Cosmic rays from active galactic nuclei

Cosmic ray (CR) acceleration at the shock created by the expanding cocoons around active galactic nuclei (AGNs) is studied. It is shown that above the energy $10^{18}$ eV the overall energy spectrum of CRs, produced during the AGN evolution and released in the intergalactic space, has the form $N\propto \epsilon^{-\gamma}$, with $\gamma\approx 2.6$, which extends up to $\epsilon_{max}\sim 10^{20}$ eV. It is concluded that cocoons shocks have to be considered as a main source of extragalactic CRs, which together with Galactic supernova remnants provide the observed CR spectrum.Comment: 9 pages, Accepted for publication in ApJ

Cosmic ray acceleration parameters from multi-wavelength observations. The case of SN 1006

The properties of the Galactic supernova remnant SN 1006 are theoretically reanalysed. Nonlinear kinetic theory is used to determine the acceleration efficiency of cosmic rays (CRs) in the supernova remnant SN 1006. The known range of astronomical parameters and the existing measurements of nonthermal emission are examined in order to define the values of the relevant physical parameters which determine the CR acceleration efficiency. It is shown that the parameter values -- proton injection rate, electron to proton ratio and downstream magnetic field strength -- are determined with the appropriate accuracy. In particular also the observed azimuthal variations in the gamma-ray morphology agree with the theoretical expectation. These parameter values, together with the reduction of the gamma-ray flux relative to a spherically symmetric acceleration geometry, allow a good fit to the existing data, including the recently detected TeV emission by H.E.S.S. SN 1006 represents the first example where a high efficiency of nuclear CR production, required for the Galactic CR sources, is consistently established.Comment: 10 pages, 6 figures, accepted for publication in A&

Theory of cosmic ray and gamma-ray production in the supernova remnant RX J0852.0-4622

Aims. The properties of the Galactic supernova remnant (SNR) RX J0852.0-4622 are theoretically analysed. Methods. An explicitly time-dependent, nonlinear kinetic model of cosmic ray (CR) acceleration in SNRs is used to describe the properties of SNR RX J0852.0-4622, the accelerated CRs and the nonthermal emission. The source is assumed to be at a distance of ~1 kpc in the wind bubble of a massive progenitor star. An estimate of the thermal X-ray flux in such a configuration is given. Results. We find that the overall synchrotron spectrum of RX J0852.0-4622 as well as the filamentary structures in hard X-rays lead to an amplified magnetic field B > 100 muG in the SNR interior. This implies that the leptonic very high energy (VHE) gamma-ray emission is suppressed, and that the VHE gamma-rays are hadronically dominated. The energy spectrum of protons produced over the life-time of the remnant until now may well reach ''knee'' energies. The derived gamma-ray morphology is consistent with the H.E.S.S. measurements. The amount of energy in energetic particles corresponds to about 35% of the hydrodynamic explosion energy. A remaining uncertainty concerns the thermal X-ray flux at 1 keV. A rough estimate, possibly not quite appropriate for the assumed wind bubble configuration, results in it being larger than the nonthermal flux at this energy. Conclusions. It is concluded that this SNR expanding into the wind bubble of a massive star in a dense gas environment can be a hadronic gamma-ray source that is consistent with all existing multi-wavelength constraints, except possibly the thermal X-ray emission.Comment: 14 pages, 8 figures, accepted for publication in A&

The theory of synchrotron emission from supernova remnants

The time-dependent nonlinear kinetic theory for cosmic ray (CR) acceleration in supernova remnants (SNRs) is applied studying the properties of the synchrotron emission from SNRs, in particular, the surface brightness-diameter ($\Sigma-D$) relation. Detailed numerical calculations are performed for the expected range of the relevant physical parameters, namely the ambient density and the supernova explosion energy. The magnetic field in SNRs is assumed to be significantly amplified by the efficiently accelerating nuclear CR component. Due to the growing number of accelerated CRs the expected SNR luminosity increases during the free expansion phase, reaches a peak value at the beginning of the Sedov phase and then decreases again, since in this stage the overall CR number remains nearly constant, whereas the effective magnetic field diminishes with time. The theoretically predicted brightness-diameter relation in the radio range in the Sedov phase is close to $\Sigma_\mathrm{R}\propto D^{-17/4}$. It fits the observational data in a very satisfactory way. The observed spread of $\Sigma_\mathrm{R}$ at a given SNR size $D$ is the result of the spread of supernova explosion energies and interstellar medium densities.Comment: 13 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Variation of cosmic ray injection across supernova shocks

The injection rate of suprathermal protons into the diffusive shock acceleration process should vary strongly over the surface of supernova remnant shocks. These variations and the absolute value of the injection rate are investigated. In the simplest case, like for SN 1006, the shock can be approximated as being spherical in a uniform large-scale magnetic field. The injection rate depends strongly on the shock obliquity and diminishes as the angle between the ambient field and the shock normal increases. Therefore efficient particle injection, which leads to conversion of a significant fraction of the kinetic energy at a shock surface element, arises only in relatively small regions near the "poles", reducing the overall CR production. The sizes of these regions depend strongly on the random background field and the Alfven wave turbulence generated due to CR streaming instability. For the cases of SN 1006 and Tycho's SNR they correspond to about 20, and for Cas A to between 10 and 20 percent of the entire shock surface. In first approximation, the CR production rate, calculated under the assumption of spherical symmetry, has therefore to be renormalized by this factor, while the shock as such remains roughly spherical.Comment: 10 pages, 4 figures. To appear in Astronomy and Astrophyics; Corrected typos, references change

TeV Gamma Rays Expected from Supernova Remnants in Different Uniform Interstellar Media

Calculations of the expected TeV $\gamma$-ray emission, produced by accelerated cosmic rays (CRs) in nuclear collisions, from supernova remnants evolving in a uniform interstellar medium (ISM) are presented. The aim is to study the sensitivity of $\gamma$-ray production to a physical parameter set. Apart from its general proportionality to N_H, it is shown that the $\gamma$-ray production essentially depends upon the ratio of the CR diffusion coefficient $\kappa$ to a critical value $\kappa_{crit}=10(B_0/5 \mu{G})(N_H/0.3 {cm}^{-3})^{-1/3}\kappa_B$, where B_0 and N_H are the magnetic field and hydrogen number density of the ISM, and $\kappa_B$ denotes the Bohm diffusion coefficient. If $\kappa$ is of the same order or lower than $\kappa_{crit}$, then the peak TeV $\gamma$-ray flux in the Sedov evolutionary phase, normalized to a distance of 1 kpc, is about 10^{-10}(N_H/0.3 {cm}^{-3}) photons cm^{-2} s^{-1}. For a CR diffusion coefficient that is significantly larger than $\kappa_{crit}$, the CR cutoff energy is less than 10 TeV and the expected $\gamma$-ray flux at 1 TeV is considerably below the presently detectable level of 10^{-12} photons cm^{-2} s^{-1}. The same is of course true for a SNR in the rarified, so-called hot ISM.Comment: 9 pages, 2 figures, to appear in Astroparticle Physic

Nonthermal properties of supernova remnant G1.9+0.3

The properties of the - presumably - youngest Galactic supernova remnant (SNR) G1.9+0.3 are investigated within the framework of nonlinear kinetic theory of cosmic ray acceleration in SNRs. The observed angular size and expansion speed as well as the radio and X-ray emission measurements are used to determine relevant physical parameters of this SNR. Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova near the Galactic center (at the distance d=8.5 kpc) the nonthermal properties are calculated. In particular, the expected TeV gamma-ray spectral energy density is predicted to be as low as $\epsilon_{\gamma}F_{\gamma} \approx 5\times 10^{-15}$ erg cm$^{-2}$ s$^{-1}$, strongly dependent ($F_{\gamma}\propto d^{-11}$) upon the source distance d.Comment: 7 pages, 5 figures, accepted for publication in Ap

Expected gamma-ray emission of supernova remnant SN 1987A

A nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants is employed to re-examine the nonthermal properties of the remnant of SN 1987A for an extended evolutionary period of 5--100 yr. It is shown that an efficient production of nuclear CRs leads to a strong modification of the outer supernova remnant shock and to a large downstream magnetic field $B_\mathrm{d}\approx 20$ mG. The shock modification and the strong field are required to yield the steep radio emission spectrum observed, as well as to considerable synchrotron cooling of high energy electrons which diminishes their X-ray synchrotron flux. These features are also consistent with the existing X-ray observations. The expected \gr energy flux at TeV-energies at the current epoch is nearly $\epsilon_{\gamma}F_{\gamma}\approx 4\times 10^{-13}$ erg cm$^2$s$^{-1}$ under reasonable assumptions about the overall magnetic field topology and the turbulent perturbations of this field. The general nonthermal strength of the source is expected to increase roughly by a factor of two over the next 15 to 20 yrs; thereafter it should decrease with time in a secular form.Comment: 7 pages, 5 figures, accepted for publication in ApJ, a number of changes have been made, even though these are not changing the main results of the pape

A semi-analytical approach to non-linear shock acceleration

Shocks in astrophysical fluids can generate suprathermal particles by first order (or diffusive) Fermi acceleration. In the test particle regime there is a simple relation between the spectrum of the accelerated particles and the jump conditions at the shock. This simple picture becomes complicated when the pressure of the accelerated particles becomes comparable with the pressure of the shocked fluid, so that the non-linear backreaction of the particles becomes non negligible and the spectrum is affected in a substantial way. Though only numerical simulations can provide a fully self-consistent approach, a more direct and easily applicable method would be very useful, and would allow to take into account the non-linear effects in particle acceleration in those cases in which they are important and still neglected. We present here a simple semi-analytical model that deals with these non-linear effects in a quantitative way. This new method, while compatible with the previous simplified results, also provides a satisfactory description of the results of numerical simulations of shock acceleration.Comment: 20 pages, 9 figures. To appear in Astroparticle Physic