1. Lecture 2: AGN Survey and Luminosity Function Xiaohui Fan AGN Summer School, USTC AGN Summer School, USTC May 25, 2007 Background: 46,420 Quasars from the SDSS Data Release Three

2. Goal Derive the density of AGNs as function of bolometric luminosity, redshift –  (L bol, z, type) Relates to: –Characterizing accretion history: Distribution functions of black hole activity as function of M BH, accrection rate and radiative efficiency and redshift –Probing galaxy/BH coevolution –Test unification model

3. Basic Issues Instead of  (L bol, z, type), we observe: –N(f, z, AGN type, selection criteria) –Selection effect Incompleteness due to selection criteria (correctable) Selection bias (e.g., optical survey missing obscured sources) –Bolometric correction –Redshift effect Flux-limited vs. volume limited, truncated data set Limited luminosity range at any given redshift, parametric vs. non-parametric K-correction

4. Outline 1.AGN surveys 2.LF parameterization and selection effects 3.Evolution of optical AGN LFs Density vs. luminosity evolution Downsizing 4.Putting things together: Soltan argument and constraints of BH accretion properties 5.Quasar Clustering

5. References Textbook: –Peterson Chaps 10 and 11 Recent Review –Osmer, astro-ph/0304150 Optical –Richards et al. 2006, AJ, 131, 2766 X-ray –Brandt and Hasinger, 2005, ARAA, 43, 827 Luminosity function methodology –Fan et al. 2001, AJ, 121, 31 Luminosity function across wavelength –Hopkins et al. 2007, ApJ, 654, 731 Soltan argument –Yu and Tremaine 2002, MRNAS, 335, 965

6. Observational Properties of AGNs Textbook definition –Small angular sizes (compact) –Cosmological distance –High luminosity? –Broad-band continuum emission –Emission Lines indicative of hard ionizing source –Variability –Polarization (subset) AGN surveys utilize one or more of these properties

7. How to find AGNs High luminosity AGNs: –L AGN >> L gal –AGN light dominates –Point source in the wavelength observed –Distinct SED Optical Color Selection –Sandage (1971) –2dF (2000): 400 deg 2 25000 quasars

8. SDSS at Your Service Courtesy of Arizona graduate students

9. SDSS Overview Primary Telescope: 2.5m wide-field (2.5 deg) Imaging Survey (wide-field 54 CCD imager) –Main Survey: 10000 deg 2 –Five bands, 3000 – 10000 Å – r lim ~ 22.5, z lim ~ 20.5 Spectroscopic Survey –10 6 galaxies (r<17.8) –10 5 quasars ( 0 < z < 6.5) –Interesting stars, radio/x-ray sources etc.

10. SDSS Color Selection Color selection –Type-1 quasars –Low-z UV-excess (UVX), Palomar-Green (PG), 2dF etc. Contaminants: brown dwarfs –High-z Lyman break, SDSS, DPOSS, APM Contaminants: late type stars, brown dwarfs >90% of known AGNs are color-selected Stellar locus quasar Z=3 Z=4 Z=5 Richards et al. 2002

11. Selection effect of color selection z=2.5-3.0 gap –Quasars have similar colors to F stars Missing redder or reddened quasars Missing obscured/type-2 objects Only sensitive to high level of activity, high AGN/host contrast

12. Slitless Spectroscopy Identify broad emission line from prism plates –Large Bright Quasar Survey (LBQS) –Hamburg ESO Survey (HES) –Palomar Grism Transit Survey Selection Effect –Strong redshift dependence –Biases towards strong emission line –Mostly on photographic plates, difficult to calibrate –Problem with crowded field

13. X-ray Surveys X-ray sky is dominated by AGNs X-ray selection sensitive to both type-1 and modestly obscured type-2 sources Chandra/XMM deep fields capable of reaching very low luminosity Host galaxy not an issue until ~10 -5~-6 Eddington luminosity Brandt and Hasinger 2005

14. Other Selection Methods Radio –Where everything started (Schmidt 1963) –~10% quasars are radio-loud –FIRST and NVSS surveys –Does radio-loud quasars evolve the same way as radio-quiet ones? Near-IR selection –KX (K-band excess) method –Less affected by reddening mid-IR selection –Dust emission peaks at rest-frame 10-50 microns –Select both type 1 and type 2 –Can select Compton-thick sources Variability Proper motion survey Serendipity (Spinrad method)

15. Quest to the Highest Redshift Quasars SDSS Radio APM CCD IR survey (UKIDSS, VISTA, LBT)

16. So how far could each of these techniques go? Lyman break: –Quasars: 6.4 –Galaxies: 7-8 Slitless spectroscopy –Quasars: 4.7 –Galaxies: 5.5 multiwavelength –Quasars: 5.2 (X-ray), maybe 7? –Quasar: 5.8 (IR) –Quasar: 6.1 (radio) –Galaxies: 5.2 (radio) Variability: –Quasar: 4.5 Luck: –Quasars: 4.3 –Galaxies: 5.8

17. Surveys of low-luminosity AGNs Low-luminosity type 1 and type 2 sources in X- ray samples Emission-line selected sources in galaxy redshift surveys: –Optical wavelength: L AGN < L host –Spectra dominated by host galaxy; stellar/ISM component –CfA redshift survey sample (1980s) –Ho, Filippenko and Sargent (1997) sample: high S/N spectra of 486 nearby galaxies; half shows AGN signatures –SDSS selection: Hao et al., Kauffmann et al., Greene et al., Zakmaska et al. (excellent Ph. D. theses!!)

18. Selection of low-luminosity AGNs Stellar spectra subtraction –Best-fit templates constructed from Principle Component Analysis Bladwin-Phillips-Telrivich Digram –Separating AGNs from starbursts Hao et al. Kauffmann et al.

19. Low-luminosity AGNs live in all kinds of galaxies Kauffmann et al.

20. Low-luminosity AGNs live in all kinds of galaxies Ho et al.

21. Two extremes from galaxy surveys The smallest broad-line AGNs (Greene, Ho, Barth) Greene et al.

22. The most luminous type-2 quasars Zakamska et al.

23. Outline 1.AGN surveys 2.LF parameterization 3.Evolution of optical and X-ray selected AGNs Density vs. luminosity evolution Downsizing The highest redshift quasars 4.Putting things together: Soltan argument and constraints of BH accretion properties 5.Quasar Clustering

24. 46,420 Quasars from the SDSS Data Release Three wavelength 4000 A9000 A redshift 0 1 2 3 5 Ly  CIV CIII MgII HH OIII FeII Ly  forest

25. Richards et al. 2006 M-z distribution from SDSS

26. Luminosity Functions: 1/V A Estimator (non-parametric) Given a single object, X, visible within some volume, V A Object Detectable Object Too Faint For a number of objects i: This 1/V A estimator is a maximum likelihood estimator Too Bright Issue: Binning; selection effcts

27. Incorporate selection effect Binning Limited luminosity coverage at given redshift

28. Maximum Likelihood Fit For small bins L i -> L i + dL, z j -> z j + dz, the likelihood that n ij are found in the bin: Where  ij is the average number expected in the bin So one wants to maximize L, or S=-2lnL,

29. Parameterization SIMPLE POINTS: There is no difference in PDE vs. PLE for power-law LF; But LF will eventually turn over for the total number to converge; The real LF is likely more complex

30. Parameterization Quasar LF: double power-law Luminosity-dependent density evolution (Schmidt and Green 1983):  (L,z) =  (L,z)  (L,z=0) overall density evolves; Shape (bright and faint end slopes) evolves as well

31. Lynden-Bell’s C - Estimator In case of density evolution: Define cumulative distributions: and Define comparable set: –for object i, where L - is the flux limit for the redshift of i (this is the luminosity and volume limited subset of i) Cumulative distribution can be estimated (in ML sense):

32. Lynden-Bell C - Estimator Maximum-Likelihood estimator Non-parametric Naturally taken into account the truncation of data (flux-limit) Luminosity evolution can be accounted for by coordinate transformation Selection function can also be incorporated

33. Selection Function Example: optical color selection Color of quasar is a function of: –Redshift –Spectral property: Continuum slope Emission line strength For high-z : random distribution of absorption systems along line of sight –Luminosity: error distribution in the survey

34. XF et al. 2001 f ~ - 

35. Model selection function Construct model quasar color sets that includes realistic distributions of quasar spectral properties and observed error distributions, then run selection algorithm on model data set –-> p(L,z,SED) Limitations –Accuracy relies on assumptions on spectral property distributions (which sometimes is derived from the same survey) –Can never correct for objects that survey is insensitive to: optical: obscured sources, very red quasars etc. –Correction is large (and sensitive) in some cases (e.g. optical: z~2.8

36. Richards et al. 2006

37. K-correction K-correction is not trivial for quasar LF evolution –Large redshift baseline –Effect of emission line in/out passbands –Dispersion in continuum distribution Richards et al. 2006

38. Outline 1.AGN surveys 2.LF parameterization 3.Evolution of optical and X-ray selected AGNs Density vs. luminosity evolution Downsizing The highest redshift quasars 4.Putting things together: Soltan argument and constraints of BH accretion properties 5.Quasar Clustering

39. Luminosity Function from 2dF Quasar Survey Boyle et al. 2001

40. Luminosity function from 2QZ Best fit model: pure luminosity evolution:  : cosmic look-back time; L *(  ) ~ exp(6  )  ~ 6;  ~ -3.3;  ~ -1.0 However… M * constant apparent mag Selection effect?? Faint end slope poorly determined From 2001 to 2004 papers Croom et al. 2004 or L(z) ~ exp(6  )

41. What’s the Faint End Slope of QLF? Hao et al. 2004 z=0 Faint slope measurement Ranges from -1.o to -2.0…  lead to large uncertainties in in the total luminosity and mass density of quasar pop.

42. SDSS quasar LF Richards et al. 2006

43. SDSS quasar LF Strong evolution in bright end slope at z>3 –Can’t be luminosity evolution all the way But doesn’t go faint enough at low-z to differentiate PLE from PDE or else Richards et al. 2006

44. density evolution of luminous quasars Exponential decline of quasar density at high redshift, different from normal galaxies Richards et al. 2006, Fan e al. 2005 SFR of galaxies Density of quasars Bouwens et al.

45. X-ray AGN LF Result 1: Downsizing of AGN activity –Quasar density peaks at z~2-3 –AGN density peaks at z~0.5 - 1 – Paradox 1: Most of BH accretion happens in quasars at high-z Most of X-ray background in Seyfert 2s at low-z

46. X-ray LF Result 2: –PLE doesn’t work; need luminosity-dependent density evolution to characterize evolution of the entire LF Miyaji et al. 2006

47. X-ray LF Result 3: –Type 2 fraction a strong function of luminosity –Paradox 2: At high (quasar) luminosity: type 2 <20%; optical color selection is highly complete since all are type 1s, and includes most of luminosity AGN population emitted in the Universe At low (Seyfert) luminosity: type 2 ~80%; optical color selection miss most of the AGNs in the Universe in terms of number

48. Outline 1.AGN surveys 2.LF parameterization 3.Evolution of optical and X-ray selected AGNs Density vs. luminosity evolution Downsizing The highest redshift quasars 4.Putting things together: Soltan argument and constraints of BH accretion properties 5.Quasar Clustering

49. Putting things together: Evolution of bolometric LF Hopkins et al. (2007): –Combines QLFs in optical, X-ray and IR –Over z=0-6 and the whole L range –Accounting for distribution of absorbing column and luminosity-dependent SEDs –Findings: PLE doesn’t work Both bright and faint-end slope evolve with z Luminosity-dependent density evolution provides good fit for all data

50. Downsizing in all bands

51. General Evolutionary Trends And a calculator: www.cfa.harvard.edu/~phopkins/Site/qlf.html http://www.cfa.harvard.edu/~phopkins/Site/qlf.html..

52. Putting things together: Soltan’s argument Soltan’s argument: QSO luminosity function  (L,t) traces the accretion history of local remnant BHs (Soltan 1982), if BH grows radiatively Total mass density accreted = total local BH mass density

53. New estimates of BH mass densities Total local BH mass density: –local BH mass function n M (M,t 0 ): SDSS early-type galaxy sample n  ( ,t 0 ) (Bernardi et al. 2001) the tight M –  relation (Tremaine et al. 2002) – ,local =(2.5  0.4)  10 5 M  /Mpc 3 (h=0.65) (Yu & Tremaine 2002) BH mass density accreted due to optically bright QSO phases: –  (L,t): 2dF QSO Redshift survey (Boyle et al. 2000) – ,acc =2.1  10 5 [0.1(1-  ) /  ] M  /Mpc 3 (Yu & Tremaine 2002) Bright quasar phase can account for most of the BH mass growth; low efficiency accretion and obscured AGN not very important

54. The history of BH mass density accreted during quasar phase Yu and Tremaine 2002

55. Update of Soltan’s argument: relations in distributions and including effects of BH mergers If local BH mass density comes from quasars, then not only the total density, but the DISTRIBUTION of BH mass should be consistent with the accretion history of quasars. Total mass density: no BH mergers: Partial mass density: assume L = L(M): total mass accreted at L>L(M0) in quasar phase = total local BH mass density at M>M0 including BH mergers  increase total mass in high-mass BHs  total mass accreted at L(M)>L(M0) in quasar phase M0 m2+m1 m2 m1

56. Comparison with observations: Discrepancy in distributions Expected inequality for partial mass density: QSO Local >10 8 M  (  m,  ,h)= (0.3,0.7,0.65) Partial mass density (distributions): Yu and Tremaine 2002

57. Comparison with observations: Discrepancy in distributions Partial mass density (distributions): Possible solutions: Luminous QSOs (L bol >10 46 erg/s) have a high-efficiency (e.g.,  ~0.2). If true, –growth of high-mass BHs (M >10 8 M  ) comes mainly from accretion during optically bright QSO phases (scarcity of Type II QSOs). –less luminous QSOs have a low efficiency (<0.1) have a high efficiency, but a significant fraction should be obscured (obscured growth for low-mass BHs, Fabian 1999). Super-Eddington luminosity (Begelman 2001, 2002). Expected inequality for partial mass density: Maximum efficiency allowed in thin-disk accretion models:  ~0.31 (Thorne 1974). QSO Local >10 8 M  (  m,  ,h)= (0.3,0.7,0.65)

58. QSO mean lifetime The mean lifetime of QSOs is comparable to the Salpeter time (the time for a BH accreting with the Eddington luminosity to e-fold in mass). ~(3-13)  10 7 yr

59. Expanding Soltan’s Argument Fitting QLF with local BHMF

60. Outline 1.AGN surveys 2.LF parameterization 3.Evolution of optical and X-ray selected AGNs Density vs. luminosity evolution Downsizing The highest redshift quasars 4.Putting things together: Soltan argument and constraints of BH accretion properties 5.Quasar Clustering

61. Galaxies are strongly clustered

62. How about quasars? 2dF SDSS Difficulty: Quasars are rare! Very large survey needed

63. quasars are as strongly clustered as galaxies

64. Idea of biased galaxy formation

65. Idea of biased galaxy/quasar formation Bias: the relative strength of clustering between galaxy (quasar) and underlying dark matter Biasing is unavoidable for rare, high-z systems Bias factor (clustering strength) is a strong function of the mass of dark matter halo that hosts galaxy (quasar) as well as redshift For a given cosmology: clustering strength constrains dark matter halo mass and its evolution

66. Clustering of Quasars What does quasar clustering tell us? –Correlation function of quasars vs. of dark matter –Bias factor of quasars  average DM halo mass –Clustering probably provides the most effective probe to the statistical properties of quasar host galaxies at high-redshift –Combining with quasar density  quasar lifetime and duty cycle

67. Evolution of Quasar Clustering SDSS quasar survey –Clustering strength strong func. of redshift –Quasar lifetime ~10-100Myrs –Quasars reside in 2-6x10 12 h -1 M sun DM halos Shen et al. 2007 z=2.9-3.5 z>3.5

68. Summary AGN Surveys –All selection methods suffer from selection effect which needs to be taken into account carefully –Optical surveys, esp. color selection are biased against obscured, reddened quasars and have low completeness at z=2.5-3.0 AGN Luminosity Function –AGN density is strong function of redshift, and peaks at z~2 –AGN LF is double power-law, with slopes also strong function of redshift –Luminosity-dependent density evolution best describes all data –Local BH density can be accounted for by accretion in quasar phase using Soltan’s argument AGN clustering –AGN are strongly clustered and strongly biased –Quasar clustering increases with redshift –Quasar clustering consistent with 10 7 yr lifetime and 10 12-13 M sun halo mass