Synchrotron function
Encyclopedia
In mathematics
the synchrotron functions are defined as follows (for x ≥ 0):
where Kj is the modified Bessel function
of the second kind. These functions are shown on the right, as the output from a plot in Mathematica
.
For further information, see High Energy Astrophysics, Malcolm S. Longair, CUP, 1990.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
the synchrotron functions are defined as follows (for x ≥ 0):
- First synchrotron function
- Second synchrotron function
where Kj is the modified Bessel function
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
of the second kind. These functions are shown on the right, as the output from a plot in Mathematica
Mathematica
Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
.
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.