Einasto profile
The Einasto profile is a mathematical function that describes how the density of a spherical stellar system varies with distance from its center. Jaan Einasto introduced his model at a 1963 conference in Alma-Ata, Kazakhstan.
The Einasto profile possesses a power law logarithmic slope of the form:
which can be rearranged to give
The parameter controls the degree of curvature of the profile. This can be seen by computing the slope on a log-log plot:
The larger, the more rapidly the slope varies with radius. Einasto's law can be described as a generalization of a power law,, which has a constant slope on a log-log plot.
Einasto's model has the same mathematical form as Sersic's law, which is used to describe the surface brightness profile of galaxies, except that the Einasto model describes a spherically symmetric density distribution in 3 dimensions, whereas the Sersic law describes a circularly symmetric surface density distribution in two dimensions.
Einasto's model has been used to describe many types of system, including galaxies, and dark matter halos.