There is a controversy about how opaque spiral galactic disks are to blue light. An analysis of the optical properties of the ESO-LV catalogue made Valentijn (Valentijn 1990) conclude that spiral galaxies, and dwarf spirals, present an obscuring component with a mean optical depth . This unexpectedly high value for has been refuted by some authors (Huizinga & Albada, 1992). Recently, Peletier et al (1995) have presented a study of the radial surface brightness profiles in B and K for a sample of 37 galaxies, statistically determining the extinction at various places in the galaxies. They have fitted quite well the observations assuming the presence of an obscuring component with the optical depth decaying exponentially , with high values for the central optical depth () , and with a scale length superior to that of the star distribution . In this paper we study the influence that a given distribution of opaque matter through the galactic disk has on the observed luminosity function (LF). If the galaxies were completely transparent, the observed LF would be independent of the inclination of the disk, but if their mean opacity is not negligible, the observed LF contains a contribution from the inclination of the galactic disk that should be estimated. The LF plays an important role in cosmology: the estimation of the mean luminosity density, the selection function , the number counts in redshift, or in magnitude, are based on the LF (Binggeli et al 1988). In a recent paper (Leroy & Portilla 1996) we demonstrated a relation between the opacity of the disk and the excess number counts of faint-blue galaxies. The conclusion was derived from a corrected LF which was obtained under three hypothesis: i) the opaque matter was formed at some recent redshift , ii) the opacity of the disk is infinite, iii) there is a universal LF represented by the Schechter function. In the present paper, we develop a method for correcting the observed LF which is valid for more realistic distributions of opaque matter, with finite mean opacity. This is done in Sect. 3 in two steps. We obtain the face on LF firstly (i.e., the observed LF corrected for effects of inclination), and then, we correct for face on extinction obtaining the true LF. The choice of the observed LF is not a trivial issue. According to Binggeli et al (1988) the existence of a universal LF is questionable. The LF of spiral galaxies has a maximum, all the Virgo spirals can be modeled by a gaussian. Therefore, we should consider each spiral type indpendently, because probably each one of them will have a different mean opacity. Unfortunately we do not have enough information about this subject. The LF of the irregular galaxies has a maximum too, shifted to the faint end. These galaxies, like the spirals, have a disk, and if they had opaque matter, they would contribute to the modification of the true LF. In this paper we shall illustrate the method, developed in Sect. (3), with two examples of LF. We shall consider a gaussian and a Schechter function. The justification of the first case is obvious. As for the second, we have two reasons. One is that we want to compare the case of finite opacity considered in this paper with the case of infinite opacity treated in the previous one. The other one is that if we consider all the spiral and the irregular galaxies jointly, the summed LF becomes flatter at the faint extrem, and a Schechter type function could be considered as a good approximation.
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997