The '''Einasto profile''' (or '''Einasto model''') is a mathematical function that describes how the density <math>\rho</math> of a spherical stellar system varies with distance <math>r</math> from its center. Jaan Einasto introduced his model at a 1963 conference in Alma-Ata, Kazakhstan.<ref>J. Einasto (1965), Kinematics and dynamics of stellar systems, ''Trudy Inst. Astrofiz. Alma-Ata'' '''5''', 87</ref>
thumb|300px|Einasto profiles. The order of <math>\alpha</math> is reversed for large radii.
The Einasto profile possesses a power law logarithmic slope of the form: <math display="block">\gamma(r) \equiv -\frac{\operatorname{d}\ln\rho(r)}{\operatorname{d}\ln r} \propto r^{\alpha}</math> which can be rearranged to give <math display="block">\rho(r) \propto \exp{(-Ar^\alpha)} .</math> The parameter <math>\alpha</math> controls the degree of curvature of the profile. This can be seen by computing the slope on a log-log plot: <math display="block">\frac{d \ln\rho}{d \ln r} \propto -r^{\alpha} .</math>
The larger <math>\alpha</math>, the more rapidly the slope varies with radius (see figure). Einasto's law can be described as a generalization of a power law, <math>\rho\propto r^{-N}</math>, 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 (i.e. projected density) 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,<ref>J. Einasto and U. Haud (1989), [http://adsabs.harvard.edu/abs/1989A%26A...223...89E Galactic models with massive corona. I - Method. II - Galaxy] ''Astron. Astrophys.'' '''223''', 89</ref> and dark matter halos.<ref>{{cite journal|last1=Navarro|first1=Julio|authorlink1=Julio Navarro (astrophysicist)|display-authors=etal|title=The inner structure of ΛCDM haloes - III. Universality and asymptotic slopes|journal=Monthly Notices of the Royal Astronomical Society|date=April 2004|volume=349|issue=3|pages=1039–1051|doi=10.1111/j.1365-2966.2004.07586.x|doi-access=free |arxiv=astroph/0311231|bibcode=2004MNRAS.349.1039N}}</ref><ref>{{cite journal | last1 = Merritt | first1 = David | authorlink1 = David Merritt | last2 = Graham | first2 = Alister | display-authors = etal | year = 2006 | title = Empirical Models for Dark Matter Halos | journal = The Astronomical Journal | volume = 132 | issue = 6 | pages = 2685–2700 | arxiv = astro-ph/0509417 | doi = 10.1086/508988 | bibcode = 2006AJ....132.2685M| s2cid = 14511019 }}</ref>{{Clear}}
==See also== * NFW profile
== References == {{reflist}}
{{Dark matter}}
== External links == *[http://adsabs.harvard.edu/abs/2005MNRAS.358.1325C Spherical galaxy models with power-law logarithmic slope]. A comprehensive paper that derives many properties of stellar systems obeying Einasto's law.
Category:Astrophysics Category:Dark matter Category:Equations of astronomy