// Workers AI · dad joke modeWhy did the synchrotron function go to therapy? It was feeling out of sync.

First and second Synchrotron functions.

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

• First synchrotron function $$F(x)=x\int _{x}^{\infty }K_{\frac {5}{3}}(t)\,dt$$
• Second synchrotron function $$G(x)=xK_{\frac {2}{3}}(x)$$

where K_j 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.

Further reading

• Longair, Malcolm S. (2011). High energy astrophysics (3rd ed.). Cambridge: Cambridge University Press. ISBN 978-0-511-93059-1. OCLC 702125055.
• Rybicki, George B. (2004). Radiative processes in astrophysics (PDF). Alan P. Lightman. Weinheim. p. 191. ISBN 978-3-527-61817-0. OCLC 212140606.{{cite book}}: CS1 maint: location missing publisher (link)