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Astron. Astrophys. 357, L1-L4 (2000)

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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):

[EQUATION]

[FORMULA] is the central luminosity density in units of [[FORMULA] pc-3], R and z are the radial resp. vertical axes in cylindrical coordinates, h is the radial scalelength, and [FORMULA] the scaleheight. [FORMULA] describes three different fitting functions for the vertical distribution: exponential, sech, and the physically motivated isothermal (sech2) case (van der Kruit 1988). [FORMULA] is the cut-off radius, where the stellar luminosity density is assumed to be zero outside, mathematically expressed by a Heaviside function H[FORMULA]. 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 [FORMULA], the scalelength h, and -height [FORMULA], the cut-off radius [FORMULA], and the function for the z-distribution [FORMULA]. 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.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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