Synchrotron function: Difference between revisions

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

In [[mathematics]] the '''synchrotron functions''' are defined as follows (for ''x'' ≥ 0):

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

where ''K''_''j'' is the modified [[Bessel function]] of the second kind. The function F(x) is shown on the right, as the output from a plot in [[Mathematica]].

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

<!-- Image with unknown copyright status removed: [[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 emission. It takes a spectrum of electrons (or any charged particle) generated by a separate 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.