2.4. Profile slopes
Given HST's ability to resolve the inner light-profiles of nearby
galaxies, the slope
of a
galaxy's nuclear (the inner few hundred parsec) stellar
distribution has become a quantity of interest.
Defining 5
![]() | (22) |
Rest et al. (2001, their Equation 8) used this to measure the nuclear slopes of `core' and `power-law' galaxies. From Equation (1) one can obtain
![]() | (23) |
This is approximately
2(R / Re)1/n (see
section 2.1). Thus, at constant
(R / Re),
is a
monotonically increasing function of the Sérsic index n
(Graham et al. 2003b).
It turns out Equation (23) is appropriate for the so-called `power-law' galaxies which are now known to possess Sérsic profiles down to their resolution limit (Trujillo et al. 2004) and would be better referred to as `Sérsic' galaxies as they do not have power-law profiles. A modification is however required for the luminous `core galaxies', and is described in Section 2.7.
Another logarithmic slope of interest is that used by Gunn & Oke (1975) and Hoessel (1980), and is defined as
![]() | (24) |
From Equation (2) one has
![]() | (25) |
where, as before, x = b(R / Re)1/n (Graham et al. 1996, their equation 8).
Figures (4) and (5) show
how
(R)
and
(R) vary with
normalised radius
R / Re for a range of different profile shapes
n.
![]() |
Figure 4. The slope of the Sérsic
profile |
![]() |
Figure 5. The slope
|
5 This
should not
be confused with the incomplete gamma function seen in Equation (3).
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