On the Baldwin effect in active galactic nuclei. I. The continuum-spectrum-mass relationship

We suggest that the Baldwin effect is a result of the spectral dependence of the line-driving ionizing continuum on the black hole mass. We derive a relationship between the mass of the central black hole and the broad emission line luminosity in active galactic nuclei (AGN). Assuming that the UV spectrum of an AGN is emitted from an optically thick medium, we find an expression for the characteristic energy of the "UV bump" in terms of the observable luminosity and emission-line width. We show empirically and analytically that the bump energy is anticorrelated with the black hole mass and with the continuum luminosity: Our model reproduces the observed inverse correlation between equivalent width and continuum luminosity, yielding an explanation of the Baldwin effect from first principles. The model gives a good fit to the Baldwin effect of the C IV line for a mean quasar extreme-ultraviolet (EUV) spectrum and for several model spectra. The model also predicts a correlation between the strength of the Baldwin effect (the slope of the equivalent width as a function of luminosity) and the ionization potential, consistent with recent data.