### Abstract

We describe the general problem of estimating black hole masses of active galactic nuclei (AGNs) by calculating the conditional probability distribution of M_{BH} given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimate M_{BH}, and we outline how to set up the conditional probability distribution of M_{BH} given the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of M _{BH} with information from an intrinsic correlation between M _{BH} and L, and from the intrinsic distribution of M_{BH}, in a manner that improves the estimates of M_{BH}. Simulation was used to assess how the distribution of M_{BH} inferred from the broad-line mass estimates differs from the intrinsic distribution, and we find that this can lead to an inferred distribution that is too broad. We use these results and a sample of 25 sources that have recent reverberation mapping estimates of AGN black hole masses to investigate the effectiveness of using the C IV emission line to estimate M_{BH} and to indirectly probe the C IV region size-luminosity (R-L) relationship. A linear regression of log L _{λ} (1549 Å) on log M_{BH} found that L _{1549} ∝ M_{BH}^{1.17±0.22}. A linear regression also found that M_{BH} ∝ L_{1549} ^{0.41±0.07}FWHM_{C IV}^{2}, implying a C IV R-L relationship of the form R_{C IV} ∝ L_{1549} ^{0.41±0.07}. Including the C IV line FWHM resulted in a reduction of a factor of ∼ 1/3 in the error in the estimates of M _{BH} over simply using the continuum luminosity, statistically justifying its use. We estimated M_{BH} from both C IV and Hβ for a sample of 100 sources, including new spectra of 29 quasars. We find that the two emission lines give consistent estimates if one assumes R ∝ L _{UV}^{1/2} for both lines.

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

Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Astrophysical Journal, Supplement Series |

Volume | 168 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2007 |

### Fingerprint

### Keywords

- Galaxies: active
- Line: profiles
- Methods: data analysis
- Methods: statistical
- Quasars: emission lines

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

**Virial masses of black holes from single epoch spectra of active galactic nuclei.** / Kelly, Brandon C.; Bechtold, Jill.

Research output: Contribution to journal › Article

*Astrophysical Journal, Supplement Series*, vol. 168, no. 1, pp. 1-18. https://doi.org/10.1086/509725

}

TY - JOUR

T1 - Virial masses of black holes from single epoch spectra of active galactic nuclei

AU - Kelly, Brandon C.

AU - Bechtold, Jill

PY - 2007/1

Y1 - 2007/1

N2 - We describe the general problem of estimating black hole masses of active galactic nuclei (AGNs) by calculating the conditional probability distribution of MBH given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimate MBH, and we outline how to set up the conditional probability distribution of MBH given the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of M BH with information from an intrinsic correlation between M BH and L, and from the intrinsic distribution of MBH, in a manner that improves the estimates of MBH. Simulation was used to assess how the distribution of MBH inferred from the broad-line mass estimates differs from the intrinsic distribution, and we find that this can lead to an inferred distribution that is too broad. We use these results and a sample of 25 sources that have recent reverberation mapping estimates of AGN black hole masses to investigate the effectiveness of using the C IV emission line to estimate MBH and to indirectly probe the C IV region size-luminosity (R-L) relationship. A linear regression of log L λ (1549 Å) on log MBH found that L 1549 ∝ MBH1.17±0.22. A linear regression also found that MBH ∝ L1549 0.41±0.07FWHMC IV2, implying a C IV R-L relationship of the form RC IV ∝ L1549 0.41±0.07. Including the C IV line FWHM resulted in a reduction of a factor of ∼ 1/3 in the error in the estimates of M BH over simply using the continuum luminosity, statistically justifying its use. We estimated MBH from both C IV and Hβ for a sample of 100 sources, including new spectra of 29 quasars. We find that the two emission lines give consistent estimates if one assumes R ∝ L UV1/2 for both lines.

AB - We describe the general problem of estimating black hole masses of active galactic nuclei (AGNs) by calculating the conditional probability distribution of MBH given some set of observables. Special attention is given to the case where one uses the AGN continuum luminosity and emission line widths to estimate MBH, and we outline how to set up the conditional probability distribution of MBH given the observed luminosity, line width, and redshift. We show how to combine the broad-line estimates of M BH with information from an intrinsic correlation between M BH and L, and from the intrinsic distribution of MBH, in a manner that improves the estimates of MBH. Simulation was used to assess how the distribution of MBH inferred from the broad-line mass estimates differs from the intrinsic distribution, and we find that this can lead to an inferred distribution that is too broad. We use these results and a sample of 25 sources that have recent reverberation mapping estimates of AGN black hole masses to investigate the effectiveness of using the C IV emission line to estimate MBH and to indirectly probe the C IV region size-luminosity (R-L) relationship. A linear regression of log L λ (1549 Å) on log MBH found that L 1549 ∝ MBH1.17±0.22. A linear regression also found that MBH ∝ L1549 0.41±0.07FWHMC IV2, implying a C IV R-L relationship of the form RC IV ∝ L1549 0.41±0.07. Including the C IV line FWHM resulted in a reduction of a factor of ∼ 1/3 in the error in the estimates of M BH over simply using the continuum luminosity, statistically justifying its use. We estimated MBH from both C IV and Hβ for a sample of 100 sources, including new spectra of 29 quasars. We find that the two emission lines give consistent estimates if one assumes R ∝ L UV1/2 for both lines.

KW - Galaxies: active

KW - Line: profiles

KW - Methods: data analysis

KW - Methods: statistical

KW - Quasars: emission lines

UR - http://www.scopus.com/inward/record.url?scp=33846849497&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846849497&partnerID=8YFLogxK

U2 - 10.1086/509725

DO - 10.1086/509725

M3 - Article

AN - SCOPUS:33846849497

VL - 168

SP - 1

EP - 18

JO - Astrophysical Journal, Supplement Series

JF - Astrophysical Journal, Supplement Series

SN - 0067-0049

IS - 1

ER -