Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum

Details Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum

2009-01-13

arxiv.org/abs/0901.1702v1

Astrophys.J.695:1273-1288,2009

Astronomy and Astrophysics

Astrophysics

High Energy Astrophysical Phenomena

38 pages, 12 figures, ApJ accepted

Scientific paper

10.1088/0004-637X/695/2/1273

We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low energy CRs and finite Alfv\'en wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration time scale to relativistic energies is much shorter than the dynamical evolution time scale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock sonic and Alfv\'enic Mach numbers and the CR injection efficiency. For the diffusion models we employ, the shock precursor structure evolves in an approximately self-similar fashion, depending only on the similarity variable, x/(u_s t). During this self-similar stage, the CR distribution at the subshock maintains a characteristic form as it evolves: the sum of two power-laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum, p_{max}(t). Based on the results of the DSA simulations spanning a range of Mach numbers, we suggest functional forms for the shock structure parameters, from which the aforementioned form of CR spectrum can be constructed. These analytic forms may represent approximate solutions to the DSA problem for astrophysical shocks during the self-similar evolutionary stage as well as during the steady-state stage if p_{max} is fixed.

Affiliated with

Also associated with

No associations

Rating

Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-71457