Biases in Virial Black Hole Masses: An SDSS Perspective

By Yue Shen, Jenny E. Greene, M. Strauss, Gordon Richards, D. Schneider. 2007

441 citations recorded by the source corpus.

We compile black hole (BH) masses for ~60,000 quasars in the redshift range 0.1≲ z≲ 4.5 included in the Fifth Data Release of the Sloan Digital Sky Survey, using virial BH mass estimators based on the Hβ, Mg II, and C IV emission lines. Within our sample, the widths of the three lines follow lognormal distributions, with means and dispersions that do not depend strongly on luminosity or redshift. The Mg II- and Hβ-estimated BH masses are consistent with one another, but there is a positive bias between the C IV- and Mg II-estimated BH masses correlated with the C IV-Mg II blueshift, suggesting that the C IV estimator is more severely affected by a disk wind. If the underlying BH mass distribution decreases with mass and the Eddington ratio distribution at fixed true BH mass has nonzero width, we show that the measured virial BH mass and Eddington ratio distributions within finite luminosity bins are subject to Malmquist bias. We present a model that reproduces the observed virial mass distribution, quasar luminosity function, and line width distribution of our sample; it has an underlying BH mass distribution dN/dlog M ∝ M−2.6 and a lognormal true Eddington ratio distribution at fixed true mass with dispersion 0.4 dex and mean dependent on BH mass. In this model, the observed virial mass (Eddington ratio) distribution for the SDSS sample is biased high (low) by ~0.6 dex within finite luminosity bins. Finally, we compare virial BH masses of radio and broad absorption line quasars with ordinary quasars matched in redshift and luminosity.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/54223dd6a3395fdcd7f0358c37eb656c963be254

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CLUSTERING OF LOW-REDSHIFT (z ⩽ 2.2) QUASARS FROM THE SLOAN DIGITAL SKY SURVEY (2008, background): “…but not necessarily unexpected, since we are essentially sampling the same type of objects i.e. luminous AGN, powered by supermassive black holes accreting at or near their Eddington limits (Kollmeier et al. 2006; Shen et al. 2008), quite possibly in similar mass environments (see Section 5).”
CONSTRAINTS ON BLACK HOLE GROWTH, QUASAR LIFETIMES, AND EDDINGTON RATIO DISTRIBUTIONS FROM THE SDSS BROAD-LINE QUASAR BLACK HOLE MASS FUNCTION (2010, background): “The major differences between our work and that of Shen et al. (2008) are that they assume a power-law distribution of MBH, and they constrain the BHMF and Eddington ratio distribution by visually matching the model distributions to the observed distributions.”
EVIDENCE FOR NON-EVOLVING Fe ii/Mg ii RATIOS IN RAPIDLY ACCRETING z ∼ 6 QSOs (2011, methodology): “…= λ Fλ(3000Å) 4πD 2 L (6) Since L(3000Å) is only a fraction of the total electromagnetic luminosity coming from the QSO, we apply the bolometric correction by Shen et al. (2008) to obtain Lbol: Lbol = 5.15 λLλ(3000Å) (7) The Eddington luminosity is defined as the maximum luminosity…”
The Spitzer/IRAC view of black hole–bulge scaling relations (2010, background): “This evolution is however not found by Labita et al. (2009) or Shen et al. (2008).”
Physical Properties of 15 Quasars at z ≳ 6.5 (2017, methodology): “We estimate Lbol using the bolometric correction by Shen et al. (2008): Lbol erg s−1 = 5.15× λLλ,3000 erg s−1 (13) The estimated values of black hole masses, bolometric luminosities and Eddington ratios for the quasars in our sample are shown in Table 8.”
Accretion-driven evolution of black holes: Eddington ratios, duty cycles and active galaxy fractions (2011, background): “Many other studies of the Edding- c© 2012 RAS, MNRAS 000, 1– ?? ton ratio distributions of quasars and active galaxies have found evidence for time evolution of λc, and in some cases for mass-dependence (e.g., McLure & Dunlop 2004; Vestergaard 2004; Heckman et al. 2005; Ballo et al. 2007; Babić et ”
COMPARING SINGLE-EPOCH VIRIAL BLACK HOLE MASS ESTIMATORS FOR LUMINOUS QUASARS (2012, methodology): “On the other hand, we confirm the poor correlation between CIV FWHM and Hβ FWHM reported earlier (e.g., Baskin & Laor 2005; Netzer et al. 2007), which was also inferred from the comparison between CIV and MgII using SDSS quasars (e.g., Shen et al. 2008).”
Accretion and star formation rates in low‐redshift type II active galactic nuclei (2009, background): “…L5100, L([O iii]λ5007) and, to a lesser extent L(Hβ) (due to blending with the broad Hβ), are directly observed and luminosity dependent bolometric corrections are known with reasonable accuracy (Marconi et al. 2004; Netzer et al. 2007; Shen et al. 2008; Vestergaard 2008; see summary in N09).”
Measuring the Masses of Supermassive Black Holes (2014, methodology): “…be expected by using FWHM (and/or Gaussian fits) instead of σline, which was indeed the case for the line-width measurements used in this study (Shen et al. 2008); the highest masses are overestimated and the lowest masses are underestimated, which would appear to rotate a distribution…”
The Hard X-Ray Spectrum as a Probe for Black Hole Growth in Radio-Quiet Active Galactic Nuclei (2008, background): “…of 35 sources), with a typical dispersion of a factor of ∼5 around that value (e.g., McLure & Dunlop 2004; Kollmeier et al. 2006; Netzer et al. 2007; Shen et al. 2008), Γ values for such sources typically lie in the narrow range of ∼1.5–2.5 (1.2–2.6 for our sample of 35 sources; see also Vignali…”
A Population of Short-Period Variable Quasars from PTF as Supermassive Black Hole Binary Candidates (2016, methodology): “…do not have a mass estimate, we draw the mass from the expected Gaussian distribution given the absolute i-band magnitude (e.g., MacLeod et al. 2010 based on the results from Shen et al. 2008), p (logMBH|Mi) = 1√ 2πs exp [ − (logMBH −m) 2 2s2 ] , (8) with m = 2.0 − 0.27Mi and s = 0.58 + 0.011Mi.”
The LABOCA survey of the Extended Chandra Deep Field-South: clustering of submillimetre galaxies (2011, methodology): “For QSOs and the population of SMGs that contain broad-line AGN, the black hole mass can be estimated using virial techniques based on the broad emission lines (e.g. Vestergaard 2002; Peterson et al. 2004; Kollmeier et al. 2006; Vestergaard & Peterson 2006; Shen et al. 2008).”
Extragalactic science, cosmology, and Galactic archaeology with the Subaru Prime Focus Spectrograph (2012, methodology): “While there are well-known uncertainties in calcul ting reliable SMBH masses using broad UV lines, we will be in a good position to compare the SMBH masses derived from different emission lines observed in the same spectra (e.g., 29 Shen et al. 2008).”
THE HIDDEN “AGN MAIN SEQUENCE”: EVIDENCE FOR A UNIVERSAL BLACK HOLE ACCRETION TO STAR FORMATION RATE RATIO SINCE z ∼ 2 PRODUCING AN MBH–M* RELATION (2012, background): “However, by selection, those AGNs have considerably higher average LBol (≈ 10 13 L⊙; e.g., Shen et al. 2008) than our samples and, as such, are less directly relevant to our analyses. the broad sṀBH PDF, indicative of the large variations in nuclear activity compared to the sSFR of the host.”
A CATALOG OF QUASAR PROPERTIES FROM SLOAN DIGITAL SKY SURVEY DATA RELEASE 7 (2010, methodology): “The current compilation extends our earlier SDSS Data Release 5 (DR5) compilation (Shen et al. 2008b) by including the post-DR5 quasars, as well as measurements based on new multiple-Gaussian fits to the lines (as discussed above).”
Properties of flat-spectrum radio-loud Narrow-Line Seyfert 1 Galaxies (2014, background): “As shown by Shen et al. (2008), mass estimates from these two lines are generally consistent.”
CHARACTERIZING THE MID-INFRARED EXTRAGALACTIC SKY WITH WISE AND SDSS (2012, methodology): “This cutoff value is very conservative comparing to the mean C IV λ1549 velocity width of 5600 km/s, estimated the SDSS QSO sample (Shen et al. 2008).”
REVERBERATION MAPPING RESULTS FOR FIVE SEYFERT 1 GALAXIES (2012, methodology): “This correlation allows one to obtain both velocity and RBLR estimates from a single calibrated spectrum, and has been used to calculate MBH in large samples of AGNs (e.g., Shen et al. 2008).”