Abstract Using the archived optical spectra of NGC 5548 between 1989 and 2001, we derived the optical spectral index by fitting the spectra in wavelength windows unaffected by strong emission lines. We found that the index is anti-correlated with the continuum luminosity at 5100Å with a correlation coefficient of -0.8. Based on the standard thin accretion disk model, we investigated whether the correlation is related to the variations of the dimensionless accretion rate \dot{m} (mass accretion rate in Eddington unit), or the inner radius of the accretion disk Rin, or both. The correlation can be modeled well using a co-variable mode of Rin/Rs=12.5 {˙{m}^{-0.8}} (Rs is Schwarzschild radius). As luminosity increases, \dot{m} increases from 0.05 to 0.16 and at the same time Rin decreases from 133.9Rs to 55.5Rs, consistent with the prediction for a transition radius within which an ADAF structure exists. We concluded that the change of both inner accretion radius and the dimensionless accretion rate are key factors for the variations of spectral index and luminosity in the optical band for NGC 5548.

Keywords accretion: accretion disks - blackhole physics - galaxies: individual (NGC 5548)

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