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 spectroscop ic results, and computed the completeness of a six-band multicolor sur vey 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 samp les 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 revise d following the development of a more sophisticated treatment of the l ine and continuum absorption from intervening matter, and the incorpor ation of the effects of quasar variability. Appendices describe the ne w model procedures. The luminosity function calculation also accounts for the range of line strength and continuum spectral index, as well a s the photometric errors. The results are presented in terms of two ma gnitudes, M(C(1216)) and M(L(1216)), logarithmic measures of the absol ute 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 param eterization 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 lu minosity function changes near the midpoint of the redshift interval, and no simple model provides a satisfactory fit over the entire redshi ft 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 s ingle power-law form are inadequate. The best fit is obtained with fun ctions of the Schechter or double power-law type, in which only the br ight end evolves, to brighter magnitudes at higher redshift. The evolu tion ceases near z = 3.3, with a marked decline in space density beyon d. 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 i s no decline beyond z = 3.3 shows a shortfall by a factor 6.1(6.5), fo r q(o) = 0.1(0.5). At the 95% confidence level there is a decline in t he 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 funct ion at z = 3.3. Our results are very similar to those obtained by Osme r a decade ago. A similar comparison against the preliminary results o f 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 qu asars 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 th e upper end of current observational limits. The line luminosity funct ion at z = 3 and 4 is computed, to compare against the forthcoming res ults of the wide-field grism survey of Schmidt et al.