Blazar synchrotron emission of instantaneously power-law injected electrons under linear synchrotron, non-linear SSC, and combined synchrotron-SSC cooling

The broadband SEDs of blazars show two distinct components which in leptonic models are associated with synchrotron and SSC emission of highly relativistic electrons. In some sources the SSC component dominates the synchrotron peak by one or more orders of magnitude implying that the electrons mainly cool by inverse Compton collisions with their self-made synchrotron photons. Therefore, the linear synchrotron loss of electrons, which is normally invoked in emission models, has to be replaced by a nonlinear loss rate depending on an energy integral of the electron distribution. This modified electron cooling changes significantly the emerging radiation spectra. It is the purpose of this work to apply this new cooling scenario to relativistic power-law distributed electrons, which are injected instantaneously into the jet. We will first solve the differential equation of the volume-averaged differential number density of the electrons, and then discuss their temporal evolution. Since any non-linear cooling will turn into linear cooling after some time, we also calculated the electron number density for a combined cooling scenario consisting of both the linear and non-linear cooling. For all cases, we will also calculate analytically the emerging optically thin synchrotron fluence spectrum which will be compared to a numerical solution. For small normalized frequencies f < 1 the fluence spectra show constant spectral indices. We find for linear cooling a_SYN = 1/2, and for non-linear cooling a_SSC = 3/2. In the combined cooling scenario we obtain for the small injection parameter b_1 = 1/2, and for the large injection parameter b_2 = 3/2, which becomes b_1 = 1/2 for very small frequencies, again. This is the same behaviour as for monoenergetically injected electrons.Comment: 24 pages, 25 figures, submitted to A&

Pair annihilation radiation from relativistic jets in gamma-ray blazars

The contribution of the pair annihilation process in relativistic electron-positron jets to the gamma-ray emission of blazars is calculated. Under the same assumptions as for the calculation of the yield of inverse Compton scattered accretion disk radiation (Dermer and Schlickeiser 1993) we calculate the emerging pair annihilation radiation taking into account all spectral broadening effects due to the energy spectra of the annihilating particles and the bulk motion of the jet. It is shown that the time-integrated pair annihilation spectrum appears almost like the well-known gamma-ray spectrum from decaying $\pi^o$-mesons at rest, yielding a broad bumpy feature located between 50 and 100 MeV. We also demonstrate that for pair densities $> 10^9$ cm$^{-3}$ in the jet the annihilation radiation will dominate the inverse Compton radiation, and indeed may explain reported spectral bumps at MeV energies. The refined treatment of the inverse Compton radiation leads to spectral breaks of the inverse Compton emission in the MeV energy range with a change in spectral index $\Delta \alpha$ larger than 0.5 as detected in PKS 0528+134 and 3C273

Influence of the source distribution on the age distribution of galactic cosmic rays

The age distribution of galactic cosmic rays in the diffusion approximation is calculated. The influence of the scale height of the spatial source distribution on the mean age of particles arriving at the solar system is discussed. The broader the source distribution with respect to the galactic plane, the longer the mean age. This result provides a natural explanation for the shorter mean age of secondary cosmic rays compared to primary cosmic rays necessary for the understanding of the observed secondary/primary ratio

Why do leaky-box models work so fine?

By introducing the concept of the age distribution of cosmic rays it is possible to decouple spatial from momentum transport, and simple leaky-box type equations result. The influence of spatial inhomogeneities, geometries, and source distributions enters the spatially homogeneous, infinite (i.e., leaky box) problem through appropriate mean lifetimes. A precise prescription of how to obtain these mean lifetimes, i.c., for comparison with data measured in the vicinity of the solar system they have to be calculated from the age distribution at the spatial position of the observer

Stochastic particle acceleration in solar flares

It is proposed that particles during the second phase of solar flares are accelerated by stochastic resonant scattering off hydromagnetic waves and first order Fermi acceleration in shock waves generated in the impulsive phase of the flare. Solutions allow arbitrary power law momentum dependences of the momentum diffusion coefficient as well as the momentum diffusion coefficient as well as the momentum loss time. The acceleration time scale to a characteristic energy approximately 100 keV for protons can be as short as 5s. The resulting electron spectra show a characteristic double power law with a transition around 200 keV and are correlated to the proton spectra evaluated under equal boundary conditions, indicating that electrons and protons are accelerated by the same mechanism. The correlation between the different spectral indices in the electron double power law and between electron and proton spectra are governed by the ratio of first to second order acceleration and therefore allow a determination of the Alfven Mach number of the shock wave

Explanation of the secondary to primary ratio within the continuous Fermi accelerator model

The secondary to primary ratio in galactic cosmic radiation at relativistic momenta is calculated in a model, where the primaries are continuously accelerated from the thermal galactic background medium by 1st and 2nd order Fermi acceleration. It is shown that the measured decrease with momentum does not exclude that cosmic rays are accelerated in the interstellar medium as a whole. Once a momentum dependence of the mean lifetime and the different spatial source distributions are adequately taken into account, the measured decreasing ratio can be explained

Cosmic-Ray Momentum Diffusion In Magnetosonic Versus Alfvenic Turbulent Field

Energetic particle transport in a finite amplitude magnetosonic and Alfvenic turbulence is considered using Monte Carlo particle simulations, which involve an integration of particle equation of motion. We show that in a low-Betha plasma cosmic ray can be the most important damping process for magnetosonic waves. Assuming such conditions we derive the momentum diffusion coefficient for relativistic particles in the presence of anisotropic finite-amplitude turbulent wave field, for flat and Kolmogorov-type turbulence spectra. We confirm the possibility of larger values of a momentum diffusion coefficient occuring due to transit-time damping resonance interaction in the presence of isotropic fast-mode waves in comparison to the Alfven waves of the same amplitude.Comment: 16 pages, 2 fig, macro for Solar Physcs, accepted for Solar Physic

Stochastic particle acceleration in flaring stars

The acceleration of electrons by the Fermi-Parker mechanisms in a quasistationary turbulent plasma of dimension l, mean magnetic field strength B, and mean number density n are considered. The electrons suffer radiative and ionization losses and have a scattering mean free path that increases linearly with their momentum. Analytic solutions for the steady-state electron energy spectra are presented. The spectra are characterized by an exponential cutoff above a given momentum determined by the synchrontron or the confinement time, depending on the physical characteristics of the accelerating region