Singular isothermal sphere profile

The singular isothermal sphere (SIS) profile is the simplest parameterization of the spatial distribution of matter in an astronomical system (e.g. galaxies, clusters of galaxies, etc.).

Density distribution
$$ \rho(r) = \frac{\sigma_{V}^{2}}{2\pi G r^{2}} $$

where σV2 is the velocity dispersion and G is the gravitational constant. The SIS profile is unphysical because of the singularity at zero radius and the fact that the total mass calculated by integrating the function out to infinite radius does not converge (i.e., is infinite). However, it is commonly utilized in the literature due to the simplicity of its form.