The singular isothermal sphere (SIS) profile is the simplest
parameterization
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, ...
of the spatial distribution of
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic par ...
in an
astronomical
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, ...
system (e.g.
galaxies
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
,
clusters of galaxies
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these obj ...
, etc.).
Density distribution
where σ
V2 is the
velocity dispersion
In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measurin ...
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
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different element ...
calculated by integrating the function out to infinite radius does not converge (i.e., is
infinite
Infinite may refer to:
Mathematics
*Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group)
Infinite ( ko, 인피니트; stylized as INFINITE) is a South Ko ...
). However, it is commonly utilized in the literature due to the simplicity of its form.
See also
*
Navarro-Frenk-White profile
References
{{reflist
Large-scale structure of the cosmos
Equations of astronomy