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Astron. Astrophys. 329, 840-844 (1998)

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4. Results and conclusions

We have developed a method to estimate the combined effect of extinction and inclination of the galactic disk on the luminosity function. The magnitude of the effect depends on the amount of opaque matter present in the disk. We have assumed exponential laws for the optical depth and the emission coefficent : [FORMULA]. We have seen in Sect. (3.1) that an inhomogeneous model with parameters [FORMULA] is equivalent to an homogeneous slab with mean opacity [FORMULA] given by the Eq. [FORMULA].

In Fig. 1 we show the corrected LF when the observed LF has been modeled by a gaussian with a mean of [FORMULA] mag. We have considered two values for the mean optical depth [FORMULA] and [FORMULA]. One sees a growth in the number of brilliant galaxies. This increment is compensated by a diminution in the faint end, under the inflexion points of the gaussian In Fig. 2 we show the corrected LF when the observed LF is a Schechter function. We have considered three different values of the mean optical depth, [FORMULA], [FORMULA], [FORMULA], and, the case [FORMULA] has also been included in order to compare with the previous paper (Leroy & Portilla 1996).


[FIGURE] Fig. 1. One shows the corrected LF when the observed LF is a gaussian with a mean of [FORMULA] mag . We assume the inclination i uniformly distributed. The dotted line corresponds to a mean opacity [FORMULA], and the dashed line to [FORMULA].

[FIGURE] Fig. 2. One shows the corrected LF when the observed LF is a Schechter function, assuming the inclination i of the galactic plane uniformly distributed, for three different values of the mean optical depth. The dash-dot line corresponds to [FORMULA], the dashed line to [FORMULA], and the dash-three dots line to [FORMULA]. The solid line represents the Schechter function, and the dotted line represents the correction for inclination effect in the case of infinite opacity.

The extinction effect is manifested as a shift of the Schechter function towards the left of the figure. For small opacities ([FORMULA]) we observe the extinction shift to the left, plus a slight growth in the number of faint galaxies (the opacity is too small to change the number of bright galaxies for the effect of inclination). This changes for [FORMULA]. One recognizes now the inclination effect as an increase in the number of bright galaxies and a decrease in the number of faint ones. In the same figure we show the inclination effect in the case of infinite optical depth. We have obtained similar results (Fig. 3) assuming that the variable [FORMULA] is uniformly distributed. In a recent paper (Leroy & Portilla 1996) we used the results for infinite optical depth to study the influence of the opacity on the faint galaxy number counts. The results obtained in this work indicate that the combined effect of a finite optical depth plus the extinction correction is similar to the inclination effect in the case of infinite opacity. We are using the results of this paper to estimate the mean luminosity density and the mass luminosity ratio. The selection function may also be influenced by these effects.

[FIGURE] Fig. 3. One shows the corrected luminosity function when the observed LF is a Schechter function, assuming [FORMULA] uniformly distributed, for two different values of the mean optical depth. The dash-dot line corresponds to [FORMULA],and the dashed line to [FORMULA]. The solid line and the dotted line represent the same as in Fig. 2.

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
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