4.7.1
Bolometric luminosities
Despite some minor shortcomings, the success of the VEDIS can also be explicitly seen in Fig. 4.8, where the bolometric quasar luminosity function (QLF) is plotted for dif- ferent redshift bins in direct comparison to the FID model. Black symbols show the observational compilation from Hopkins et al. (2007c), the green lines correspond to the output of the FID model and the red lines illustrate the result from the VEDIS model, where a reasonably good agreement is achieved with observations for the whole redshift range. At redshift z = 5, a change in number density by about an order
Figure 4.8: Bolometric quasar luminosity functions for different redshifts. Black symbols show the observational compilation of Hopkins et al. (2007c), the green solid line corresponds to the output of the FID model and the red line illustrates the results from the VEDIS model. For the VEDIS model, a reasonably good agreement with observations can be obtained.
of magnitude is obtained due to the heavy seeding scenario and the large scatter in the accreted black hole mass in the VEDIS model compared to the FID model. For the redshift range between 1.5−3, the additional model extensions do not cause any
significant differences. However, for low redshifts, in particular at z = 0.1, the de-
creasing sub-Eddington limit leads to a discrepancy in AGN number densities at the high-luminous end by2−3orders of magnitude. Moreover, at the low-luminosity end,
one can still see a change in VEDIS model by almost one order of magnitude as AGN are assumed to be additionally triggered by disk instabilities. One can conclude, owing to the better match to the observed QLF in the VEDIS model than in the FID model, that the additional assumptions might be important and non-negligible ingredients for galaxy formation and the connected black hole growth and, in particular, for the ob- served downsizing trend.
Figure 4.9: Hard X-ray AGN luminosity function for different redshifts ranges. Black symbols show the observational compilation of Aird et al. (2010), the green solid lines correspond to the output of the FID model and the blue dashed lines illustrates the same results with dust correction.
4.7.2
Hard X-ray luminosities
Besides comparing the model output to the bolometric luminosities from the obser- vational compilations of Hopkins et al. (2007c), the predicted bolometric luminosities from the model are converted into hard X-ray luminosities in order to compare them directly to the observed hard X-ray luminosities of a recent observational study from
Aird et al. (2010). In order to calculate the hard X-ray luminosities, we use the bolo- metric correction according toMarconi et al.(2004), where the hard X-ray luminosities are approximated by the following third-degree polynomial fit:
log(LHXR/Lbol) =−1.54−0.24L−0.012L2+ 0.0015L3 (4.30) with L = log(Lbol/L")−12. These corrections are derived from template spectra, which are truncated at λ > 1 µm in order to remove the IR bump and which, and hence the bolometric corrections, are assumed to be independent of redshift. More- over, a dust correction for the model luminosities is additionally assumed, as suggested
Figure 4.10: Hard X-ray AGN luminosity function for different redshifts ranges. Black symbols show the observational compilation of Aird et al. (2010), the red solid lines correspond to the output of the VEDIS model and the blue dashed lines illustrates the same results with dust correction.
by different observational studies (Ueda et al., 2003; Hasinger, 2004; La Franca et al.,
2005), where they show that the fraction of obscured AGN is luminosity dependent and decreases with increasing luminosity. However, whether there exists an additional redshift dependence of the obscured fraction is under current, intense debate. Studies from Ballantyne et al. (2006) and Gilli et al.(2007) propose a strong evolution of the obscured AGN population (a relatively increasing fraction of obscured AGN with in- creasing redshift) to reproduce the properties of the X-ray backround, whereas Ueda et al. (2003) andSteffen et al.(2003) do not find a clear dependence of the obscuration on redshift. In this thesis, I follow a recent observational study from Hasinger (2008), where they investigate a sample of X-ray selected AGN from ten independent samples. They find that the fraction of obscured AGN increases strongly with decreasing lu- minosity and increasing redshift. Following Hasinger (2008), the obscured fraction of AGN is modeled and approximated by this equation (see also Fanidakis et al. (2010)):
Fitting this equation to observations, as it is shown inHasinger(2008), results in a value for the exponent of α= 0.62. However, in this study, it is found that an even stronger
redshift dependence is needed to be consistent with the observations (α ≈0.8). With
calculating the obscured fraction of AGN in the hard X-ray band, the visible fraction of AGN fvis = 1−fobsc can be modeled, and thus the visible number density of AGN in the hard X-ray range can be approximated by:
Φvis(LHXR) = fvis×Φtotal(LHXR) (4.32) Fig. 4.9 shows the hard X-ray luminosity function for different redshift ranges. The black symbols illustrate the observations from Aird et al. (2010), the green lines show the predictions from the fiducial model without dust correction, whereas the blue dashed lines correspond to the number densities of visible AGN. At low redshift (z = 0−1), the fiducial model under-predicts moderately luminous AGN and over-
predicts luminous AGN, as already seen for the bolometric luminosity functions in Fig.
4.8. As expected, in this redshift range, dust correction plays only a minor role and leads to small differences at the low luminosity end. Turning to higher redshiftz >1.5,
the high luminosity end is only slightly overestimated anymore. However, at the low luminosity end the fiducial model without dust correction extremely over-predicts the number densities of these objects. Therefore, considering the number densities only of the visible fraction of AGN leads to a significantly better agreement with the ob- servations at the low mass end. This shows clearly, that the model output confirms the observational finding of the existence of a strong redshift dependence in the ob- scured fraction of AGN. Besides, we can conclude that dust correction alone seems not to a be sufficient process in order to reproduce downsizing in the FID model, as at low redshift, the dust correction can account neither for the excess of luminous AGN nor for the lack of moderately luminous AGN. Considering the output of the VEDIS model, Fig. 4.10illustrates the corresponding hard X-ray luminosities (solid, red lines) compared to the observations (black symbols). The blue, dashed lines show the results considering in addition the dust correction for the VEDIS model. Compared to the FID model, the predictions of the VEDIS model lead to a significant better agreement with the observations at redshifts z ≤ 1 as through the additional modifications the
number density of luminous AGN is reduced and the amount of moderately luminous AGN gets increased, as it was already shown for the bolometric luminosity function above. The results including dust obscuration show still a fairly good match with ob- servations at this redshift range. Therefore, one can conclude that the best-fit VEDIS model combined with a redshift and luminosity dependent dust obscuration correction is successful in predicting the observed hard X-ray luminosity function for the whole, observed redshift range. Note that Fanidakis et al. (2010) use the same bolometric conversion for calculating hard X-ray luminosities and the almost the same dust ob- scuration correction (they use a smaller value for α). They show that they are able
to match the hard X-ray luminosity functions from an observational study ofHasinger et al. (2005). However, their predictions are only illustrated for a comparatively small redshift range of 0.2< z < 1.6, where they have not applied any dust obscuration to
Figure 4.11: Eddington-ratio distributions for the FID, VE, VEDI and VEDIS mod- els. Different colors correspond to different redshifts. It shows that most black holes are not radiating at the Eddington-limit. This is in qualitative agreement with observa- tions (Vestergaard, 2003;Kollmeier et al., 2006;Kelly et al.,2010;Schulze & Wisotzki,
2010). Moreover, with decreasing redshift, the peak of the distribution is shifted towards smaller Eddington-ratios and the distributions are broadened.
their hard X-ray luminosities.