On the predictive power of the minimum energy condition. I. Isotropic steady-state configurations.
Abstract
We calculate the steady-state number and energy densities for cosmic ray protons and electrons, respectively. Application on the minimum energy method is given under the assumption of an acceleration process, which leads to the same total injection rates with the same power law in momentum for both species of particles. The asymptotic formula makes it possible to base the magnetic field estimate by the minimum energy condition on a more physical ground, relying on assumptions like the standard ratio of 100 between the energy densities in protons and in electrons. The possible contributions from secondary electrons are discussed. With this procedure, the predictive power of the minimum energy method on the magnetic field strength is strongly enhanced, depending only on the validity of equipartition in general and on the dominance of power-law injection in momentum. Applying this revised minimum energy method to the data on M51 yields a mean magnetic field strength of about 6.5 micro-G, which is a factor of 2 lower than previous findings. This difference is mainly due to an overestimate of the cosmic ray energy density in the standard method.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- March 1993
- Bibcode:
- 1993A&A...270...91P
- Keywords:
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- Cosmic Rays;
- Electron Energy;
- Particle Acceleration;
- Proton Energy;
- Synchrotron Radiation;
- Interstellar Magnetic Fields;
- Isotropic Media;
- Magnetic Field Configurations;
- Space Radiation