A WIDE-FIELD MULTICOLOR SURVEY FOR HIGH-REDSHIFT QUASARS, Z-GREATER-THAN-OR-EQUAL-TO-2.2 .3. THE LUMINOSITY FUNCTION

In two previous papers we presented the aims, methods, and spectroscopic results, and computed the completeness of a six-band multicolor survey for high-redshift quasars, covering an effective area of 43.0 deg(2), to m(or) = 20.0. In this paper the complete sample of 86 quasars 2.2 less than or equal to z < 4.5 is combined with other published samples to determine the continuum and line luminosity functions, Phi(C), Phi(L), over the redshift range 2.0 less than or equal to z < 4.5. The estimate of the completeness of our multicolor sample has been revised following the development of a more sophisticated treatment of the line and continuum absorption from intervening matter, and the incorporation of the effects of quasar variability. Appendices describe the new model procedures. The luminosity function calculation also accounts for the range of line strength and continuum spectral index, as well as the photometric errors. The results are presented in terms of two magnitudes, M(C(1216)) and M(L(1216)), logarithmic measures of the absolute continuum flux under the Ly alpha/N v emission line, and of the Ly alpha/N v line luminosity. Additionally the intrinsic distribution of continuum spectral indices alpha is derived. This completes the parameterization of the rest-frame UV spectral-energy distributions of the quasar population, in the four-dimensional space with axes M(C(1216)), M(L(1216)), alpha, z. The nature of the evolution of the continuum luminosity function changes near the midpoint of the redshift interval, and no simple model provides a satisfactory fit over the entire redshift range 2.0 less than or equal to z < 4.5. For redshifts z < 3.5, no-evolution luminosity functions, and luminosity functions of evolving single power-law form are inadequate. The best fit is obtained with functions of the Schechter or double power-law type, in which only the bright end evolves, to brighter magnitudes at higher redshift. The evolution ceases near z = 3.3, with a marked decline in space density beyond. Comparison of the number of survey quasars in the redshift range 3.5 less than or equal to z < 4.5 against the number expected if there is no decline beyond z = 3.3 shows a shortfall by a factor 6.1(6.5), for q(o) = 0.1(0.5). At the 95% confidence level there is a decline in the space density of quasars M(C) < -25.6(< -24.5) between redshifts 3.3 and 4.0 by a factor greater than 3.1(> 3.3). These limits include an allowance for the uncertainty in the estimate of the luminosity function at z = 3.3. Our results are very similar to those obtained by Osmer a decade ago. A similar comparison against the preliminary results of the brighter survey of Irwin et al. indicates that the amount of the decline is approximately independent of absolute magnitude, brighter than the above limits. The observed decline in the space density of quasars beyond z = 3.3 is compatible with a constant true space density and obscuration by dust in intervening damped Ly alpha systems only if the parameters of the obscuration (dust to gas ratio, etc.) are at the upper end of current observational limits. The line luminosity function at z = 3 and 4 is computed, to compare against the forthcoming results of the wide-field grism survey of Schmidt et al.