Synchrotron function: Difference between revisions

Revision as of 23:55, 3 November 2005

Revision as of 00:44, 4 November 2005

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:<math>f(x) = x K_{\frac{2}{3}}(x)</math>

where ''K''_''j'' is the modified [[Bessel function]] of the second kind. This is needed when calculating the spectra for different types ofThe synchrotron emssion.functions look It takes a number of spectrum of electrons generated by a seperate process (such as a power law distribution of electrons and positrons) and convertslike this to the spectrum of photons generated in the magnetic field by the input electrons.:

[[Image:Firstsynchfunction.jpg|thumb|First synchrotron function, F(x)]]

[[Image:secondsynchfunction.jpg|thumb|Second synchrotron function, G(x)]]

== Use in Astrophysics ==

In astrophysics, x is usually a ratio of frequencies, that is, the frequency over a critical frequency (critical frequency is the frequency at which most synchrotron radiation is radiated). This is needed when calculating the spectra for different types of synchrotron emssion. It takes a spectrum of electrons (or any charged particle) generated by a seperate process (such as a power law distribution of electrons and positrons from a constant injection spectrum) and converts this to the spectrum of photons generated by the input electrons/positrons.

For further information, see ''High Energy Astrophysics'', Malcolm S. Longair, CUP, 1990.