EDDINGTON-LIMITED ACCRETION AND THE BLACK HOLE MASS FUNCTION AT REDSHIFT 6

We present discovery observations of a quasar in the Canada–France High-z Quasar Survey (CFHQS) at redshift z = 6.44. We also use near-infrared spectroscopy of nine CFHQS quasars at z ∼ 6 to determine black hole masses. These are compared with similar estimates for more luminous Sloan Digital Sky Survey quasars to investigate the relationship between black hole mass and quasar luminosity. We find a strong correlation between Mg ii FWHM and UV luminosity and that most quasars at this early epoch are accreting close to the Eddington limit. Thus, these quasars appear to be in an early stage of their life cycle where they are building up their black hole mass exponentially. Combining these results with the quasar luminosity function, we derive the black hole mass function at z = 6. Our black hole mass function is ∼104 times lower than at z = 0 and substantially below estimates from previous studies. The main uncertainties which could increase the black hole mass function are a larger population of obscured quasars at high redshift than is observed at low redshift and/or a low quasar duty cycle at z = 6. In comparison, the global stellar mass function is only ∼102 times lower at z = 6 than at z = 0. The difference between the black hole and stellar mass function evolution is due to either rapid early star formation which is not limited by radiation pressure as is the case for black hole growth or inefficient black hole seeding. Our work predicts that the black hole mass–stellar mass relation for a volume-limited sample of galaxies declines rapidly at very high redshift. This is in contrast to the observed increase at 4 < z < 6 from the local relation if one just studies the most massive black holes.

[1]  F. Walter,et al.  IONIZATION NEAR ZONES ASSOCIATED WITH QUASARS AT z ∼ 6 , 2010, 1003.0016.

[2]  A. Merloni,et al.  The building up of the black hole–stellar mass relation , 2010, 1001.5407.

[3]  C. Steinhardt,et al.  The quasar mass—luminosity plane — III. Smaller errors on virial mass estimates , 2009, 0912.0734.

[4]  R. McLure,et al.  THE CANADA–FRANCE HIGH-z QUASAR SURVEY: NINE NEW QUASARS AND THE LUMINOSITY FUNCTION AT REDSHIFT 6 , 2009, 0912.0281.

[5]  P. Fosalba,et al.  ON THE RADIATIVE EFFICIENCIES, EDDINGTON RATIOS, AND DUTY CYCLES OF LUMINOUS HIGH-REDSHIFT QUASARS , 2008, 0810.4919.

[6]  P. Best,et al.  CO-EVOLUTION OF CENTRAL BLACK HOLES AND GALAXIES , 2010 .

[7]  J. Trump,et al.  ON THE COSMIC EVOLUTION OF THE SCALING RELATIONS BETWEEN BLACK HOLES AND THEIR HOST GALAXIES: BROAD-LINE ACTIVE GALACTIC NUCLEI IN THE zCOSMOS SURVEY , 2009, 0910.4970.

[8]  K. Wada,et al.  FORMATION OF HIGH-REDSHIFT (z>6) QUASARS DRIVEN BY NUCLEAR STARBURSTS , 2009, 0910.1379.

[9]  M. Franx,et al.  UV CONTINUUM SLOPE AND DUST OBSCURATION FROM z ∼ 6 TO z ∼ 2: THE STAR FORMATION RATE DENSITY AT HIGH REDSHIFT , 2009, 0909.4074.

[10]  R. Somerville.  Empirical constraints on the evolution of the relationship between black hole and galaxy mass: scatter matters , 2009, 0908.0927.

[11]  B. Peterson.  Toward Precision Measurement of Central Black Hole Masses , 2009, Proceedings of the International Astronomical Union.

[12]  H. Rix,et al.  NEAR-INFRARED SPECTROSCOPY OF SDSS J0303 − 0019: A LOW-LUMINOSITY, HIGH-EDDINGTON-RATIO QUASAR AT z ∼ 6 , 2009, 0907.0435.

[13]  G. Richards,et al.  A SURVEY OF z ∼ 6 QUASARS IN THE SLOAN DIGITAL SKY SURVEY DEEP STRIPE. II. DISCOVERY OF SIX QUASARS AT zAB>21 , 2009, 0905.4126.

[14]  Cambridge,et al.  Growing the first bright quasars in cosmological simulations of structure formation , 2009, 0905.1689.

[15]  T. O. S. University,et al.  MASS FUNCTIONS OF THE ACTIVE BLACK HOLES IN DISTANT QUASARS FROM THE LARGE BRIGHT QUASAR SURVEY, THE BRIGHT QUASAR SURVEY, AND THE COLOR-SELECTED SAMPLE OF THE SDSS FALL EQUATORIAL STRIPE , 2009, 0904.3348.

[16]  Paul S. Smith,et al.  ACCEPTED FOR PUBLICATION IN THE ASTROPHYSICAL JOURNAL Preprint typeset using LATEX style emulateapj v. 04/20/08 HIGH-REDSHIFT SDSS QUASARS WITH WEAK EMISSION LINES , 2022 .

[17]  Ralf Bender,et al.  THE ASTROPHYSICAL JOURNAL Preprint typeset using L ATEX style emulateapj v. 10/09/06 THE M–σ AND M–L RELATIONS IN GALACTIC BULGES, AND DETERMINATIONS OF THEIR INTRINSIC SCATTER , 2008 .

[18]  K. Bundy,et al.  THE EVOLUTIONARY HISTORY OF LYMAN BREAK GALAXIES BETWEEN REDSHIFT 4 AND 6: OBSERVING SUCCESSIVE GENERATIONS OF MASSIVE GALAXIES IN FORMATION , 2009, 0902.2907.

[19]  R. McLure,et al.  SIX MORE QUASARS AT REDSHIFT 6 DISCOVERED BY THE CANADA–FRANCE HIGH-z QUASAR SURVEY , 2009, 0901.0565.

[20]  B. Peterson,et al.  SYSTEMATIC UNCERTAINTIES IN BLACK HOLE MASSES DETERMINED FROM SINGLE-EPOCH SPECTRA , 2008, 0810.3234.

[21]  P. Hopkins,et al.  QUASARS ARE NOT LIGHT BULBS: TESTING MODELS OF QUASAR LIFETIMES WITH THE OBSERVED EDDINGTON RATIO DISTRIBUTION , 2008, 0809.3789.

[22]  P. Natarajan,et al.  Is there an upper limit to black hole masses , 2008, 0808.2813.

[23]  Youjun Lu,et al.  Toward Precise Constraints on the Growth of Massive Black Holes , 2008, 0808.3777.

[24]  F. Walter,et al.  Formation of a Quasar Host Galaxy through a Wet Merger 1.4 Billion Years after the Big Bang , 2008, 0808.3774.

[25]  A. Myers,et al.  Constraining the quasar population with the broad-line width distribution , 2008, 0807.1155.

[26]  Xiaohui Fan,et al.  Thermal Emission from Warm Dust in the Most Distant Quasars , 2008, 0806.3022.

[27]  S. Driver,et al.  On the galaxy stellar mass function, the mass-metallicity relation, and the implied baryonic mass function , 2008, 0804.2892.

[28]  T. Treu,et al.  Cosmic Evolution of Black Holes and Spheroids. III. The MBH-σ* Relation in the Last Six Billion Years , 2008, 0804.0235.

[29]  Edward J. Wollack,et al.  FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION , 2008, 0803.0547.

[30]  R. Maiolino,et al.  The Effect of Radiation Pressure on Virial Black Hole Mass Estimates and the Case of Narrow-Line Seyfert 1 Galaxies , 2008, 0802.2021.

[31]  G. Richards,et al.  Mass Functions of the Active Black Holes in Distant Quasars from the Sloan Digital Sky Survey Data Release 3 , 2007, 0801.0243.

[32]  USA,et al.  SELF-CONSISTENT MODELS OF THE AGN AND BLACK HOLE POPULATIONS: DUTY CYCLES, ACCRETION RATES, AND THE MEAN RADIATIVE EFFICIENCY , 2007, 0710.4488.

[33]  G. Richards,et al.  Biases in Virial Black Hole Masses: An SDSS Perspective , 2007, 0709.3098.

[34]  S. Okamura,et al.  The Subaru/XMM-Newton Deep Survey (SXDS). IV. Evolution of Lyα Emitters from z = 3.1 to 5.7 in the 1 deg2 Field: Luminosity Functions and AGN , 2007, 0707.3161.

[35]  T. D. Matteo,et al.  Direct Cosmological Simulations of the Growth of Black Holes and Galaxies , 2007, 0705.2269.

[36]  O. Shemmer,et al.  THE ASTROPHYSICAL JOURNAL,???:???–???, 200????????? Preprint typeset using L ATEX style emulateapj v. 12/14/05 BLACK-HOLE MASS AND GROWTH RATE AT HIGH REDSHIFT , 2007 .

[37]  Robert H. Becker,et al.  A SURVEY OF z ∼ 6 QUASARS IN THE SLOAN DIGITAL SKY SURVEY DEEP STRIPE. I. A FLUX-LIMITED SAMPLE AT zAB < 21 , 2007, 0708.2578.

[38]  Xiaohui Fan,et al.  Gemini Near-Infrared Spectroscopy of Luminous z ∼ 6 Quasars: Chemical Abundances, Black Hole Masses, and Mg II Absorption , 2007, 0707.1663.

[39]  H. Rix,et al.  Black Hole Masses and Enrichment of z ~ 6 SDSS Quasars , 2007, 0707.1662.

[40]  Thierry Forveille,et al.  Four Quasars above Redshift 6 Discovered by the Canada-France High-z Quasar Survey , 2007, 0706.0914.

[41]  S. Tremaine,et al.  Selection Bias in Observing the Cosmological Evolution of the M•-σ and M•-L Relationships , 2007, 0705.4103.

[42]  L. Wisotzki,et al.  The transverse proximity effect in spectral hardness on the line of sight towards HE 2347-4342 , 2007, 0704.0187.

[43]  J. Bolton,et al.  The observed ionization rate of the intergalactic medium and the ionizing emissivity at z≥ 5: evidence for a photon-starved and extended epoch of reionization , 2007, astro-ph/0703306.

[44]  A. Szalay,et al.  Clustering of High-Redshift (z ≥ 2.9) Quasars from the Sloan Digital Sky Survey , 2007, astro-ph/0702214.

[45]  S. Mathur,et al.  On the Faint End of the High-Redshift Active Galactic Nucleus Luminosity Function , 2007, astro-ph/0701515.

[46]  J. Rhoads,et al.  The GLARE Survey – II. Faint z≈ 6 Lyα line emitters in the HUDF , 2007, astro-ph/0701211.

[47]  M. Bernardi,et al.  On the Inconsistency between the Black Hole Mass Function Inferred from M•-σ and M•-L Correlations , 2006, astro-ph/0609297.

[48]  P. Hopkins,et al.  Formation of z~6 Quasars from Hierarchical Galaxy Mergers , 2006, astro-ph/0608190.

[49]  G. Richards,et al.  An Observational Determination of the Bolometric Quasar Luminosity Function , 2006, astro-ph/0605678.

[50]  Max Pettini,et al.  A Spectroscopic Survey of Redshift 1.4 ≲ z ≲ 3.0 Galaxies in the GOODS-North Field: Survey Description, Catalogs, and Properties , 2006, astro-ph/0609296.

[51]  P. Hopkins,et al.  An Upper Limit to the Degree of Evolution between Supermassive Black Holes and Their Host Galaxies , 2006, astro-ph/0608091.

[52]  J. Brinkmann,et al.  Probing the Evolution of Infrared Properties of z ∼ 6 Quasars: Spitzer Observations , 2006, astro-ph/0608006.

[53]  M. Rees,et al.  Quasars at z = 6: The Survival of the Fittest , 2006, astro-ph/0607093.

[54]  J. Lehár,et al.  Probing the Coevolution of Supermassive Black Holes and Galaxies Using Gravitationally Lensed Quasar Hosts , 2006, astro-ph/0603248.

[55]  Astronomy,et al.  The Radius-Luminosity Relationship for Active Galactic Nuclei: The Effect of Host-Galaxy Starlight on Luminosity Measurements , 2006, astro-ph/0602412.

[56]  A. Szalay,et al.  Spectral Energy Distributions and Multiwavelength Selection of Type 1 Quasars , 2006, astro-ph/0601558.

[57]  Robert H. Becker,et al.  Constraining the Evolution of the Ionizing Background and the Epoch of Reionization with z ∼ 6 Quasars. II. A Sample of 19 Quasars , 2005, astro-ph/0512082.

[58]  Arjun Dey,et al.  Black Hole Masses and Eddington Ratios at 0.3 < z < 4 , 2005, astro-ph/0508657.

[59]  G. Kauffmann,et al.  The many lives of active galactic nuclei: cooling flows, black holes and the luminosities and colour , 2005, astro-ph/0508046.

[60]  P. Hopkins,et al.  A Unified, Merger-driven Model of the Origin of Starbursts, Quasars, the Cosmic X-Ray Background, Supermassive Black Holes, and Galaxy Spheroids , 2005, astro-ph/0506398.

[61]  Volker Springel,et al.  The Many lives of AGN: Cooling flows, black holes and the luminosities and colours of galaxies , 2006, astro-ph/0602065.

[62]  J. Dunlop,et al.  On the evolution of the black‐hole/spheroid mass ratio , 2005, astro-ph/0510121.

[63]  D. Grupe,et al.  The Locus of Highly Accreting Active Galactic Nuclei on the MBH-σ Plane: Selections, Limitations, and Implications , 2005, astro-ph/0507624.

[64]  D. M. Alexander,et al.  The Relationship between Stellar and Black Hole Mass in Submillimeter Galaxies , 2005, astro-ph/0507610.

[65]  M. Rees,et al.  Rapid Growth of High-Redshift Black Holes , 2005, astro-ph/0506040.

[66]  P. Hopkins,et al.  The Evolution of the MBH-σ Relation , 2005, astro-ph/0506038.

[67]  Mark Lacy,et al.  The obscuration by dust of most of the growth of supermassive black holes , 2005, Nature.

[68]  W. Percival,et al.  Imaging of SDSS z > 6 Quasar Fields: Gravitational Lensing, Companion Galaxies, and the Host Dark Matter Halos , 2005, astro-ph/0503202.

[69]  T. D. Matteo,et al.  Energy input from quasars regulates the growth and activity of black holes and their host galaxies , 2005, Nature.

[70]  S. Shapiro.  Spin, Accretion, and the Cosmological Growth of Supermassive Black Holes , 2004, astro-ph/0411156.

[71]  T. D. Matteo,et al.  Modelling feedback from stars and black holes in galaxy mergers , 2004, astro-ph/0411108.

[72]  Jaiyul Yoo,et al.  Formation of the Black Holes in the Highest Redshift Quasars , 2004, astro-ph/0406217.

[73]  A. Loeb,et al.  A large neutral fraction of cosmic hydrogen a billion years after the Big Bang , 2004, Nature.

[74]  Hans-Walter Rix,et al.  On the Black Hole Mass-Bulge Mass Relation , 2004, astro-ph/0402376.

[75]  R. Maiolino,et al.  Local supermassive black holes, relics of active galactic nuclei and the X-ray background , 2003, astro-ph/0311619.

[76]  J. Dunlop,et al.  The cosmological evolution of quasar black hole masses , 2003, astro-ph/0405393.

[77]  G. Granato,et al.  A Physical Model for the Coevolution of QSOs and Their Spheroidal Hosts , 2003, astro-ph/0307202.

[78]  Takamitsu Miyaji,et al.  Cosmological Evolution of the Hard X-Ray Active Galactic Nucleus Luminosity Function and the Origin of the Hard X-Ray Background , 2003, astro-ph/0308140.

[79]  M. A. Strauss,et al.  Molecular gas in the host galaxy of a quasar at redshift z = 6.42 , 2003, Nature.

[80]  V. Narayanan,et al.  A Survey of z > 5.7 Quasars in the Sloan Digital Sky Survey. II. Discovery of Three Additional Quasars at z > 6 , 2003, astro-ph/0301135.

[81]  S. Wagner,et al.  Caught in the act: A helium-reionizing quasar near the line of sight to Q0302-003 , 2002, astro-ph/0211035.

[82]  M. Giavalisco,et al.  The Population of Faint Optically Selected Active Galactic Nuclei at z ~ 3 , 2002, astro-ph/0205142.

[83]  S. Tremaine,et al.  Observational constraints on growth of massive black holes , 2002, astro-ph/0203082.

[84]  Z. Haiman,et al.  Quasar Strömgren Spheres Before Cosmological Reionization , 2000, astro-ph/0006376.

[85]  Ralf Bender,et al.  A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion , 2000, astro-ph/0006289.

[86]  D. Merritt,et al.  A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies , 2000, astro-ph/0006053.

[87]  Paul S. Smith,et al.  Reverberation Measurements for 17 Quasars and the Size-Mass-Luminosity Relations in Active Galactic Nuclei , 1999, astro-ph/9911476.

[88]  M. Malkan,et al.  Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei. I. Comparing the Photoionization and Reverberation Techniques , 1999, astro-ph/9905224.

[89]  S. Tremaine,et al.  The Demography of Massive Dark Objects in Galaxy Centers , 1997, astro-ph/9708072.

[90]  P. Scheuer.  Lobe asymmetry and the expansion speeds of radio sources , 1995 .

[91]  P. Padovani,et al.  UNIFIED SCHEMES FOR RADIO-LOUD ACTIVE GALACTIC NUCLEI , 1995, astro-ph/9506063.

[92]  Robert Antonucci,et al.  Unified models for active galactic nuclei and quasars , 1993 .

[93]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[94]  R. Blandford,et al.  Quasar evolution and the growth of black holes , 1992 .

[95]  A. Lawrence.  The relative frequency of broad-lined and narrow-lined active galactic nuclei: implications for unified schemes , 1991 .

[96]  J. Cannizzo,et al.  The Disk Accretion of a Tidally Disrupted Star onto a Massive Black Hole , 1990 .

[97]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .