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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>[[Jaan Einasto|J. Einasto]] (1965), Kinematics and dynamics of stellar systems, ''Trudy Inst. Astrofiz. Alma-Ata'' '''51''', 87</ref>
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[[Image:Einasto.jpg|thumb|left|Einasto profiles.]]
 
The Einasto profile has the form
 
:<math>
\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>
d\ (\log\rho)/d\ (\log 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.
 
Einasto's model has been used to describe many types of system, including [[galaxy|galaxies]]<ref>[[Jaan Einasto|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 halo]]s.<ref>{{cite journal
  | last1 = Merritt  | first1 = David | authorlink1 = David Merritt | last2 = Graham
| first2 = Alister | last3 = et al. | year = 2006
| title = Empirical Models for Dark Matter Halos | journal = The Astronomical Journal
| volume = 132 | issue = 6 | pages = 2685–2700 | arxiv = astro-ph/0509417
| bibcode = 2006AJ....132.2685M | doi = 10.1086/508988
| url = http://adsabs.harvard.edu/abs/2006AJ....132.2685M}}</ref>
 
== References ==
{{reflist}}
 
== 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]]

Latest revision as of 14:46, 5 December 2014

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