The Soft XRay Luminosity Function and Space Density Evolution

Using the sample of 000 type-1 AGN, Hasinger, Miyaji, and Schmidt [36] have employed two different methods to derive the AGN-1 X-ray luminosity function and its evolution. The first method uses a variant of the 1 /Va method, which was developed in [56]. The binned luminosity function in a given red-shift bin zi is derived by dividing the observed number Nobs(Lx, zi) by the volume appropriate to the red-shift range and the survey X-ray flux limits and solid angles. To evaluate the bias in this value caused by a gradient of the luminosity function across the bin, each of the luminosity functions is fitted by an analytical function. This function is then used to predict Nmdl(Lx,zi). Correcting the luminosity function by the ratio Nobs/Nmdl takes care of the bias to first order. Figure 25.6 shows the luminosity function derived this way in different red-shift shells. A change of shape of the luminosity function with red-shift is clearly seen and can thus rule out simple density or luminosity evolution models. In a second step, instead of binning into red-shift shells, the sample has been cut into different luminosity classes and the evolution of the space density with red-shift was computed.

The second method uses a variant of the 1 /Vmax method. Individual Vmax of the ROSAT Bright Survey (RBS) sources [74] are used to evaluate the zero-redshift luminosity function. This is free of the bias described above: using this luminosity function to derive the number of expected RBS sources matches the observed numbers precisely. In the subsequent derivation of the evolution, i.e., the space density as a function of redshift, binning in luminosity and red-shift is introduced to allow evaluation of the results. Bias at this stage is avoided by iterating the parameters of an analytical representation of the space density function. Together with the zero-redshift luminsity function this is used to predict Nmod(Lx,zi) for the surveys. The observed densities in the bins are derived by multiplying the space density value by the ratio Nobs (Lx, Zi) /Nmod (Lx, Zi).

The other difference between the two methods is in the treatment of missing red-shifts for optically faint objects. In the binned method, all AGN without

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42 43 44 45 46 47 40 42 43 44 45 46 47 48 42 43 44 45 46 47 48 Log Lx [h^2 erg s"1]

Fig. 25.6 The soft X-ray luminosity function of the type-1 AGN sample in different red-shift shells for the nominal case as labeled. The error bars correspond to 68% Poisson errors of the number of AGNs in the bin. The best-fit two power-law model for the 0.015 < z < 0.2 shell are overplotted in the higher red-shift panels for reference. The dotted and dashed lines give the best-fit PLE and LDDE models (from [36])

red-shift with R > 24.0 were in turn assigned the central red-shift of each red-shift bin to derive an upper boundary to the luminosity function. In the unbinned method, the optical magnitudes of the RBS sources were used to derive the optical red-shift limit corresponding to R = 24.0. The Vmax values for surveys spectroscopically or photometrically incomplete beyond R = 24.0 (such as CDF-N) were based on the smaller of the X-ray and optical red-shift limits.

Figure 25.7 shows a direct comparison between the binned and unbinned determinations of the space density, which agree very well within statistical errors. The fundamental result is that the space density of lower-luminosity AGN- peaks at significantly lower red-shift than that of the higher-luminosity (QSO-type) AGN. Also, the amount of evolution from red-shift zero to the peak is much less for lower-luminosity AGN. The result is consistent with previous determinations based on

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Fig. 25.7 Comparison between the space densities derived with two different methods. The data points with error bars refer to the binned treatment using the Nobs/Nmdl method, the dashed error bars corresponding to the maximum contribution of unidentified sources. The solid lines, the filled circles and the dashed lines refer to the unbinned method. (from [36])

Redshift

Fig. 25.7 Comparison between the space densities derived with two different methods. The data points with error bars refer to the binned treatment using the Nobs/Nmdl method, the dashed error bars corresponding to the maximum contribution of unidentified sources. The solid lines, the filled circles and the dashed lines refer to the unbinned method. (from [36])

less sensitive and/or complete data, but for the first time our analysis shows a high-red-shift decline for all luminosities LX < 1045ergs_1 (at higher luminosities the statistics is still inconclusive). Albeit the different approaches and the still existing uncertainties, it is very reassuring that the general properties and absolute values of the space density are very similar in the two different derivations in.

A luminosity-dependent density evolution (LDDE) model has been fit to the data. Even though the sample is limited to soft X-ray-selected type-1 AGN, the redshift dependence of the space density is similar to that obtained by Ueda et al. (2003) for the intrinsic (deabsorbed) luminosity function of hard X-ray selected obscured and unobscured AGN, except for the normalization, where Ueda et al. reported a value about five times higher. However, with ^250 AGN selected at considerably brighter fluxes than the 1000 AGN-1 sample of [36], the statistical quality and parameter range of the Ueda et al. sample is not sufficient to, e.g., constrain the decline of the

AGN space density at high red-shift. Very recently, Barger et al., [4] have presented X-ray luminosity function analyses both in the hard and soft X-ray bands, based on the CDF-N, CDF-S, CLASXS, and ASCA surveys. Again, their results are in good agreement with the soft XLF discussed above and the hard XLF presented by Ueda et al.; however, they still suffer from substantial identification incompleteness. Also, their results on broad-line AGN are not directly comparable to the type-1 AGN sample discussed here, because they only include the optically classified type-1 AGN and thus miss most of the low-luminosity unabsorbed AGN-1. The space density of soft X-ray selected high-luminosity QSOs has been compared to the one of luminous optically- and radio-selected QSOs by [90], who concluded that a substantial high-red-shift decline is observed in all wavebands.

These new results paint a dramatically different evolutionary picture for low-luminosity AGN compared to the high-luminosity QSOs. While the rare, high-luminosity objects can form and feed very efficiently rather early in the Universe, with their space density declining more than two orders of magnitude at red-shifts below z = 2, the bulk of the AGN has to wait much longer to grow with a decline of space density by less than a factor of 10 below a red-shift of one. The late evolution of the low-luminosity Seyfert population is very similar to that which is required to fit the Mid-infrared source counts and background [18] and also the bulk of the star formation in the Universe [48], while the rapid evolution of powerful QSOs traces more the merging history of spheroid formation [17].

This kind of antihierarchical Black Hole growth scenario is not predicted in most semi-analytic models based on Cold Dark Matter structure formation models (e.g. [41,94]). This could indicate two modes of accretion and black hole growth with radically different accretion efficiency. A self-consistent model of the black hole growth which can simultaneously explain the antihierarchical X-ray space density evolution and the local black hole mass function derived from the MBH - a relation assuming two radically different modes of accretion has recently been presented in [55].

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