Toomre's model n is the potential obtained by differentiating the surface density of a disk Kuzmin model
![](http://scienceworld.wolfram.com/astronomy/timg27.gif)
times with respect to
The result is a potential of a disk with surface density
![](http://scienceworld.wolfram.com/astronomy/timg30.gif)
where
![](http://scienceworld.wolfram.com/astronomy/timg31.gif)
This is Toomre's model n. As![](http://scienceworld.wolfram.com/astronomy/timg32.gif)
![](http://scienceworld.wolfram.com/astronomy/timg33.gif)
but
as
.
![](http://scienceworld.wolfram.com/astronomy/timg27.gif)
![](http://scienceworld.wolfram.com/astronomy/timg28.gif)
![](http://scienceworld.wolfram.com/astronomy/timg29.gif)
![](http://scienceworld.wolfram.com/astronomy/timg30.gif)
where
![](http://scienceworld.wolfram.com/astronomy/timg31.gif)
This is Toomre's model n. As
![](http://scienceworld.wolfram.com/astronomy/timg32.gif)
![](http://scienceworld.wolfram.com/astronomy/timg33.gif)
but
![](http://scienceworld.wolfram.com/astronomy/timg34.gif)
![](http://scienceworld.wolfram.com/astronomy/timg32.gif)
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