Comments on ‘on the formation of energy spectra in synchrotron sources’ by Donald B. Melrose

It is argued that the stationary energy spectrum given by Melrose (1969) for synchrotron sources resulting from systematic acceleration, energy-space diffusion, and synchrotron losses is unphysical as it requires a constant flow of particles in energy space. The general stationary solution is given. The asymptotic behavior of the time-dependent spectrum is found to depend critically on the boundary conditions; specifically, a stationary flat spectrum does arise for special boundary conditions, but it remains uncertain whether or not the boundary conditions applicable to a real synchrotron source will allow an initially steep spectrum to evolve toward a stationary flat spectrum.     

Radio spectra of synchrotron sources with spherical symmetry

This paper deals with the radio spectra of synchrotron sources with spherically symmetric non-homogeneities. It is pointed out that the Type-c spectra can be produced by such a non-homogeneity even if the source is optically thin. This model is particularly advantageous in interpreting sources with no compact characteristics and yet showing a Type-c spectrum, and the observed decrease in source size with increasing frequency. In addition, it is possible to give a uniform interpretation of the four spectral types on the basis of such a non-homogeneity.     

On the isotropization of electrons in synchrotron sources

Electrons radiating synchrotron radiation develop a pitch angle anisotropy, and so become unstable to the coherent emission of hydromagnetic waves. The evolution of the coupled system of anisotropic electrons and waves is studied in the absence of any dissipation of the waves in the ambient medium. The anisotropy of the electrons approaches a steady state in which the anisotropy is energy independent and of orderv _A/c (v _A=Alfvén speed). The conditions for this small degree of anisotropy to be maintained are examined.Due to this scattering the bend in the synchrotron spectrum, from an inverse power law with index to one with index 4/3+1, due to an initial or recurrent injection of electrons, could only occur at infrared or higher frequencies.     

Inversion of synchrotron spectra

The problem of synchrotron radiation spectra is treated from the viewpoint of deconvolving the spectrum of ultrarelativistic source electrons from the observed photon spectrum. It is shown that for homogeneous sources the problem amounts to inversion of a Meijer transform with a modified Bessel finction kernel. A precise analytic inversion is only possible in the complex plane but Meijer transform tables are available for a wide range of functions. More convenient inversion formulae prove possible by use of a Laplace transform approximation or by analysing the spectra in terms of their integral moments. The filtering property of the transform is also established showing that the contribution to the synchrotron spectrum of high frequency components in the electron spectrum declines exponentially with their frequency. Thus, as with other Laplace-like transforms, only a few terms in an electron spectrum expansion can be deconvolved for any plausible noise level in the synchrotron spectrum.     

Inverse compton scattering in anisotropic synchrotron sources

Models of compact, high brightness temperature sources such as quasars and active galactic nuclei often predict substantial inverse-compton scattered flux to be produced at high frequencies. As these fluxes are not observed, it is necessary to assume that extreme relativistic and/or anisotropic effects dominate the source. The often used equations to include these effects however are derived with several simplifying assumptions, which may not always be consistent with the derived source parameters (for example, the assumption of no time dependence in a violently variable quasar may not be appropriate). We therefore present here an explicit derivation of the dependence of the rate of inverse compton scattering on anisotropies in the source, to emphasise the importance and number of assumptions required in the derivation.     

Compton scattering in sources with synchrotron reabsorption

By considering the consecutive effects of synchrotron reabsorption, Compton scattering and other kinds of energy losses of relativistic electrons, it may be possibile to form a universal distribution of electrons in the region of reabsorption (synchrotron reactor). This will be either a power law with a power index of the energy spectrumn _r=3–5, or a relativistic Maxwell distribution with an electron temperatureT _e=4T _b(1+), where is the ratio of Compton (or other losses) to synchrotron losses, andT _bis the brightness temperature of the radiation. Since the total energy losses of electrons in the reactor is equal to zero, this ensures the continuous existence and accumulation of relativistic electrons in the region of reabsorption and their associated hard scattered radiation. Multiple Compton scattering produces a specific stepped power distribution of scattered radiation by which we can identify the reactor. In the nuclei of quasars W _Hand, therefore,n _r=3; hence the spectral index of scattered radiation in the corresponding ranges (optical, UV, X- and -ray) is .Consideration of other kinds of losses and gains of energy by electrons can lead to the dependencen =3–5(E) — where (E) may have either positive or negative values—which, in turn, leads to the frequency dependence of the spectral index of scattered radiation = 1 – (), |()| < 1, |(E)| < 1.Within the framework of the model being considered, the physical parameters of the nucleus of quasar 3C 273 are calculated.     

Correlations between synchrotron and self-compton spectra

UV-X-ray radiation has been observed in some synchrotron radio sources and some authors have suggested that both may originate in the “synchrotron self-Compton” effect. A number of relations between the synchrotron and the Compton spectra so produced are given in this paper which will provide criteria for testing the correctness of this effect and may also be useful in the evaluation of the physical parameters of the sources.     

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.     

On the sources of ultraviolet absorption in spectra of Titan and the outer planets

In response to the observations of the ultravioler deficiencies shown by all of the outer planets and Titan, models have been proposed to explain the low albedos by absorption by particles in the upper atmospheres of these objects. These particles are generally believed to be photochemically formed from gases in the upper atmospheres, primarily methane and hydrogen. Such processes may also be operative on Titan. The results of some laboratory experiments of the proton irradiation of mixtures of gases including CH₄ H₂, NH₃, etc., have shown that liquid and solid materials are produced that are strong ultraviolet absorbers. However, the material produced from the CH₄ + H₂ mixture was colorless, indicating that species containing elements other than carbon and hydrogen are necessary for the production of color. Two such elements are nitrogen (as NH₃ or N₂) and sulfur (as H₂S) and colored materials have been produced from such mixtures. None of these materials has spectral properties identical to those shown by the planets. Therefore it is necessary that mixtures (and/or cloud layers) of the photochemical materials be present.     

On a possible mechanism responsible for the differential energy spectrum of relativistic electrons and non-linear low-frequency spectra of cosmic radio sources

The paper suggests an explanation of the deviations from the power law which are observed in frequency spectra of discrete radio sources at decametric wavelengths. It has been shown that a possible mechanism of the deviations is a combined effect of the stimulated and spontaneous scattering of relativistic electrons in the turbulent plasma of a source, as well as ionization energy losses thereof. The distribution function of the relativistic electrons, empirically established in an earlier paper (Braudeet al., 1971) has been derived from the kinetic equation. For a number of discrete sources the turbulence energy density and the plasma concentration are deduced with the aid of experimental data on low-frequency radio spectra.

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Thermal synchrotron radiation and gamma-ray burst spectra

The standard classical expressions for the thermal synchrotron (TS) radiation from an optically thin thermal plasma are shown to be inapplicable at photon energiesEkT since they neglect quantum effects. Quantum relationships are obtained for the TS spectral emissivity, opacity, and polarization. The quantum TS spectra are much softer atEkT than the classical ones. The TS radiation exhibits strong linear polarization in the classical domain, whereas the quantum effects reduce the polarization at highE. Expressions for the classical TS luminosity are obtained with quantum corrections which turn out to be significant for (B/B _c )(kT/mc ²)10^–2(B _c =4.41×10¹³ G).Fitting the gamma-ray burst (GRB) spectra by the classical TS law (see, e.g., Lianget al., 1983) is incorrect in cases wherekT is less than the maximum detected photon energy. The continua of the GRB spectra in the rangeE20 keV-2 MeV (Mazetset al., 1981a; Andreevet al., 1983) can be fitted satisfactorily by the quantum TS spectra. The results of this fitting may suggest the existence of temperatures much higher (up to 10 MeV), and of magnetic fields much lower (down to 10⁹ G) than those usually accepted. Under these conditions the thickness of the TS sources (10³–10⁴ cm) could be comparable with their transverse dimensions (in contrast to sources with ordinary temperatures and fields), if they lie within a few kpc. The quantum TS spectra are too soft to account for the hard components (up to tens of MeV) of the GRB spectra detected by the Solar Maximum Mission (Nolanet al., 1984), unless the temperatures are unreasonably high.A straightforward TS interpretation of the GRB spectra seems to be unrealistic. Most probably, the continuum radiation escapes from an optically thick, strongly magnetized, highly non-stationary, hot plasma near the surface of a neutron star.     

The circular polarization of sources of synchrotron radiation

The degree of circular polarizationp _c is calculated for two models of a source of synchrotron radiation:

1. A source with an inhomogeneous magnetic field and isotropic angular distribution of the electrons with respect to the magnetic field;
2. A source with a homogeneous magnetic field and anisotropic angular distribution of the electrons in which the anisotropy of angular distribution substantially increases with the electron energy.

The first model can be used to describe extended radio-sources; and the second, to describe compact radio-sources. For those sources, whose observed polarization properties correspond to the first model, we obtain an integral equation which connects the observed distribution of the sources with the extent of their linear and circular polarization (p _l andp _c ) and the unknown distribution of the sources over the strengthB and the degree of homogeneity ?=(B ₀/B)² of the magnetic field;B ₀ is a homogenous field,B ₀?B. A solution of the integral equation obtained is found for a particular case. This solution makes it possible to determine the distribution of different types of sources over ? if the distribution of these sources in the extent of linear polarization is known. The formulae obtained make it possible to indicate which sources with a known degree of linear polarization should be expected to exhibit highest circular polarization. In the discussion of the first model the question is raised as to the information one can get about the magnetic field by using observations of both linear and circular polarization for a separate source, and for a number of sources. It is shown that the determination of the most probable values ofB and ? in a separate source based on the known values ofp _l andp _c for the source, is possible only if one knows the distribution overB and ? of the sources of the type to which the source in question belongs. The observational data now available make it possible to find the distribution of the sources only over ?. Since the distribution overB and ? is at present unknown, even a very strong upper limit forp _c in the case of a separate source does not enable us to give an exact upper limit for the strength of the magnetic field in this source. In the first model the upper limit for the magnetic field can be obtained only if the upper limit ofp _c is known for a certain number of sourcesN, withN?1. This limit allows for much stronger fields than are usually admitted. This last fact should be taken into consideration when one deals with the results of observations of circular polarization in sources with strong magnetic fields. The first model presents some difficulties when we compare it with observations of some compact sources. The second model can explain why one observes in these sources a violation of the lawp _c ～v ^?1/2 and a change of sign inp _c when the frequency of the observationsv changes.     

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 synchrotron radiation model for extragalactic infrared sources

For a number of extragalactic sources of infrared radiation, for example some quasars and nuclei of Class I Seyfert galaxies that are also radio sources, there is a characteristic maximum in the radiation spectrum atv10¹¹ Hz. We discuss a model in which this feature is regarded as intrinsic to the process of electron production, and in which the radiation is produced by the synchrotron mechanism. A two-component version of the model can be employed in the interpretation of the composite radiation spectra of several sources — 3C 84 (NGC 1275), 3C 120 and 3C 273.     

On the type of spectra of S-component sources and their correlation with flare occurrence

From solar maps at 8.6 mm wavelength and total flux measurements at wavelengths of 1.7 cm to 122 cm, various spectra of the slowly varying component have been studied. The main distinction between these various types of spectra is the slope of the spectra toward wavelengths of less than 2 cm.It has been shown that the probability of flare occurrence is correlated with the type of the source spectra. It is proposed that enhanced flare production occurs from a source of SVC whose spectrum has a peak around 6–10 cm wavelength but whose slope is flatter around 8 mm, but steeper toward longer centimeter wavelengths, than in the case of normal SVC-spectra attributed to gyro resonance radiation. The implications of such spectra in terms of changes in magnetic field structure before the occurrence of a flare are discussed.     

Thermal synchrotron radiation and its Comptonization in compact X-ray sources

We investigate the process of synchrotron radiation from thermal electrons at semirelativistic and relativistic temperatures. We find an analytic expression for the emission coefficient for random magnetic fields with an accuracy significantly higher than those derived previously. We also present analytic approximations to the synchrotron turnover frequency, treat Comptonization of self-absorbed synchrotron radiation, and give simple expressions for the spectral shape and the emitted power. We also consider modifications of the above results by bremsstrahlung.
We then study the importance of Comptonization of thermal synchrotron radiation in compact X-ray sources. We first consider emission from hot accretion flows and active coronae above optically thick accretion discs in black hole binaries and active galactic nuclei (AGNs). We find that for plausible values of the magnetic field strength, this radiative process is negligible in luminous sources, except for those with hardest X-ray spectra and stellar masses. Increasing the black hole mass results in a further reduction of the maximum Eddington ratio from this process. Then, X-ray spectra of intermediate-luminosity sources, e.g. low-luminosity AGNs, can be explained by synchrotron Comptonization only if they come from hot accretion flows, and X-ray spectra of very weak sources are always dominated by bremsstrahlung. On the other hand, synchrotron Comptonization can account for power-law X-ray spectra observed in the low states of sources around weakly magnetized neutron stars.