar radio emission during large solar flares on October 28, 2003, and December 6 and 13, 2006.     

Decimetric type III radio bursts and associated hard X-ray spikes

A detailed comparison is made between hard X-ray spikes and decimetric type III radio bursts for a relatively weak solar flare on 1981 August 6 at 10: 32 UT. The hard X-ray observations were made at energies above 30 keV with the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission and with a balloon-born coarse-imaging spectrometer from Frascati, Italy. The radio data were obtained in the frequency range from 100 to 1000 MHz with the analog and digital instruments from Zürich, Switzerland. All the data sets have a time resolution of 0.1 s or better. The dynamic radio spectrum shows many fast drift type III radio bursts with both normal and reverse slope, while the X-ray time profile contains many well resolved short spikes with durations of 1 s. Some of the X-ray spikes appear to be associated in time with reverse-slop bursts suggesting either that the electron beams producing the radio bursts contain two or three orders of magnitude more fast electrons than has previously been assumed or that the electron beams can trigger or occur in coincidence with the acceleration of additional electrons. One case is presented in which a normal slope radio burst at 600 MHz occurs in coincidence with the peak of an X-ray spike to within 0.1 s. If the coincidence is not merely accidental and if it is meaningful to compare peak times, then the short delay would indicate that the radio signal was at the harmonic and that the electrons producing the radio burst were accelerated at an altitude of 4 × 10⁹ cm. Such a short delay is inconsistent with models invoking cross-field drifts to produce the electron beams that generate type III bursts but it supports the model incorporating a MASER proposed by Sprangle and Vlahos (1983).