Astron. Astrophys. 346, 329-339 (1999)

2. Particle acceleration in SNRs

It is generally believed that cosmic ray production in SNRs occurs through the process of diffusive shock acceleration operating at the strong shock waves generated by the interaction between the ejecta from the supernova explosion and the surrounding medium. Significant effort has been put into developing dynamical models of SNR evolution which incorporate, at varying levels of detail, this basic acceleration and injection process (one of the major advantages of shock acceleration is that it does not require a separate injection process). Qualitatively the main features can be crudely summarised as follows.

In a core collapse SN the collapse releases roughly the gravitational binding energy of a neutron star, some , but most of this is radiated away in neutrinos. About is transferred, by processes which are still somewhat obscure, to the outer layers of the progenitor star which are then ejected at velocities of a few percent of the speed of light. Initially the explosion energy is almost entirely in the form of kinetic energy of these fast-moving ejecta. As the ejecta interact with the surrounding circumstellar and interstellar material they drive a strong shock ahead into the surrounding medium. The region of very hot high pressure shocked material behind this forward shock also drives a weaker shock backwards into the ejecta giving rise to a characteristic forward reverse shock pair separated by a rather unstable contact discontinuity.

This initial phase of the remnant evolution lasts until the amount of ambient matter swept up by the remnant is roughly equal to the original ejecta mass. At this so-called sweep-up time, , the energy flux through the shocks is at its highest, the expansion of the remnant begins to slow down, and a significant part of the explosion energy has been converted from kinetic energy associated with the bulk expansion to thermal (and non-thermal) energy associated with microscopic degrees of freedom of the system. The remnant now enters the second, and main, phase of its evolution in which there is rough equipartition between the microscopic and macroscopic energy densities. The evolution in this phase is approximately self-similar and resembles the exact solution obtained by Sedov for a strong point explosion in a cold gas.

It is important to realise that the approximate equality of the energy associated with the macroscopic and microscopic degrees of freedom in the Sedov-like phase is not a static equilibrium but is generated dynamically by two competing processes. As long as the remnant is compact the energy density, and thus pressure, of the microscopic degrees of freedom is very much greater than that of the external medium. This strong pressure gradient drives an expansion of the remnant which adiabatically reduces the microscopic degrees of freedom of the medium inside the remnant and converts the energy back into bulk kinetic energy of expansion. At the same time the strong shock which marks the boundary of the remnant converts this macroscopic kinetic energy of expansion back into microscopic internal form. Thus there is a continuous recycling of the original explosion energy between the micro and macro scales. This continues until either the external pressure is no longer negligible compared to the internal, or the time-scales become so long that radiative cooling becomes important. The time scales for the conversion of kinetic energy to internal energy and vice versa are roughly equal and of order the dynamical time scale of the remnant which is of order the age of the remnant, hence the approximately self-similar evolution.

In terms of particle acceleration the theory assumes that strong collisionless shocks in a tenuous plasma automatically and inevitably generate an approximately power law distribution of accelerated particles which connects smoothly to the shock-heated particle distribution at `thermal' energies and extends up to a maximum energy constrained by the shock size, speed, age and magnetic field. The acceleration mechanism is a variant of Fermi acceleration based on scattering from magnetic field structures on both sides of the shock. A key point is that these scattering structures are not those responsible for general scattering on the ISM, but strongly amplified local structures generated in a non-linear bootstrap process by the accelerated particles themselves. As long as the shock is strong it will be associated with strong magnetic turbulence which drives the effective local diffusion coefficient down to values close to the Bohm value. As pointed out by Achterberg et al. (1994) the extreme sharpness of the radio rims of some shell type SNRs can be interpreted as observational evidence for this type of effect. The source of free energy for the wave excitation is of course the strong gradient in the energetic particle distribution at the edge. Thus in the interior of the remnant, where the gradients are absent or much weaker, we do not expect such low values of the diffusion coefficient.

The net effect is that the edge of the remnant, as far as the accelerated particles are concerned, is both a self-generated diffusion barrier and a source of freshly accelerated particles. Except at the very highest energies the particles produced at the shock are convected with the post-shock flow into the interior of the remnant and effectively trapped there until the shock weakens to the point where the self-generated wave field around the shock can no longer be sustained. At this point the diffusion barrier collapses and the trapped particle population is free to diffuse out into the general ISM.

In terms of bulk energetics, the total energy of the accelerated particle population is low during the first ballistic phase of the expansion (because little of the explosion energy has been processed through the shocks) but rises rapidly as . During the sedov-like phase the total energy in accelerated particles is roughly constant at a significant fraction of the explosion energy (0.1 to 0.5 typically; see e.g. Berezhko & Völk, 1997). However, this is because of the dynamic recycling described above. Any individual particle is subject to adiabatic losses on the dynamical time-scale of the remnant, while the energy lost this way goes into driving the shock and thus generating new particles, distributed over the whole energy spectrum.

© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999
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