Inclination-dependent luminosity function of spiral galaxies in the Sloan Digital Sky Survey: Implications for dust extinction

Using a sample of 61,506 spiral galaxies selected from the SDSS DR2, we examine the luminosity function (LF) of spiral galaxies with different inclination angles. We find that the characteristic luminosity of the LF, L*, decreases with increasing inclination, while the faint-end slope, alpha, depends only weakly on it. The inclination dependence of the LF is consistent with that expected from a simple model in which the optical depth is proportional to the cosine of the inclination angle, and we use a likelihood method to recover both the coefficient in front of the cosine, gamma, and the LF for galaxies viewed face-on. The value of gamma is quite independent of galaxy luminosity in a given band, and the values of gamma obtained in this way for the five SDSS bands give an extinction curve that is a power law of wavelength (tau proportional to lambda(-n)), with a power index of n = 0.96 +/- 0.04. Using the dust extinction for galaxies obtained by Kauffmann and coworkers, we derive an "extinction-corrected'' luminosity function for spiral galaxies. Dust extinction makes M* dimmer by similar to 0.5 mag in the z band and by similar to 1.2 mag in the u band. Since our analysis is based on a sample in which selection effects are well under control, the dimming of edge-on galaxies relative to face-on galaxies is best explained by assuming that galaxy disks are optically thick in dust absorption.