SYNCHROTRON AND SYNCHROTRON SELF-ABSORPTION FOR A POWER-LAW PARTICLE DISTRIBUTION: ASYMPTOTIC FORMS FOR FINITE ENERGY RANGE
- Research Center in Astronomy, Astrophysics and Geophysics, B.P. 63, Algiers Observatory, Bouzareah, Algiers (Algeria)
- University of Sciences and Technology H. Boumediene, Faculty of Physics, Laboratory of Nuclear Sciences, B.P. 32, 16111 Bab Ezzouaz, Algiers (Algeria)
We calculate and plot the synchrotron power, P {sub n}u, the absorption coefficient, alpha{sub n}u, and the source function, S {sub n}u, for a power-law distribution of charged particles with Lorentz parameter values gamma{sub 1} <= gamma <= gamma{sub 2}. For this purpose, we define parametric functions Z{sub p} (x, eta), H{sub p} (x, eta), and Y{sub p} (x, eta) with eta = gamma{sub 2}/gamma{sub 1}, such that P {sub n}u propor to Z{sub p} (gamma{sup -2} {sub 1}nu/nu{sub 0}, eta), alpha{sub n}u propor to H{sub p} (gamma{sup -2} {sub 1}nu/nu{sub 0}, eta), and S {sub n}u propor to Y{sub p} (gamma{sup -2} {sub 1}nu/nu{sub 0}, eta). Corresponding asymptotic forms are also calculated and plotted for three frequency ranges, i.e., x << 1, 1 << x << eta{sup 2}, and x >> eta{sup 2}, especially in the case of finite parameter eta. Asymptotic forms of the middle range are possible for functions Z{sub p} and Y{sub p} for p>1/3, and for function H{sub p} for all positive values of index p. A characteristic value, eta {sub c}(p, epsilon) (with epsilon << 1), is then defined for each of the above functions so that for eta approx> eta {sub c}(p, epsilon) the middle range asymptotic forms could be considered. Further calculation details are also presented and discussed.
- OSTI ID:
- 21389322
- Journal Information:
- Astrophysical Journal, Vol. 707, Issue 1; Other Information: DOI: 10.1088/0004-637X/707/1/278; ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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