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We present partial-correlation analyses that examine the strengths of the relationships between LUV, LX, AlphaOX, and redshift for optically-selected AGNs. We extend the work of Strateva et al. (2005), that analyzed optically-selected AGNs from the Sloan Digital Sky Survey (SDSS), by including 52 moderate-luminosity, optically-selected AGNs from the COMBO-17 survey with corresponding deep (~250 ks to 1 Ms) X-ray observations from the Extended Chandra Deep Field-South. The COMBO-17 survey extends ~3 magnitudes deeper than the SDSS and probes the moderate-luminosity AGNs that numerically dominate the AGN population in the Universe. We also include recently published observations of 19 high-redshift, optically-selected AGNs, and 46 luminous, low-redshift AGNs from the Bright Quasar Survey. The full sample used in our analysis consists of 333 AGNs, extending out to z~6, with 293 (88%) having X-ray detections. The sample spans five decades in UV luminosity and four decades in X-ray luminosity. We confirm that AlphaOX is strongly anti-correlated with LUV (13. 6 sigma), the highest significance found for this relation to date, and find evidence suggesting that the slope of this relation may be dependent on LUV. We find that no significant correlation exists between AlphaOX and redshift (1. 3 sigma), and constrain the maximum evolution of AGN UV-to-X-ray flux ratios to be less than 30% (1 sigma) out to z=5. Using our sample's high X-ray detection fraction, we also find a significant anti-correlation (3. 0 sigma) between AlphaOX and LX. We make comparisons to earlier studies on this topic and discuss implications for X-ray vs. optical luminosity functions.
Steffen et al. (2006) studied this question.