On particle acceleration around shocks. IV. Particle spectrum as a function of the equation of state of the shocked plasma

We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically, we consider the effect of energy exchange between the electron and proton thermal components downstream and the effect of generation of a turbulent magnetic field in the downstream plasma. The slope of the spectrum turns out to be appreciably affected by all these phenomena, especially in the Newtonian and transrelativistic regimes, while in the ultrarelativistic limit the universal spectrum s approximate to 4.3 seems to be a very solid prediction.