systematic effects in measurement of bh masses by emission...
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Systematic Effects in Measurement of BH Masses by Emission-Line
Reverberation of AGN
Dan Li University of Florida
April 4, 2008
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Systematic Effects in Measurement of Black Hole Masses by Emission-
Line Reverberation of Active Galactic Nuclei:
Eddington Ratio and Inclination
(Suzy Collin et al. 2006)
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Reverberation Mapping
VP: Virial Product
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Reverberation Mapping
VP: Virial Product
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Reverberation Mapping
Some arguments for the validity of RM Higher-ionization lines closer to the central
BH shorter τ Shorter τ broader line (consistent with the
virial prediction):
RBLR-L (size-luminosity relationship)
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MBH-σ* Relationship
In addition, AGNs show a similar MBH-σ* relationship as observed in quiescent galaxies.
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Accuracy of the RM Measurements
Can be determined through a comparison between RM and other independent methods;
MBH-σ* relationship of the quiescent galaxies (no other options…)
How accurate can we reproduce a same MBH-σ* relationship based on the RM? What is the scaling factor f ?
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The Scale Factor f
How can we characterize the width of the broad-line profile?
Approach: examine various ways of determining the line-width that is used as ΔV and attempt to identify systematic effects or biases.
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The Scale Factor f
Mean or RMS (root-mean-square) Spectrum?
Line-Width Measures: FWHM or σline ? FWHM: zeroth-order moment σline: second-order moment
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The Scale Factor f
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The Scale Factor f
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The Scale Factor f
Profile Type FWHM/σ
Gaussian 2.35 Rectangular 3.46 Triangular 2.45 Edge-on rotating ring 2.83
Lorentzian 0
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The Scale Factor f Population 1:
FWHM/σ < 2.35
Population 2:
FWHM/σ > 2.35
Population A:
σ < 2000 kms-1
Population B:
σ > 2000 kms-1
(Sulentic et al. 2000)
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The Scale Factor f
Comparison with Masses based on σ*
σ* of 16 AGNs are available Assuming that the AGN MBH-σ*
relationship is identical to that for quiescent galaxies:
(Tremaine et al. 2002)
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The Scale Factor f
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The Scale Factor f
Some Conclusions: σline is a less biased measure of the
velocity dispersion than is FWHM; It is possible to correct VPf to obtain an
unbiased BH mass
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The Scale Factor f
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The Scale Factor f
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The Scale Factor f
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The Scale Factor f FWHM/ σline is not correlated with BH mass, or with luminosity.
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Influence of BLR Inclination
Try to find out the influence of BLR inclination through modeling the BLR with some simple but plausible structure and dynamics
A thin flat disk can not explain the strength of the broad-lines
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Influence of BLR Inclination
The BLR as a Flared Disk
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Influence of BLR Inclination
The BLR as a Warped Disk
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Influence of BLR Inclination
A Two-Component BLR:A Disk and a Wind
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Influence of BLR Inclination
A Simple Parameterization (zeroth approximation of the three cases above)
Thus, in these “thick disk” models:
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Influence of BLR Inclination
The ratio of the VP in the thick disk model to the VP in the general case (isotropic case):
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Influence of BLR Inclination
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Influence of BLR Inclination
Furthermore, we can compute how many objects would have a given value of A by assuming that their inclinations are distributed randomly in a range of i≤i0
(The cumulative fraction of AGNs for which VPthick disk/VPisotropic is smaller than a given value)
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Influence of BLR Inclination
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Influence of BLR Inclination Cumulative fraction of real observations:
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Influence of BLR Inclination Cumulative fraction of Population 1 & 2:
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Discussion
Why is the FWHM more dependent on the inclination than the line dispersion ?
Why is there a big variation of the FWHM/ σline among the AGNs ? -- gravitational instability, inflated inner hot disk, wind …