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Register a new userLuminosity-Dependent Quasar Lifetimes: A New Interpretation of the Quasar Luminosity Function
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Philip F. Hopkins
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We propose a new interpretation of the quasar luminosity function (LF), derived from physically motivated models of quasar lifetimes and light curves. In our picture, quasars evolve rapidly and their lifetime depends on both their instantaneous and peak luminosities. We study this model using simulations of galaxy mergers that successfully reproduce a wide range of observed quasar phenomena. With lifetimes inferred from the simulations, we deconvolve the observed quasar LF from the distribution of peak luminosities, and show that they differ qualitatively, unlike for the simple models of quasar lifetimes used previously. We find that the bright end of the LF traces the intrinsic peak quasar activity, but that the faint end consists of quasars which are either undergoing exponential growth to much larger masses and higher luminosities, or are in sub-Eddington quiescent states going into or coming out of a period of peak activity. The break in the LF corresponds directly to the maximum in the intrinsic distribution of peak luminosities, which falls off at both brighter and fainter luminosities. Our interpretation of the quasar LF provides a physical basis for the nature and slope of the faint-end distribution, as well as the location of the break luminosity.
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We consider implications of our new model of quasar lifetimes and light curves for the quasar luminosity function (LF) at different frequencies and redshifts. In our picture, quasars evolve rapidly and the lifetime depends on both their instantaneous and peak luminosities. The bright end of the LF traces the peak intrinsic quasar activity, but the faint end consists of quasars which are either undergoing exponential growth to much larger masses and luminosities, or are in sub-Eddington quiescent states going into or coming out of a period of peak activity. The break in the observed LF corresponds directly to the maximum in the intrinsic distribution of peak luminosities, which falls off at both brighter and fainter luminosities. We study this model using simulations of galaxy mergers which successfully reproduce a wide range of observed quasar phenomena, including the observed column density distribution. By combining quasar lifetimes and the distribution of maximum quasar luminosities determined from the observed hard X-ray LF with the corresponding luminosity and host-system dependent column densities, we produce the expected soft X-ray and B-band LFs. Our predictions agree exceptionally well with the observed LFs at all observed luminosities, over the redshift range considered (z < 1), without invoking any ad hoc assumptions about an obscured population of sources. Our results also suggest that observed correlations in hard X-ray samples between the obscured fraction of quasars and luminosity can be explained in the context of our model by the expulsion of surrounding gas due to heating from accretion feedback energy as a quasar nears its peak luminosity and final black hole mass.
We determine the number counts and z=0-5 luminosity function for a well-defined, homogeneous sample of quasars from the Sloan Digital Sky Survey (SDSS). We conservatively define the most uniform statistical sample possible, consisting of 15,343 quasars within an effective area of 1622 deg^2 that was derived from a parent sample of 46,420 spectroscopically confirmed broad-line quasars in the 5282 deg^2 of imaging data from SDSS Data Release Three. The sample extends from i=15 to i=19.1 at z<3 and to i=20.2 for z>3. The number counts and luminosity function agree well with the results of the 2dF QSO Survey, but the SDSS data probe to much higher redshifts than does the 2dF sample. The number density of luminous quasars peaks between redshifts 2 and 3, although uncertainties in the selection function in this range do not allow us to determine the peak redshift more precisely. Our best fit model has a flatter bright end slope at high redshift than at low redshift. For z<2.4 the data are best fit by a redshift-independent slope of beta = -3.1 (Phi(L) propto L^beta). Above z=2.4 the slope flattens with redshift to beta=-2.37 at z=5. This slope change, which is significant at a >5-sigma level, must be accounted for in models of the evolution of accretion onto supermassive black holes.
We apply a simple statistical method (Derenzo & Hildebrand 1969) to estimating the completeness of quasar surveys. It requires that an area has been covered by two or more, preferably different, selection techniques. We use three suitable data sets with separate selections from: variability and UV-excess (170 quasars); objective prism and UV-excess (141 quasars); multicolour and X-ray ({it ROSAT,} 19 quasars). We find that, for selection by UV-excess, the common limit of $U-B le -0.35 pm -0.05$ leads to losses of $sim 35%$, typically missing low-luminosity $(M_{B} gtrsim -24.5)$ quasars, independently of redshift. Systematic incompleteness will therefore affect the new generation of large quasar surveys that select by $U-B le -0.35$. By correcting for this incompleteness, we find, from the first data set ($B < 21.0$ and $z < 2.2$), that the evolution of the quasar luminosity function (LF) is best described by joint luminosity and density evolution. When extrapolated to $z = 0$, the LF matches that of local Seyfert galaxies better than any previous determination. The LF shows an increase in the number of low-luminosity quasars at low redshifts and of brighter quasars at intermediate redshifts, relative to the LF of Boyle et al. (1990). This result is consistent with models in which quasars fade from an initial bright phase.
In this paper, we provide updated constraints on the bolometric quasar luminosity function (QLF) from $z=0$ to $z=7$. The constraints are based on an observational compilation that includes observations in the rest-frame IR, B band, UV, soft and hard X-ray in past decades. Our method follows Hopkins et al. 2007 with an updated quasar SED model and bolometric and extinction corrections. The new best-fit bolometric quasar luminosity function behaves qualitatively different from the Hopkins et al. 2007 model at high redshift. Compared with the old model, the number density normalization decreases towards higher redshift and the bright-end slope is steeper at $zgtrsim 2$. Due to the paucity of measurements at the faint end, the faint end slope at $zgtrsim 5$ is quite uncertain. We present two models, one featuring a progressively steeper faint-end slope at higher redshift and the other featuring a shallow faint-end slope at $zgtrsim 5$. Further multi-band observations of the faint-end QLF are needed to distinguish between these models. The evolutionary pattern of the bolometric QLF can be interpreted as an early phase likely dominated by the hierarchical assembly of structures and a late phase likely dominated by the quenching of galaxies. We explore the implications of this model on the ionizing photon production by quasars, the CXB spectrum, the SMBH mass density and mass functions. The predicted hydrogen photoionization rate contributed by quasars is subdominant during the epoch of reionization and only becomes important at $zlesssim 3$. The predicted CXB spectrum, cosmic SMBH mass density and SMBH mass function are generally consistent with existing observations.
We have conducted a spectroscopic survey to find faint quasars (-26.0 < M_{1450} < -22.0) at redshifts z=3.8-5.2 in order to measure the faint end of the quasar luminosity function at these early times. Using available optical imaging data from portions of the NOAO Deep Wide-Field Survey and the Deep Lens Survey, we have color-selected quasar candidates in a total area of 3.76 deg^2. Thirty candidates have R <= 23 mags. We conducted spectroscopic followup for 28 of our candidates and found 23 QSOs, 21 of which are reported here for the first time, in the 3.74 < z <5.06 redshift range. We estimate our survey completeness through detailed Monte Carlo simulations and derive the first measurement of the density of quasars in this magnitude and redshift interval. We find that the binned luminosity function is somewhat affected by the K-correction used to compute the rest-frame absolute magnitude at 1450A. Considering only our R <= 23 sample, the best-fit single power-law (Phi propto L^beta) gives a faint-end slope beta = -1.6+/-0.2. If we consider our larger, but highly incomplete sample going one magnitude fainter, we measure a steeper faint-end slope -2 < beta < -2.5. In all cases, we consistently find faint-end slopes that are steeper than expected based on measurements at z ~ 3. We combine our sample with bright quasars from the Sloan Digital Sky Survey to derive parameters for a double-power-law luminosity function. Our best fit finds a bright-end slope, alpha = -2.4+/-0.2, and faint-end slope, beta = -2.3+/-0.2, without a well-constrained break luminosity. This is effectively a single power-law, with beta = -2.7+/-0.1. We use these results to place limits on the amount of ultraviolet radiation produced by quasars and find that quasars are able to ionize the intergalactic medium at these redshifts.
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