We present a complete solution to the cyclotron-synchrotron radiation that results from an isotropic distribution of electrons moving in a magnetic field. We make no approximations in the calculations other than artificially broadening the harmonics by a small amount in order to facilitate the numerics. In contrast to previous calculations, we sum over all relevant harmonics and integrate over all particle and observer angles relative to the magnetic field. We present emission spectra for electron temperatures T = 5 x 108 K, 109 K, 2 x 1010 K to 3.2 x 1010 K, and provide simple fitting formulae that give a fairly accurate representation of the detailed results. For T ≥ 3.2 x 1010 K, the spectrum is represented well by the asymptotic synchrotron formula, which is obtained by assuming that the radiating electrons have Lorentz factors large compared to unity. We give an improved fitting formula for this asymptotic case as well.
The Astrophysical Journal
- Pub Date:
- July 1996
- MAGNETIC FIELDS;
- RADIATION MECHANISMS: THERMAL;
- 17 pages, 6 Postscript figures, tarred and gzipped. Accepted to The Astrophysical Journal. Also available at this http://cfa-www.harvard.edu/~rohan/