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*Astron. Astrophys. 357, L1-L4 (2000)*
## 3. Analysis
### 3.1. Disk model and fitting
Our model, as described in detail in Paper I and II, for the
three-dimensional luminosity distribution for galactic disks is based
upon the fundamental work of van der Kruit and Searle (1981a):
is the central luminosity density
in units of [ pc^{-3}],
*R* and *z* are the radial resp. vertical axes in
cylindrical coordinates, *h* is the radial scalelength, and
the scaleheight.
describes three different fitting
functions for the vertical distribution: exponential, sech, and the
physically motivated isothermal (sech^{2}) case (van der Kruit
1988). is the cut-off radius, where
the stellar luminosity density is assumed to be zero outside,
mathematically expressed by a Heaviside function
H. These radii are defined at the
position where the radial profiles bend nearly vertical into the
noise, whereby a mean value is taken for the two different sides.
Depending on the inclination angle *i*, we numerically
integrate this 3D-model along the line of sight and compare the
two-dimensional result with the observed CCD image, leading to six
free fitting parameters: the inclination *i*, the central
luminosity density , the scalelength
*h*, and -height , the cut-off
radius , and the function for the
z-distribution . After our discussion
about two different fitting methods in Paper II, we finally used
our implemented "downhill simplex-method" (Nelder & Mead, 1965) to
minimize the difference between model and observed disk. The possible
influence of these parameters on the neglected dust distribution is
estimated in Paper II.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000
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