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Biases in Virial Black Hole Masses: an SDSS Perspective

Biases in Virial Black Hole Masses: an SDSS Perspective. Yue Shen (Princeton) with Jenny Green, Michael Strauss, Gordon Richards and Don Schneider. Virial Estimators. Virial method: Reverberation mapping reveals a R-L relation Three virial estimators:

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Biases in Virial Black Hole Masses: an SDSS Perspective

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  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. Log FWHM (km/s) Log FWHM (km/s) Distributions of FWHMs • The FWHMs are distributed as a log-normal, with typical dispersion ~0.1-0.2 dex; and they are weakly dependent on either luminosity or redshift.

  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: • 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 0.3-0.4 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

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