### 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) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Astrophysical Journal, Supplement Series |

Volume | 168 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2007 |

### Keywords

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

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science