Biases in Virial Black Hole Masses: an SDSS Perspective
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Transcript of 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:
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