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We propose a new approximation for the cyclo-synchrotron emissivity of a single electron. In the second part of this work, we discuss a simple application for our approximation, and investigate the heating of electrons through the self-absorption process. Finally, we investigate the self-absorbed part of the spectrum produced by a power-law population of electrons. In comparison to earlier approximations, our formula provides a few significant advantages. Integration of the emissivity over the whole frequency range, starting from the proper minimal emitting frequency, gives the correct cooling rate for any energy particle. Further, the spectrum of the emission is well approximated over the whole frequency range, even for relatively low particle energies (beta << 0.1), where most of the power is emitted in the first harmonic. In order to test our continuous approximation, we compare it with a recently derived approximation of the first ten harmonics. Finally, our formula connects relatively smooth to the synchrotron emission at beta=0.9. We show that the self-absorption is a very efficient heating mechanism for low energy particles, independent of the shape of the particle distribution responsible for the self-absorbed synchrotron emission. We find that the energy gains for low energy particles are always higher than energy losses by cyclo-synchrotron emission. We show also that the spectral index of the self-absorbed part of the spectrum at very low frequencies differs significantly from the well known standard relation I(nu) ~ nu^(5/2)., Comment: 9 pages, 4 figures, accepted for publication in A&A

There still exists the possibility that the phenomenon of gamma-ray bursts (GRBs) is a mixture of events of different nature, even within the class of long (>2 s) bursts. We try to put statistical constraints on a possible non-cosmological component using the uniform GRB catalog of Stern & Tikhomirova obtained from an overall scan of the full 9.1 year BATSE 1024 ms data. The sample consists of 3906 GRBs and includes non-triggered bursts with peak fluxes down to 0.1 photons cm$^{-2}$ s$^{-1}$. We find no significant deviations from isotropy. The constraints on a non-cosmological population are still weak. The allowed contribution of a GRB subpopulation originating from an extended galactic halo is about 60% and the upper limit on an Eucledian component (e.g., nearby galactic or non-cosmological extragalactic GRBs) is 23%. The results concern mainly the class of long GRBs., Comment: 6 pages, 3 figures, 2 tables, submitted to MNRAS

The source population of gamma-ray bursts (GRBs) declines towards the present epoch being consistent with the measured decline of the star formation rate. We show this using the brightness distribution of 3255 long BATSE GRBs found in an off-line scan of the BATSE continuous 1.024 s count rate records. The significance of this conclusion is enhanced by the detection of three GRBs with known redshifts brighter than 10^{52} erg/s during the last two years. This is an argument in favor of the generally believed idea that GRBs are strongly correlated with the star production, at least on cosmological time scales, and favors the association of long GRBs with collapses of supermassive stars. However, we still cannot rule out neutron star mergers if the typical delay time for binary system evolution is relatively short. If we assume a steep decline of the GRB population at z>1.5, then their luminosity function can be clearly outlined. The luminosity function is close to a power law, dN/dL ~ L^{-1.4}, for low luminosities over at least 1.7 orders of magnitude. Then the luminosity function breaks to a steeper slope or to an exponential decline around L = 3*10^{51} erg/s in the 50-300 keV range assuming isotropic emission., Comment: revised version, to appear in ApJ (2002, V.569, N.1), 12 pages, 2 tables, 10 figures

Power density spectra (PDSs) of long gamma-ray bursts (GRBs) provide useful information on GRBs, indicating their self-similar temporal structure. The best power-law PDSs are displayed by the longest bursts (T_90>100 s) in which the range of self-similar time scales covers more than 2 decades. Shorter bursts have apparent PDS slopes more strongly affected by statistical fluctuations. The underlying power law can then be reproduced with high accuracy by averaging the PDSs for a large sample of bursts. This power law has a slope approximately equal to -5/3 and a sharp break at about 1 Hz. The power-law PDS provides a new sensitive tool for studies of GRBs. In particular, we calculate the PDSs of bright bursts in separate energy channels. The PDS flattens in the hard channel (h\nu>300 keV) and steepens in the soft channel (h\nu<50 keV), while the PDS of bolometric light curves approximately follows the -5/3 law. We then study dim bursts and compare them to the bright ones. We find a strong correlation between the burst brightness and the PDS slope. This correlation shows that the bursts are far from being standard candles and dim bursts should be intrinsically weak. The time dilation of dim bursts is probably related to physical processes occurring in the burst rather than to a cosmological redshift., Comment: 9 pages, accepted to ApJ

We present preliminary results of an off-line search for non-triggered gamma-ray bursts (GRBs) in the BATSE daily records for about 5.7 years of observations. We found more GRB-like events than the yield of the similar search of Kommers et al. (1998) and extended the Log N - log P distribution down to $\sim$ 0.1 ph cm$^{-2}$ s$^{-1}$. The indication of a turnover of the log N - log P at a small P is not confirmed: the distribution is straight at 1.5 decades with the power law index -.6 and cannot be fitted with a standard candle cosmological model., Comment: 4 pages, LaTeX, to appear in Proceedings "Gamma Ray Bursts in the Afterglow Era", Rome, November 1998, A&AS, 1999

The Rossi X-ray Timing Explorer made a short (10 ks) observation of the radio galaxy Centaurus A on 14 August 1996. Analysis of the combined 2.5-240 keV spectrum has revealed a heavily absorbed(NH=9.42+/-0.24 e22 cm-2) primary power law (index=1.86+/-0.015) and an iron line due to fluorescence of cold matter (EW=162+/-25 eV). Flux from either a jet, primary flux scattered into the line of sight, or primary flux seen through a partial absorber was not required. The iron line width is unresolved at the 95% confidence level (sigma < 0.54 keV). No significant variability in the iron line flux is seen from measurements over the last two decades, while the overall continuum flux varied by more than a factor of four, which implies that the line emission region is distant from that of the primary emission. While radio-quiet Seyfert galaxies exhibit spectral components attributable to Compton reflection from cold matter, Cen A reveals no such component (exposed solid angle ratio < 0.09). This supports unified models of active galaxies that have little difference between Seyfert 2 and low luminosity radio galaxies, Comment: 24 pages, 3 figures, accepted to The Astrophysical Journal

We apply Fourier analysis to 214 light curves of long gamma-ray bursts and study the statistical properties of their power density spectra (PDSs). The averaged PDS is found to follow a power law of index -5/3 over almost 2 decades of frequency with a break at about 2 Hz. Individual PDSs are exponentially distributed around the power law. It provides evidence that the diversity of the bursts is due to random realizations of the same process which is self-similar over the full range of time-scales. The -5/3 slope of the average spectrum may indicate that gamma-ray bursts are related to a phenomenon well studied in hydrodynamics - fully developed turbulence., Comment: accepted to ApJ Letters

The high energy continuum in Seyfert galaxies and galactic black hole candidates is likely to be produced by a thermal plasma. There are difficulties in understanding what can keep the plasma thermal, especially during fast variations of the emitted flux. Particle-particle collisions are too inefficient in hot and rarefied plasmas, and a faster process is called for. We show that cyclo-synchrotron absorption can be such a process: mildly relativistic electrons thermalize in a few synchrotron cooling times by emitting and absorbing cyclo-synchrotron photons. The resulting equilibrium function is a Maxwellian at low energies, with a high energy tail when Compton cooling is important. Assuming that electrons emit completely self absorbed synchrotron radiation and at the same time Compton scatter their own cyclo-synchrotron radiation and ambient UV photons, we calculate the time dependent behavior of the electron distribution function, and the final radiation spectra. In some cases, the 2-10 keV spectra are found to be dominated by thermal synchrotron self-Compton process rather than by thermal Comptonization of UV disk radiation., Comment: 8pages, MN.sty, accepted for pubblication in MNRAS