A formula that gives the observed surface brightness profile of elliptical galaxies as a function of projected radial distance R,
A modified version is given by Binney and Tremaine (1987, p. 39). Let
be the spherical luminosity density, and 
the observed brightness. Then
where a is the core radius, r is the radius, R is the projected radius, and
Then
Let
so
If the density is given by
where
is the mass to luminosity ratio and j(r) is the luminous density, then
The potential energy is therefore
(1)
A modified version is given by Binney and Tremaine (1987, p. 39). Let
be the spherical luminosity density, and the observed brightness. Then(2)
where a is the core radius, r is the radius, R is the projected radius, and
Then
(3)
Let
(4)
so
(5)
If the density is given by
(6)
where
is the mass to luminosity ratio and j(r) is the luminous density, then (7)
(8)
The potential energy is therefore
(5)
(10)
回复Comments
{commenttime}{commentauthor}
{CommentUrl}
{commentcontent}