Inclination‐dependent Luminosity Function of Spiral Galaxies in the Sloan Digital Sky Survey: Implications for Dust Extinction

Abstract

Using a samples of 61506 spiral galaxies selected from the SDSS DR2, we\nexamine the luminosity function (LF) of spiral galaxies with different\ninclination angles. We find that the characteristic luminosity of the LF,\n$L^*$, decreases with increasing inclination, while the faint-end slope,\n$\\alpha$, depends only weakly on it. The inclination-dependence of the LF is\nconsistent with that expected from a simple model where the optical depth is\nproportional to the cosine of the inclination angle, and we use a likelihood\nmethod to recover both the coefficient in front of the cosine, $\\gamma$, and\nthe LF for galaxies viewed face-on. The value of $\\gamma$ is quite independent\nof galaxy luminosity in a given band, and the values of $\\gamma$ obtained in\nthis way for the 5 SDSS bands give an extinction curve which is a power law of\nwavelength ($\\tau\\propto\\lambda^{-n}$), with a power index $n=0.96\\pm0.04$.\nUsing the dust extinction for galaxies obtained by Kauffmann et al. (2003), we\nderive an `extinction-corrected' luminosity function for spiral galaxies. Dust\nextinction makes $M^*$ dimmer by about 0.5 magnitudes in the $z$-band, and\nabout 1.2 magnitudes in the $u$- band. Since our analysis is based on a sample\nwhere selection effects are well under control, the dimming of edge-on galaxies\nrelative to face-on galaxies is best explained by assuming that galaxy disks\nare optically thick in dust absorptions.\n