Nonlinear theory of cosmic rays acceleration by steady stellar wind

Physics

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We consider the model of particles acceleration to reletevistic energies by spherical symmetric strong shock wave of stellar wind. It's supposed, that the particles are accelerated by the Fermi mechanism. The effect of the accelerated particles on the hydrodynamic parametres of stellar wind is also taken into account. Our method allows to find the self-consistent steady solution for a strong shock, significantly modified by accelerated particles. On the hydrodynamic stage we give the pressure of accelerated particles and find the profile of hydrodynamical stream as a solution of hydrodynamic equations. On the kinetic stage we calculate the spectrum of accelerated particles and determine its pressure by self-consistent method. In this report we also discuss possibility of nonthermal X-ray radiation and give recommendations for observations. 1 Statement of problem . Interaction of strong stellar wind with surrounding medium creates shock fronts (Weaver et al.,1977), which is capable of generating accelerated particles. The linear theory of acceleration process by spherical steady shock wave in stellar wind was developed in papers (Webb et al.,1983),(Klepach et al.,1997),(Toptygin,1999). If acceleration is efficient enough, nonlinear effect of accelerated particles on the stellar wind dynamics is significant (see solution of analogous problem for supernova explosion in Toptygin(2000)). The consideration of nonlinear effects is important for correct calculation of the energetic spectrum of accelerated particles and energy distribution between relativistic particles and hot surrounding gas. In the given paper we consider nonlinear problem formation of the energetic spectrum of accelerated particles by stellar wind shock wave. We take into account the back effect of particles on hydrodynamics of the stellar wind. In stellar

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