Supernovae remnant shock waves could be at the origin of cosmic rays up to
energies in excess of the knee ($E\simeq3\cdot 10^{15} $eV) if the magnetic
field is efficiently amplified by the streaming ...of accelerated particles in the
shock precursor. This paper follows up on a previous paper \citep{pell05} which
derived the properties of the MHD turbulence so generated, in particular its
anisotropic character, its amplitude and its spectrum. In the present paper, we
calculate the diffusion coefficients, also accounting for compression through
the shock, and show that the predicted three-dimensional turbulence spectrum
$k_\perp S_{3\rm d}(k_\parallel,k_\perp)\propto
k_\parallel^{-1}k_\perp^{-\alpha}$ (with $k_\parallel$ and $k_\perp$ the
wavenumber components along and perpendicular to the shock normal) generally
leads to Bohm diffusion in the parallel direction. However, if the anisotropy
is constrained by a relation of the form $k_\parallel \propto k_\perp^{2/3}$,
which arises when the turbulent energy cascade occurs at a constant rate
independent of scale, then the diffusion coefficient loses its Bohm scaling and
scales as in isotropic Kolmogorov turbulence. We show that these diffusion
coefficients allow to account for X-ray observations of supernova remnants.
This paper also calculates the modification of the Fermi cycle due to the
energy lost by cosmic rays in generating upstream turbulence and the
concomittant steepening of the energy spectrum. Finally we confirm that cosmic
rays can produced an amplified turbulence in young SNr during their free
expansion phase such that the maximal energy is close to the knee and the
spectral index is close to 2.3 in the warm phase of the interstellar medium
The present work investigates the calculation of absorption and emission cyclotron line profiles in the non-relativistic and trans-relativistic regimes. We provide fits for the ten first harmonics ...with synthetic functions down to 10^(-4) of the maximum flux with an accuracy of 20 per cent at worst. The lines at a given particle energy are calculated from the integration of the Schott formula over the photon and the particle solid angles relative to the magnetic field direction. The method can easily be extended to a larger number of harmonics. We also derive spectral fits of thermal emission line plasmas at non-relativistic and trans-relativistic temperatures extending previous parameterisations.
Supernovae remnant shock waves could be at the origin of cosmic rays up to energies in excess of the knee (\(E\simeq3\cdot 10^{15} \)eV) if the magnetic field is efficiently amplified by the ...streaming of accelerated particles in the shock precursor. This paper follows up on a previous paper \citep{pell05} which derived the properties of the MHD turbulence so generated, in particular its anisotropic character, its amplitude and its spectrum. In the present paper, we calculate the diffusion coefficients, also accounting for compression through the shock, and show that the predicted three-dimensional turbulence spectrum \(k_\perp S_{3\rm d}(k_\parallel,k_\perp)\propto k_\parallel^{-1}k_\perp^{-\alpha}\) (with \(k_\parallel\) and \(k_\perp\) the wavenumber components along and perpendicular to the shock normal) generally leads to Bohm diffusion in the parallel direction. However, if the anisotropy is constrained by a relation of the form \(k_\parallel \propto k_\perp^{2/3}\), which arises when the turbulent energy cascade occurs at a constant rate independent of scale, then the diffusion coefficient loses its Bohm scaling and scales as in isotropic Kolmogorov turbulence. We show that these diffusion coefficients allow to account for X-ray observations of supernova remnants. This paper also calculates the modification of the Fermi cycle due to the energy lost by cosmic rays in generating upstream turbulence and the concomittant steepening of the energy spectrum. Finally we confirm that cosmic rays can produced an amplified turbulence in young SNr during their free expansion phase such that the maximal energy is close to the knee and the spectral index is close to 2.3 in the warm phase of the interstellar medium
This paper investigates the nature of the MHD turbulence excited by the streaming of accelerated cosmic rays in a shock wave precursor. The two recognised regimes (non-resonant and resonant) of the ...streaming instability are taken into account. We show that the non-resonant instability is very efficient and saturates through a balance between its growth and non-linear transfer. The cosmic-ray resonant instability then takes over and is quenched by advection through the shock. The level of turbulence is determined by the non-resonant regime if the shock velocity \(V_{\rm sh}\) is larger than a few times \(\xi_{\rm CR} c\), where \(\xi_{\rm CR}\) is the ratio of the cosmic-ray pressure to the shock kinetic energy. The instability determines the dependence of the spectrum with respect to \(k_\parallel\) (wavenumbers along the shock normal). The transverse cascade of Alfvén waves simultaneously determines the dependence in \(k_{\perp}\). We also study the redistribution of turbulent energy between forward and backward waves, which occurs through the interaction of two Alfvén and one slow magneto-sonic wave. Eventually the spectra at the longest wavelengths are found almost proportional to \(k_{\parallel}^{-1}\). Downstream, anisotropy is further enhanced through the compression at shock crossing.
Stellar clusters are potential acceleration sites of very-high-energy (VHE, E > 100GeV) particles since they host supernova remnants (SNRs) and pulsar wind nebulae (PWNe). Additionally, in stellar ...clusters, particles can also be accelerated e.g. at the boundaries of wind-blown bubbles, in colliding wind zones in massive binary systems or in the framework of collective wind or wind/supernova(SN) ejecta scenarios. Motivated by the detection of VHE gamma-ray emission towards Westerlund 2 and assuming similar particle acceleration mechanisms at work, Westerlund 1 is an even more promising target for VHE gamma-ray observations given that massive star content and distance are more favorable for detectable VHE gamma-ray emission compared to Westerlund 2. Here, H.E.S.S. observations of massive stellar clusters in general with special emphasis on the most massive stellar cluster in the galaxy, Westerlund 1 are summarized.
