Synchrotron and Synchrotron Self-Absorption for a Power-Law Particle Distribution: Asymptotic forms for Finite Energy Range

Details Synchrotron and Synchrotron Self-Absorption for a Power-Law Particle Distribution: Asymptotic forms for Finite Energy Range Synchrotron and Synchrotron Self-Absorption for a Power-Law Particle Distribution: Asymptotic forms for Finite Energy Range

Dec 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009apj...707..278f&link_type=abstract

The Astrophysical Journal, Volume 707, Issue 1, pp. 278-282 (2009).

Astronomy and Astrophysics

Astronomy

3

Gamma Rays: Bursts, Radiation Mechanisms: Non-Thermal

Scientific paper

We calculate and plot the synchrotron power, P ν, the absorption coefficient, αν, and the source function, S ν, for a power-law distribution of charged particles with Lorentz parameter values γ1 <= γ <= γ2. For this purpose, we define parametric functions Zp (x, η), Hp (x, η), and Yp (x, η) with η = γ2/γ1, such that P ν vprop Zp (γ-2 1ν/ν0, η), αν vprop Hp (γ-2 1ν/ν0, η), and S ν vprop Yp (γ-2 1ν/ν0, η). Corresponding asymptotic forms are also calculated and plotted for three frequency ranges, i.e., x Lt 1, 1 Lt x Lt η2, and x Gt η2, especially in the case of finite parameter η. Asymptotic forms of the middle range are possible for functions Zp and Yp for p>1/3, and for function Hp for all positive values of index p. A characteristic value, η c (p, ɛ) (with ɛ Lt 1), is then defined for each of the above functions so that for η gsim η c (p, ɛ) the middle range asymptotic forms could be considered. Further calculation details are also presented and discussed.

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