Figure: The Gaussian distribution
From Wikipedia, the free encyclopedia
A Gaussian function (named after Carl Friedrich Gauss) is a function of the form:
for some real constants a > 0, b, and c.
Gaussian functions with c2 = 2 are eigenfunctions of the Fourier transform. This means that the Fourier transform of a Gaussian function, f, is not only another Gaussian function but a scalar multiple of f.
Gaussian functions are among those functions that are elementary but lack elementary antiderivatives. Nonetheless their improper integrals over the whole real line can be evaluated exactly (see Gaussian integral):
On first order, stellar Velocity Profiles (VPs) in galaxies are often well approximated by Gaussian functions. However, departures from perfect
"Gaussianity" (on a few percents level) have been detected and
included in the modelling of stellar motions in some galaxies (the full line-of-sight velocity profile shapes can be used as observational constraints for the models). The assumption
of perfectly Gaussian VPs can be abandoned, but it still provides a good first-order approximation.
In particular, this has played an important role in the discovery (or confirmation) of
massive black holes in the centers of galaxies, like for example in the
compact elliptical galaxy M32, a satellite of the Andromeda spiral galaxy and in the discovery of massive dark halos around elliptical galaxies, like NGC 2434.
Two-dimensional Gaussian function
A 2-D Gaussian curve.
A particular example of a two-dimensional Gaussian function is
Here the coefficient A is the amplitude, xo,yo is the center and σx, σy are the x and y spreads of the blob.
The figure on the left was created using A = 1, xo = 0, yo = 0, σx = σy = 1.
Credit: Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Gaussian_function
