Particle acceleration in winds of star clusters

The origin of cosmic rays in our Galaxy remains a subject of active debate. While supernova remnant shocks are often invoked as the sites of acceleration, it is now widely accepted that the difficulties of such sources in reaching PeV energies are daunting and it seems likely that only a subclass of rare remnants can satisfy the necessary conditions. Moreover the spectra of cosmic rays escaping the remnants have a complex shape that is not obviously the same as the spectra observed at the Earth. Here we investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters’ winds in the interstellar medium. While the main limitation to the maximum energy in supernova remnants comes from the need for effective wave excitation upstream so as to confine particles in the near-shock region and speed up the acceleration process, at the termination shock of star clusters the confinement of particles upstream in guaranteed by the geometry of the problem. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for powerful clusters in the high end of the luminosity tail for these sources. A crucial role in this problem is played by the dissipation of energy in the wind to magnetic perturbations. Under reasonable conditions the spectrum of the accelerated particles has a power law shape with a slope 4÷4.3, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.

Study of the Electron Distribution Function Downstream of the Solar Wind Termination Shock: A Touch with the Interstellar Medium

We theoretically describe the evolution of the solar wind electron distribution function downstream of the termination shock under the influence of electron impact ionizations of interstellar H- and He- atoms that enter the heliosheath from the upwind hemisphere and continue to move along the heliotail region. We start from a kinetic phasespace transport equation in the bulk frame of the heliosheath plasma flow that takes into account convective changes, cooling processes, whistler wave-induced energy diffusion, and electron injection into and removal from velocity-space cells due to electron impact ionization processes of interstellar neutral atoms. From this kinetic equation we can ascend to an associated pressure moment of the electron distribution function and there with arrive at a so-called pressure transport equation describing the evolution of the electron pressure in the bulk-velocity frame of the plasma flow. Assuming that the local electron distribution can be represented by a kappa function with a K- parameter that varies with the streamline coordinate s, we obtain an ordinary differential equation for K as function of s. With this result we first gain the heliosheath electron distribution function downstream of the termination shock, and at second, obtain a newly based estimate of the ionization probability of interstellar neutral atoms like H and He at the passage over the heliosheath. The latter information will enable us to quantitatively predict the interstellar inflow of neutral He- and H- atoms into the heliosheath. As we shall show the effect of H- and He impact ionizations especially gives its signature to the electron distribution along the extended down-tail region of the heliosheath. This is why we especially study this 100AU- extended down-tail region here in this article.