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The dependence of the X-ray-to-optical luminosity ratio on optical luminosity and redshift for optically selected QSOs is studied, largely on the basis of two, complete, magnitude-limited samples (Bright Quasar Survey /1983/ and Braccesi Faint /1984/) which were observed with the Einstein Observatory. Heterogeneous samples are established as adequate for the study of that dependence. Optimal choices for increasing the size of the data set for such a study are pointed out. The previous results of Avni and Tananbaum for alpha0, x(z, Lopt) are confirmed and strengthened, and the numerical sensitivity to changes in the values of q0 and of the optical spectral index is evaluated. It is shown that the large majority, probably all, of optically selected QSOs are X-ray loud; no more than a few percent can be X-ray quiet. Thus X-ray emission appears to be a universal property of QSOs. It is shown that comparisons of optically selected QSOs with X-ray selected QSOs are numerically sensitive to the details of the input ingredients. A residual discrepancy of about a factor of 2 between calculated and observed X-ray number counts is found. Directions for further research that are important for understanding the full bivariate optical-X-ray evolution and luminosity function for QSOs are discussed.
Avni et al. (Sun,) studied this question.