Inclination-Dependent Luminosity Function Of Spiral Galaxies And The Statistic Analysis For Dust Extinction

Based on the second major data release(DR2) of the Sloan Digital Sky Sur-vey(SDSS), we build complete samples of spiral galaxies for all 5 broad optical bandsof SDSS, u,g,r,i,z. The sample of each band is divided into 15 sub-samples accord-ing to the apparent axis ratio b/a which is the indicator of the inclination of spiralgalaxies. We examine the luminosity function (LF) of each sub-sample, and we findthat the characteristic luminosity, M^*, decreases with increasing inclination, whilethe faint-end slope,α, depends weakly on the inclination. In details, the characteristicmagnitude M^* of edge-on spirals is 1.5mag fainter than that of face-on ones for u band,and the same difference for z band is some 0.54mag. The inclination dependence ofthe LF approve that the spirals are the optical thick systems and the dust is distributedon the disk of spirals.We assume a simple linear model△M^* =-γlog(b/a) to investigate quantitativelythe relation between the LFs and the inclination. The fitting results show that the modelcan be used to describe the inclination dependence of LFs for all 5 bands, b/a is onlyan apparent indicator of the inclination, which represents the truth inclination whenthe disk of the spirals is round and infinite thin. Considering the thickness and theintrinsic ellipticity of the real disks, we estimate the inclinationsθusing Monte Carlosimulation. Displacing b/a with cosθ, the linear model is better to describe the LFsdependence of the inclinations for each band.The values ofγfor the 5 SDSS bands give an extinction curveτ_λ∝(λ/5500(?))^-nwith a power index of n=0.96±0.04.Furthermore, using the dust extinction A_z for the galaxies obtained by Kauffmannand coworkers, we check the luminosity dependence of the spiral galaxies extinctionand find that the extinction is nearly independent on the luminosity. Based on thedust extinction A_z, we derive the'extinction-corrected' luminosity functions of the spi-ral galaxies for all 5 SDSS band, and the results show that the dust extinction makesM^* dimmer by 0.5 mag and 1.2mag in the z band and the u band respectively. There-fore there is significant difference between the 'extinction-corrected' LFs and apparent ones.