### Abstract

We present an estimate of the black hole mass function of broad-line quasars (BLQSOs) that self-consistently corrects for incompleteness and the statistical uncertainty in the mass estimates, based on a sample of 9886 quasars at 1 < z < 4.5 drawn from the Sloan Digital Sky Survey (SDSS). We find evidence for "cosmic downsizing" of black holes in BLQSOs, where the peak in their number density shifts to higher redshift with increasing black hole mass. The cosmic mass density for black holes seen as BLQSOs peaks at z ∼ 2. We estimate the completeness of the SDSS as a function of the black hole mass and Eddington ratio, and find that at z > 1 it is highly incomplete at Mbh ≲ 10^{9} M_{⊙} and L/L_{Edd} ≲ 0.5. We estimate a lower limit on the lifetime of a single BLQSO phase to be t_{bl} > 150 ± 15 Myr for black holes at z = 1 with a mass of M_{bh} = 10^{9} M_{⊙}, and we constrain the maximum mass of a black hole in a BLQSO to be ∼3 × 10^{10} M _{⊙}. Our estimated distribution of BLQSO Eddington ratios peaks at L/L_{Edd} ∼ 0.05 and has a dispersion of ∼0.4 dex, implying that most BLQSOs are not radiating at or near the Eddington limit; however, the location of the peak is subject to considerable uncertainty. The steep increase in number density of BLQSOs toward lower Eddington ratios is expected if the BLQSO accretion rate monotonically decays with time. Furthermore, our estimated lifetime and Eddington ratio distributions imply that the majority of the most massive black holes spend a significant amount of time growing in an earlier obscured phase, a conclusion which is independent of the unknown obscured fraction. These results are consistent with models for self-regulated black hole growth, at least for massive systems at z > 1, where the BLQSO phase occurs at the end of a fueling event when black hole feedback unbinds the accreting gas, halting the accretion flow.

Original language | English (US) |
---|---|

Pages (from-to) | 1315-1334 |

Number of pages | 20 |

Journal | Astrophysical Journal |

Volume | 719 |

Issue number | 2 |

DOIs | |

State | Published - Aug 20 2010 |

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### Keywords

- Black hole physics
- Galaxies: active
- Galaxies: luminosity function
- Galaxies: nuclei
- Galaxies: statistics
- Mass function
- Quasars: general

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*719*(2), 1315-1334. https://doi.org/10.1088/0004-637X/719/2/1315

**Constraints on black hole growth, quasar lifetimes, and Eddington ratio distributions from the SDSS broad-line quasar black hole mass function.** / Kelly, Brandon C.; Vestergaard, Marianne; Fan, Xiaohui; Hopkins, Philip; Hernquist, Lars; Siemiginowska, Aneta.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 719, no. 2, pp. 1315-1334. https://doi.org/10.1088/0004-637X/719/2/1315

}

TY - JOUR

T1 - Constraints on black hole growth, quasar lifetimes, and Eddington ratio distributions from the SDSS broad-line quasar black hole mass function

AU - Kelly, Brandon C.

AU - Vestergaard, Marianne

AU - Fan, Xiaohui

AU - Hopkins, Philip

AU - Hernquist, Lars

AU - Siemiginowska, Aneta

PY - 2010/8/20

Y1 - 2010/8/20

N2 - We present an estimate of the black hole mass function of broad-line quasars (BLQSOs) that self-consistently corrects for incompleteness and the statistical uncertainty in the mass estimates, based on a sample of 9886 quasars at 1 < z < 4.5 drawn from the Sloan Digital Sky Survey (SDSS). We find evidence for "cosmic downsizing" of black holes in BLQSOs, where the peak in their number density shifts to higher redshift with increasing black hole mass. The cosmic mass density for black holes seen as BLQSOs peaks at z ∼ 2. We estimate the completeness of the SDSS as a function of the black hole mass and Eddington ratio, and find that at z > 1 it is highly incomplete at Mbh ≲ 109 M⊙ and L/LEdd ≲ 0.5. We estimate a lower limit on the lifetime of a single BLQSO phase to be tbl > 150 ± 15 Myr for black holes at z = 1 with a mass of Mbh = 109 M⊙, and we constrain the maximum mass of a black hole in a BLQSO to be ∼3 × 1010 M ⊙. Our estimated distribution of BLQSO Eddington ratios peaks at L/LEdd ∼ 0.05 and has a dispersion of ∼0.4 dex, implying that most BLQSOs are not radiating at or near the Eddington limit; however, the location of the peak is subject to considerable uncertainty. The steep increase in number density of BLQSOs toward lower Eddington ratios is expected if the BLQSO accretion rate monotonically decays with time. Furthermore, our estimated lifetime and Eddington ratio distributions imply that the majority of the most massive black holes spend a significant amount of time growing in an earlier obscured phase, a conclusion which is independent of the unknown obscured fraction. These results are consistent with models for self-regulated black hole growth, at least for massive systems at z > 1, where the BLQSO phase occurs at the end of a fueling event when black hole feedback unbinds the accreting gas, halting the accretion flow.

AB - We present an estimate of the black hole mass function of broad-line quasars (BLQSOs) that self-consistently corrects for incompleteness and the statistical uncertainty in the mass estimates, based on a sample of 9886 quasars at 1 < z < 4.5 drawn from the Sloan Digital Sky Survey (SDSS). We find evidence for "cosmic downsizing" of black holes in BLQSOs, where the peak in their number density shifts to higher redshift with increasing black hole mass. The cosmic mass density for black holes seen as BLQSOs peaks at z ∼ 2. We estimate the completeness of the SDSS as a function of the black hole mass and Eddington ratio, and find that at z > 1 it is highly incomplete at Mbh ≲ 109 M⊙ and L/LEdd ≲ 0.5. We estimate a lower limit on the lifetime of a single BLQSO phase to be tbl > 150 ± 15 Myr for black holes at z = 1 with a mass of Mbh = 109 M⊙, and we constrain the maximum mass of a black hole in a BLQSO to be ∼3 × 1010 M ⊙. Our estimated distribution of BLQSO Eddington ratios peaks at L/LEdd ∼ 0.05 and has a dispersion of ∼0.4 dex, implying that most BLQSOs are not radiating at or near the Eddington limit; however, the location of the peak is subject to considerable uncertainty. The steep increase in number density of BLQSOs toward lower Eddington ratios is expected if the BLQSO accretion rate monotonically decays with time. Furthermore, our estimated lifetime and Eddington ratio distributions imply that the majority of the most massive black holes spend a significant amount of time growing in an earlier obscured phase, a conclusion which is independent of the unknown obscured fraction. These results are consistent with models for self-regulated black hole growth, at least for massive systems at z > 1, where the BLQSO phase occurs at the end of a fueling event when black hole feedback unbinds the accreting gas, halting the accretion flow.

KW - Black hole physics

KW - Galaxies: active

KW - Galaxies: luminosity function

KW - Galaxies: nuclei

KW - Galaxies: statistics

KW - Mass function

KW - Quasars: general

UR - http://www.scopus.com/inward/record.url?scp=78049512439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78049512439&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/719/2/1315

DO - 10.1088/0004-637X/719/2/1315

M3 - Article

AN - SCOPUS:78049512439

VL - 719

SP - 1315

EP - 1334

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -