3.1. Disk model and fitting
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 (sech2) 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