Acceleration of relativistic electrons in plasma reactors and non-linear spectra of cosmic radio sources

A second approximation to the theory of turbulent plasma reactors in connection with the problem of interpretation of the non-linear spectra of cosmic radio sources has been investigated by the authors (Kaplan and Lomadze, 1977; Lomadze, 1977). The present paper discusses the basic results received for a Compton reactor with plasma waves of phase velocities smaller than the velocity of light, as well as for the synchrotron reactor. The distortion of the distribution function of relativistic electrons caused by their diffusion from the reactor is also presented as an example.     

The interpretation of non-linear radio spectra of discrete radio sources by a general mechanism

The analysis of discrete radio sources spectra in the range 10–5000 MHz reveals that deviations from a power law in the low-frequency region may be due to distortion of differential energy spectra of relativistic electrons at low energies. An empirical expression for an energy-spectrum law was found to be in a good agreement with most of the radio spectra measured. The main physical parameters of 92 sources are evaluated. It is concluded that a low-energy electron excess exists with respect to the lawE ^– in most of the discrete sources which radiate non-linear low-frequency spectra.The forms of radio and energy spectra are further considered in a logarithmic scale.     

On the spectrum of relativistic electrons accelerated in cosmic-ray sources

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE ^–0, with 01.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN _n (E)=K _n E ^– _n, _n = + 2, =w cr/(w–w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w _turb, the total energy density. We obtain =2.5 in agreement with observations on the natural assumption that =0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with _{0 n} = + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.     

Formation of universal and diffusion regions of non-linear spectra of relativistic electrons in spatially limited sources

It is demonstrated that in the case of hard injection of relativistic electrons accompanied by the joint action of synchrotron (Compton) losses and energy-dependent spatial diffusion, a spectrum with breaks is formed containing universal (with index =2) and diffusion regions, both independent of the injection spectrum. The effect from non-linearity of the electron spectrum is considered in averaged electromagnetic spectra for various geometries of sources (sphere, disk, arm). It is shown that a universal region (with index =0.5) can occur in the radiation spectrum.     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

The energy spectrum of cosmic ray electrons between 10 and 1000 GeV

Measurements made by the Bombay Group on the fluxes of cosmic ray electrons in the energy range 10–1000 GeV have been compared with those of other workers in the same energy domain with a view to understand the present confused situation on the existing observations at these high energies. Such an analysis clearly brings out the current situation in its true perspective and highlights the care and emphasis to be placed on future experimentation in this important field.     

On a possible source of energy for the ejection of matter from cosmic objects

The transformation of the energy of an accelerating, expanding universe into internal energy of cosmic objects is discussed. The well known fact that Hubble expansion is observed on scale lengths two or more orders of magnitude smaller than the “cells of homogeneity” is taken into account, along with observational data indicating that this expansion also takes place on the scale of the solar system. Changes in the potential energy of individual model objects are examined on this basis and it is shown that the potential energy increases, thereby threatening the continued existence of these objects. An expression is obtained for the mass which can attain the escape energy within a given energy accumulation time. Some estimates are made for the assumed masses of galactic clusters. Over a period of 10⁷ years a protocluster can accumulate enough energy for ejection of a clump of matter with a mass equal to that of our galaxy.     

On the effect of the distribution function of the injected or formed relativistic particles on the frequency spectra of the radio sources

In the present paper a model of the cosmic radio source with plasma, relativistic electrons and chaotic magnetic fields is considered. It is assumed that the energy changes of relativistic electrons which are due to spontaneous scattering on the transverse and Langmuir plasmons take place in this radio source. For such a radio source the kinetic equation has been solved in the presence of the injected or formed secondary electrons and the frequency spectrum has been obtained.     

On the modulation and energy spectrum of highly charged cosmic ray nuclei

The intensity and energy spectrum of cosmic ray VH-nuclei (20Z30) has been measured in a stack of nuclear emulsions exposed over Fort Churchill in 1968. The integral intensity above 300 MeV/nucleon was 1.04±0.04 nuclei m^–2 sr^–1 s^–1 and three differential intensities were measured below 750 MeV/nucleon. Because of the current controversy regarding the true intensities of helium nuclei at this phase of the solar cycle we have also measured these nuclei, obtaining results intermediate between those quoted by other workers. Comparison of these results on the VH-and helium nuclei with those obtained in previous observations made at times of low solar modulation leads to the conclusion that there is no significant charge dependence in the modulation process. This conclusion is in conflict with an earlier analysis but depends on results of improved statistical weight and greater reliability for the VH nuclei and on our measurement of the helium nuclei in the same detector.Supported by the Office of Naval Research under Contract No. N00014-67-A-0113-0021.     

On the formation of energy spectra in synchrotron sources

The observed energy spectra in synchrotron sources are power laws,N (E)=KE ^–, with the distribution in peaked around 2.5. These are consistent with initially injected spectra with between 1 and 2, subsequently steepened by synchrotron losses. Contrary to the results of Kardashev (1962), it is shown that statistical acceleration when coupled with synchrotron losses lead naturally to the formation of flat stationary spectra with 1. These stationary spectra have bends near the energy at which synchrotron losses balance the energy gains by acceleration. Above this bend the spectrum tends to =2. The time evolution of an initial spectrum towards the stationary spectrum is investigated. It is suggested that the initially flat spectra with 1 to 1.5 observed in some variable sources result from an incomplete approach to the stationary spectrum, and that in sources with constant acceleration spectra with 2 are to be expected.     

Evidence for a common origin of the electrons responsible for the impulsive X-ray and type III radio bursts

Observations of impulsive solar flare X-rays 10 keV made with the OGO-5 satellite are compared with ground based measurements of type III solar radio bursts in 10–580 MHz range. It is shown that the times of maxima of these two emissions, when detectable, agree within 18 s. This maximum time difference is comparable to that between the maxima of the impulsive X-ray and impulsive microwave bursts. In view of the various observational uncertainties, it is argued that the observations are consistent with the impulsive X-ray, impulsive microwave, and type III radio bursts being essentially simultaneous. The observations are also consistent with 10–100 keV electron streams being responsible for the type III emission. It is estimated that the total number of electrons 22 keV required to produce a type III burst is 10³⁴. The observations indicate that the non-thermal electron groups responsible for the impulsive X-ray, impulsive microwave, and type III radio bursts are accelerated simultaneously in essentially the same region of the solar atmosphere.     

On a possible mechanism of zebra-pattern generation in solar radio emission

A mechanism is proposed for the generation of zebra-patterns in solar radio bursts due to the excitation of nonlinear ion-sound waves in a nonisothermal plasma and their scattering on fast particles. The appearance of the ion sound at the fundamental frequency can take place in the interaction of two opposing Alfvén or whistler waves. The presence of quasi-equidistant stripes in electro-magnetic radiation is ultimately determined by weak ion-sound dispersion resulting in the formation of higher harmonics.     

Non-IO-related radio emissions and the modulation of relativistic electrons in the Jovian magnetosphere

The modulations of the non-Io-related radio emissions in hectometric and decametric wave frequencies are examined, and compared with the observed variation of the MeV electron fluxes in the morning sector of the Jovian magnetosphere. It is suggested that these radio emissions are controlled by the behaviour of these electrons in this sector.     

Prospects for radio detection of ultra-high energy cosmic rays and neutrinos

The origin and nature of the highest energy cosmic ray events is currently the subject of intense investigation by giant air shower arrays and fluorescent detectors. These particles reach energies well beyond what can be achieved in ground-based particle accelerators and hence they are fundamental probes for particle physics as well as astrophysics. One of the main topics today focuses on the high energy end of the spectrum and the potential for the production of high-energy neutrinos. Above about 10²⁰ eV cosmic rays from extragalactic sources are expected to be severely attenuated by pion photoproduction interactions with photons of the cosmic microwave background. Investigating the shape of the cosmic ray spectrum near this predicted cut-off will be very important. In addition, a significant high-energy neutrino background is naturally expected as part of the pion decay chain which also contains much information.Because of the scarcity of these high-energy particles, larger and larger ground-based detectors have been built. The new generation of digital radio telescopes may play an important role in this, if properly designed. Radio detection of cosmic ray showers has a long history but was abandoned in the 1970s. Recent experimental developments together with sophisticated air shower simulations incorporating radio emission give a clearer understanding of the relationship between the air shower parameters and the radio signal, and have led to resurgence in its use. Observations of air showers by the SKA could, because of its large collecting area, contribute significantly to measuring the cosmic ray spectrum at the highest energies. Because of the large surface area of the moon, and the expected excellent angular resolution of the SKA, using the SKA to detect radio Cherenkov emission from neutrino-induced cascades in lunar regolith will be potentially the most important technique for investigating cosmic ray origin at energies above the photoproduction cut-off.     

Ballistic and diffusive components in the dynamic spectra of ultrahigh energy cosmic rays from nearby transient sources

Ultrahigh energy cosmic rays (UHECRs, E > 10¹⁸ eV) from extragalactic sources deviate in the galactic and intergalactic magnetic fields, which explains the diffusive character of their propagation, the isotropization of their total flux, and the absence of UHECR clusters associated with individual sources. Extremely high energy cosmic rays (E > 10^19.7 eV) are scattered mainly in localized magnetized structures, such as galaxy clusters, filaments, etc., with a mean free path of tens of megaparsecs; therefore, in the case of nearby transient sources, a substantial contribution to the observed flux is expected from unscattered and weakly scattered particles, which may be a decisive factor in the identification of these sources. We propose a method for calculating the time evolution of the UHECR energy spectra based on analytical solutions of the transport equation with the explicit determination of the contributions from scattered and unscattered particles. As examples, we consider the cases of transient activity of the nearest active galactic nucleus, Centaurus A, and the acceleration of UHECRs by a young millisecond pulsar.     

A search for steep low-frequency radio spectra among quasars and clusters of galaxies

Using published flux densitiesS at low frequenciesv, radio spectra were constructed for 3C, 4C, and 4CT radio sources in Abell clusters of galaxies, radio galaxies outside Abell clusters, and quasars with known redshifts. About half the sources in rich Abell clusters (richness classesR>-2) have steep spectra between 38 and 178 MHz with spectral indices ₃₈ ¹⁷⁸ > whereSv ^–. However, radio galaxies outside clusters have values of ₃₈ ¹⁷⁸ 1.2, and no steep spectra were found among 170 quasars. The radio sources in rich clusters are probably confined by intergalactic gas, and the steep spectra develop over a period of 10⁹ yr as relativistic electrons lose energy. The absence of steep spectra among quasars does not necessarily mean that quasars never occur in rich clusters of galaxies, since quasars are probably being observed only in their early high-luminosity phases. The possibility that some quasar events occur in the nuclei of the dominant cD galaxies in clusters is discussed, but quasar events may occur in more than one type of galaxy.     

On the requirements for acceleration mechanisms to produce flattened heavy particle cosmic ray energy spectra

The recently observed flattening of the energy spectra of highZ particles is investigated in terms of the limits it places on acceleration mechanisms. The possibility of a new mechanisms is suggested.