1. Demography how many AGN in the sky? - number counts of normal galaxies radio sources optically selected AGN X-ray selected AGN how many AGN per cubic Mpc? - Luminosity functions and their evolution normal galaxies optically selected AGN X-ray selected AGN QSO: probes of high z Universe - Supermassive black hole volume density

2. Number counts Flux limited sample: all sources in a given region of the sky with flux > than some detection limit Flim. Consider a population of objects with the same L Assume Euclidean space

3. Number counts Test of evolution of a source population (e.g. radio sources). Distances of individual sources are not required, just fluxes or magnitudes: the number of objects increases by a factor of 10 0.6 =4 with each magnitude. So, for a constant space density, 80% of the sample will be within 1 mag from the survey detection limit. If the sources have some distribution in L:

4. Problems with the derivation of the number counts Completeness of the samples. Eddington bias: random error on mag measurements can alter the number counts. Since the logN-logFlim are steep, there are more sources at faint fluxes, so random errors tend to increase the differential number counts. If the tipical error is of 0.3 mag near the flux limit, than the correction is  15%. Variability. Internal absorption affects “ color ” selection. SED, ‘ K-correction ’, redshift dependence of the flux (magnitude).

5. Radio sources number counts

6. Galaxy number counts

7. Optically selected AGN number counts Z<2.2 B=22.5  100 deg -2 B=19.5  10 deg -2 z>2.2 B=22.5  50 deg -2 B=19.5  1 deg -2 B-R=0.5

8. X-ray AGN number counts OUV sel. AGN=0.3 R=22 ==> 3  10 -15  1000deg -2 R=19 ==> 5  10 -14  25deg -2 The surface density of X-ray selected AGN is 2-10 times higher than OUV selected AGN

9. The V/V max test Marteen Schmidt (1968) developed a test for evolution not sensitive to the completeness of the sample. Suppose we detect a source of luminosity L and flux F >F lim at a distance r in Euclidean space: If we consider a sample of sources distributed uniformly, we expect that half will be found in the inner half of the volume V max and half in the outer half. So, on average, we expect V/V max =0.5

10. The V/V max test In an expanding Universe the luminosity distance must be used in place of r and r max and the constant density assumption becomes one of constant density per unit comuving volume.

11. Luminosity function In most samples of AGN > 0.5. This means that the luminosity function cannot be computed from a sample of AGN regardless of their z. Rather we need to consider restricted z bins. More often sources are drawn from flux-limited samples, and the volume surveyed is a function of the Luminosity L. Therefore, we need to account for the fact that more luminous objects can be detected at larger distances and are thus over-represented in flux limited samples. This is done by weighting each source by the reciprocal of the volume over which it could have been found:

12. Luminosity function

13. Galaxy luminosity functions B band rest frame

14. OUV selected AGN luminosity function AAT 2dF survey

15. OUV selected AGN luminosity function  -3.5,  -1.5 k  3.5

16. OUV selected AGN luminosity function

17. OUV selected AGN LF SDSS survey

18. X-ray selected AGN luminosity functions luminosity dependent density evolution

19. 2-10 keV AGN luminosity function models LDDE with variable absorbed AGN fraction La Franca et al. 2005 2-10keV 0.5-2keV

20. Comparison with HC models

21. The cosmic backgrounds energy densities

22. Assume that the intrinsic spectrum of the sources making the CXB has  E =1 I 0 =9.8  10 -8 erg/cm 2 /s/sr  ’ =4  I 0 /c

23. Optical (and soft X-ray) surveys gives values 2-3 times lower than those obtained from the CXB (and of the F.&M. and G. et al. estimates)

24. Black hole mass density A ~ 5x10 39 erg s -1 Mpc -3 A (1-  ) L Bol  BH ~ ——————  c 2 L X  =0.1 L Bol /L X =40  BH ~ 3x10 -5 M Θ Yr -1 Mpc -3  BH ~ 4x10 5 M Θ Mpc -3..

25. BH growth

26. CXB and SMBH census Two seminal results: 1.The discovery of SMBH in the most local bulges; tight correlation between M BH and bulge properties. 2.The BH mass density obtained integrating the AGN L.-F. and the CXB  that obtained from local bulges  most BH mass accreted during luminous AGN phases! Most bulges passed a phase of activity: Complete SMBH census and full understanding of AGN evolution to understand galaxy evolution

27. Local SuperMassive Black Hole AGN are powered by accretion on a SuperMassive Black Hole of 10 6 -10 10 M, Thus SMBH should exist in the nuclei of all galaxies that have experimented a violently active phase. Are all local SMBH relics of AGN activity? Do other mechanisms, as merging, play a role? There are strong correlations between the BH mass and host galaxy properties: bulge luminosity and mass and central stellar velocity dispersion. These correlations can be used to estimate the mass function of local BH and thus their total mass density  BH in the local Universe. Is possible to answer this question comparing the local BH mass function with that of AGN

28. The mass function of local BH -  (x)dx number of galaxies per unit of comoving volume with observable x between x and x + dx - logM BH = a + blogx log linear correlation between the BH mass and the observable x -  (M BH ) intrinsic dispersion; it is similar for all the correlations is one refers only to galaxies with secure BH detection - P(logM BH | logx)=(2  ) -1/2 exp-[0.5(logM BH -a-blogx/  (M BH )) 2 ] probability that the M BH is between logM BH and logM BH + dlogM BH for a given logx assuming a normal distribution -  (M BH, x) dM BH dx=[P(logM BH |logx)/M BH log10] dM BH  (x)dx Number of BH with mass between M BH and M BH +dM BH, and observable between x and x + dx

29. Then the local BH mass function is … and the total mass density of local BH is if the observable x is the bulge luminosity L It is important to test that the M BH -  and M BH -L bul correlation derived from a selected sample are consistent. The selected sample is a SDSS sample of 9000 early type galaxy for which it is possible to determine independently the velocity and luminosity functions.

30. BHMF from the MBH-s correlation M BH -  correlation from a group of selected early type of galaxy with secure determination of BH mass is: The M BH -  correlation from a group of selected early type of galaxy with secure determination of BH mass is: log M BH =(8.30  0.07)+(4.11  0.33)(log  -2.3) The assumed velocity function is that by Sheth et al. 2003 for early type galaxy. 1000 Montecarlo realization of the BH mass function were computed by randomly varying the input parameters. These parameters are assumed normally distributed, and their 1  uncertainties are given by their measurement errors. Two BHMF with  (M BH )=0 and  (M BH )=0.3.

31. BHMF from the M BH -L bul correlation M BH -L bul correlation from the group of selected early type galaxy with secure determination of BH mass in the K band is: The M BH -L bul correlation from the group of selected early type galaxy with secure determination of BH mass in the K band is: log M BH =(8.21  0.07)+(1.13  0.12)(logL K,bul -10.9) The luminosity function is that by Bernardi et al. 2003. In the case of S0 galaxy the bulge luminosity has to be corrected for a factor  m, and is related to the total luminosity by:  bulge (m)=f S0  (m-  m)/(f E +f S0 ) f E ~0.1, f S0 ~0.2 The correction factor  m is few dependent on the photometrical band, thus in the computation of the bulge luminosity function is possible to assume the B band. The use of the M BH -  correlation is more secure because it has not to be corrected for the bulge fraction, but it is more difficult to measure

32. The BHMFs derived from the two correlations The effect of a dispersion in the correlation is that to softening the decrease of the BHMF at high mass thus increasing the total density The use of the same intrinsic dispersion provide consistently BHMF ’ s with the same mass densities  BH

33. The BHMF for Early Type Galaxies Can the use of luminosity functions from different galaxy survey and photometric band affect the determination of BHMF in early type galaxy? Bernardi et al.: SDSS (3500-9000 A) sample of 9000 early type galaxies; Marzke et al.: CfA survey (B(0)≤14.5); the luminosity function is for morphological type and the luminosities are in Zwicky magnitudes Kochanek et al.: luminosity function in the K band Nakamura et al.: SDSS sample; luminosity function in the r* band The different BHMF are in good agreement. Discrepancies arise only at low mass, M BH <10 8 M 0, and are due to the extrapolation of the different functions adopted to fit the data.

34. The BHMF for all Galaxy types It has been derived using both the M BH -L bul and the M BH -  correlations. All the BHMF ’ s and the BH densities  BH are in agreement within the errors. The best estimate in the density of local massive BH is  BH =4.6·10 5 M 0 Mpc -3 About the 70% of this density is given by early type galaxies.

35. The Mass Function of AGN Relics I. The continuity Equation The continuity equation links the relic BHMF N(M, t) to the AGN luminosity function  (L, z). AGN are powered by mass accretion on the central massive BH.  is the mean accretion rate on the BH of mass M During the BH accretion the AGN luminosity is L=  L Edd and the mass is converted in energy with efficiency  : The intrinsic AGN luminosity is directly related to the BH accretion.  (L, t) dLog L=  (M, t) N(M, t) dM  M=BH with mass M active at t The right term of the eq. containing the source function is equal to zero. All processes, such as merging, that can create or destroy a BH are neglected; the rate is very uncertain and strongly depends on the model adopted.

36. A fraction  of the mass is converted in energy and escape from the BH with constant  and Integration with initial condition  [M, t(z s )]=1, i.e. all the BH are active at the starting redshift z s. Integration on the mass M gives the density of AGN relics: with

37. II. The Bolometric Corrections AGN luminosity is determined in a limited energy band b; a suitable bolometric correction, f bol, b =L/L b is required. The observed luminosity is given by the integral of the observed Spectral Energy Distribution. The IR radiation is reprocessed, thus a correction is required. A template spectrum is constructed. Optical-UV band: broken power-law  1 =-0.44 1  m-1300 A (L ~  )  2 =-1.76 1200-500 A X-ray band: simple power law + reflection component  =1.9, E b =500 keV The spectrum, and thus the bolometric corrections, are assumed to be independent on the redshift.

38. III. The Luminosity Function of AGN AGN surveys are performed in limited spectral bands. The LF found in literature describe only a fraction of the AGN population, i.e. a fraction of the local BHMF. Boyle et al. 2000 : B band, all the population of red quasar is missed Soft X-ray (0.5-2 keV): all sources with important absorption are missed, N H >10 22 cm -2 Hard X-ray (2-10 keV): the most of AGNs; object with N H >10 24 cm -2 are missed The first two LFs function are in good agreement at high luminosity. The third LF samples a larger fraction of AGN population at all luminosities. Differential comoving energy density Objects with L>10 12 L 0 provide ~ 50 % of the total energy High and low luminosity objects have similar redshift distributions U=1.5·10 -15 erg cm -2  BH =2.2·10 5 M 0 Mpc -3

39. Integration of the continuity equation with =1,  =0.1 and z s =3 give …. The hard X-ray LF gives the greater number of AGN relics The number of relic at z=0 is greater than the number of relic at z s. BH growth mainly at z ≤ z s. At higher z BH have too little time to growth. The relic BHMF is substantially independent on z s, if z s >2.5. Solid line z=0, Dotted line z=z s, Dashed line only AGN with L >10 12 L 0 The higher mass BH today growth during the quasar phase (L>10 12 L 0 ). If <1, the BH can accrete more mass. The number of relic with high mass increases.

40. Comparison between local BH’s and AGN relics No correction for missing AGN population Relic BHMF corrected using hard X-ray LF and accounting for Compton Thick AGN ’ s EXCELLENT AGREEMENT! Local BH ’ s are AGN relics mainly grown during active phases of host galaxy Agreement obtained with ε = 0.1 and λ = 1 Merging processes not important (at least for z < 3)

41. Constraints from the X-ray Background It is possible to estimate the expected mass density of relic BH’s from XRB where The average redshift of X-ray sources emitting the XRB is… Perfectly consistent with the local estimate for  = 0.1 (consistency requires 0.07<  < 0.27)

42. Accretion efficiency and Eddington ratio Consider the average square deviation between the logarithms of local and relic BHMF ’ s Acceptance region (k 2 ≤ 1)  = 0.054, non-rotating Schwarzschild BH  = 0.42, maximally rotating Kerr BH Best values (k 2 = k 2 min ):  = 0.08, = 0.5 BH ’ s should be slowly rotating k 2 ≤ 0.7 2 which corresponds to the “ canonical ” case ( ε = 0.1, λ = 1) 0.1 < λ < 1.7 BH ’ s grow during luminous accretion phases close to the Eddington limit

43. Growth and accretion history of massive BH’s Redshift dependence of ρ BH BH ’ s accretion proportional to star formation rate + feedback from AGN ’ s explain the observed correlations M BH -  and M BH - L bul with host galaxies Cosmic BH ’ s accretion rate

44. High mass BH’s grow earlier than low mass BH’s

45. The lifetime of active BH’s The active time is  ~ 1.5 ·10 8 yr M BH > 10 9 M o  ~ 4.5 ·10 8 yr M BH < 10 8 M o  ~ 10 9 yr smaller  and AGN’s which leave smaller relic masses need longer active phases Results in agreement with upper limit of 10 9 yr set by variability timescale

46. Summary Local BH’s are AGN relics mainly grown during active phases of host galaxy, in which accreting matter was converted into radiation with efficiencies ε = 0.04 – 0.16 at a fraction λ = 0.1 – 1.7 of the Eddington luminosity Merging processes are not important at redshift z < 3 BH’s growth is anti-hierarchical The average total lifetime of AGN’s active phases ranges between 10 8 and 10 9 yr depending on the BH mass Local BHMFRelic BHMF Consistent and in agreement with XRB constraints