Active Galactic Nuclei in the Sloan Digital Sky Survey: II. Emission-Line Luminosity Function

The emission line luminosity function of active galactic nuclei (AGN) is measured from about 3000 AGN included in the main galaxy sample of the Sloan Digital Sky Survey within a redshift range of $0<z<0.15$. The $\Ha$ and [OIII]$\lambda 5007$ luminosity functions for Seyferts cover luminosity range of $10^{5-9}$$L_\odot$ in H$\alpha$ and the shapes are well fit by broken power laws, without a turnover at fainter nuclear luminosities. Assuming a universal conversion from emission line strength to continuum luminosity, the inferred B band magnitude luminosity function is comparable both to the AGN luminosity function of previous studies and to the low redshift quasar luminosity function derived from the 2dF redshift survey. The inferred AGN number density is approximately 1/5 of all galaxies and about $6\times 10^{-3}$ of the total light of galaxies in the $r$-band comes from the nuclear activity. The numbers of Seyfert 1s and Seyfert 2s are comparable at low luminosity, while at high luminosity, Seyfert 1s outnumber Seyfert 2s by a factor of 2-4. In making the luminosity function measurements, we assumed that the nuclear luminosity is independent of the host galaxy luminosity, an assumption we test {\it a posteriori}, and show to be consistent with the data. Given the relationship between black hole mass and host galaxy bulge luminosity, the lack of correlation between nuclear and host luminosity suggests that the main variable that determines the AGN luminosity is the Eddington ratio, not the black hole mass. This appears to be different from luminous quasars, which are most likely to be shining near the Eddington limit.