1. Biases in Virial Black Hole Masses: an SDSS Perspective
Yue Shen (Princeton)
with Jenny Green, Michael Strauss, Gordon Richards and Don Schneider

2. Virial Estimators Virial method:
Reverberation mapping reveals a R-L relation
Three virial estimators:
Hbeta (Kaspi et al. 2000; Vestergaard 2002; McLure & Jarvis 2002; Vestergaard & Peterson 2006), Halpha (Grene & Ho 2005)
MgII (McLure & Jarvis 2002; McLure & Dunlop 2004)
CIV (Vestergaard 2002; Vestergaard & Peterson 2006)
It is the only practical way to measure BH mass for large samples, based on single-epoch spectra.
Various issues: line width, the R-L relation

3. How well do these various virial calibrations agree with each other?
A statistical comparison between two virial estimators using the SDSS quasar sample.
Whichever calibration we use, we use the same original definitions of line widths and luminosities.

4. SDSS quasar sample
The spectroscopic DR5 quasar catalog (Schneider et al. 2007): 77,429 quasars (about half were uniformly selected, flux limited to i=19.1 at z<3 and i=20.2 at z>3)

5. Distributions of FWHMs
The FWHMs are distributed as a log-normal, with typical dispersion ~ dex; and they are weakly dependent on either luminosity or redshift.
Log FWHM (km/s)

6. Comparison between two estimators
MgII versus Hbeta

7. Comparison between two estimators
CIV versus MgII
difference in the CIV line:
line profile: non-Gaussian, asymmetric;
CIV-MgII blueshift;
contaminated by a non-virial disk wind component?

8. CIV versus MgII
Larger FWHMs for larger blueshifts

9. The cosmic evolution of virial BH masses

10. A possible Malmquist-type bias
for large complete samples
caused by the imperfectness of the BH mass indicator, and bottom-heavy intrinsic BH mass distribution
MC simulations

11. Malmquist bias Assumptions: Observations:
The underlying true BH mass distribution
True Eddington-ratio distribution at fixed BH mass
Virial estimators give the correct mean and uncertainty in BH mass estimations, and this uncertainty is attributed to the uncorrelated rms scatter in luminosity and in line width.
Observations:
Bolometric luminosity function
Observed distributions of FWHMs, virial masses and Eddington-ratios based on virial masses in each luminosity bin
The quoted dex uncertainty in virial mass estimators

12. Model details Power-law underlying BH mass distribution with slope
True Eddington-ratio distribution at fixed BH mass
FWHM
Uncertainty in virial estimators

13. Comparison in two redshift ranges
MgII: 0.7<z<1.0
CIV: 1.9<z<2.1

14. Comparison in two redshift ranges
Model Parameters
Typical Eddington ratio for a 1e8 solar mass BH: Log(Lbol/LEdd) ~ -1.3

15. Summary
Two biases: CIV virial mass versus blueshift; Malmquist bias
We need better understanding of BLR geometry and the systematics in virial estimators (form and scatter)
Future Work
More realistic underlying BH mass distribution and Eddington ratio distribution
Connections to quasar clustering