Inclination-Dependent Luminosity Function of Spiral Galaxies in the Sloan Digital Sky Survey: Implication for Dust Extinction

Using a samples of 61506 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 where 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 5 SDSS bands give an extinction curve which is a power law of wavelength ($\tau\propto\lambda^{-n}$), with a power index $n=0.96\pm0.04$. Using the dust extinction for galaxies obtained by Kauffmann et al. (2003), we derive an `extinction-corrected' luminosity function for spiral galaxies. Dust extinction makes $M^*$ dimmer by about 0.5 magnitudes in the $z$-band, and about 1.2 magnitudes in the $u$- band. Since our analysis is based on a sample where 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 absorptions.