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Synchrotron function

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First and second Synchrotron functions.

In mathematics the synchrotron functions are defined as follows (for x ≥ 0):[1]

  • First synchrotron function
  • Second synchrotron function

where Kj is the modified Bessel function of the second kind.

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.

References

  1. ^ Fouka, M.; Ouichaoui, S. (2013-01-29). "Analytical Fits to the Synchrotron Functions". Research in Astronomy and Astrophysics. 13 (6): 680–686. arXiv:1301.6908. Bibcode:2013RAA....13..680F. doi:10.1088/1674-4527/13/6/007. S2CID 118480582.

Further reading