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:

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

,log log( ) 2 logBH virM a b L V

2

BH

RVM

G

• 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.

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)

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.

Log

FW

HM

(k

m/s

)

Log

FW

HM

(k

m/s

)

Comparison between two estimators

• MgII versus Hbeta

og ( )HBHL M M

og(

)MgII

BH

LM

M

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 compo

nent?

CIV versus MgII

• Larger FWHMs for larger blueshifts

The cosmic evolution of virial BH masses

93 10 M

1010 M

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

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 B

H 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 Eddin

gton-ratios based on virial masses in each luminosity bin The quoted 0.3-0.4 dex uncertainty in virial mass estimator

s

Model details• Power-law underlying BH mass distribution with sl

ope • True Eddington-ratio distribution at fixed BH mass

• FWHM

• Uncertainty in virial estimators

M

,1 2

BH truebolE

Edd

MLLog C C Log

L M

,

1( )

2 BH true FWHMLog FWHM Log M a b Log L

2 2 2 2( ) ( ) (2 )vir E SED FWHMb b

Comparison in two redshift ranges

MgII: 0.7<z<1.0 CIV: 1.9<z<2.1

( ) ( / )BH bol EddLogM M Log L L LogFWHM ( ) ( / )BH bol EddLogM M Log L L LogFWHM

Comparison in two redshift ranges

Model Parameters

Typical Eddington ratio for a 1e8 solar mass BH: Log(Lbol/LEdd) ~ -1.3

Summary• Two biases: CIV virial mass versus blueshi

ft; 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 Eddin

gton ratio distribution• Connections to quasar clustering