systematic effects in measurement of bh masses by emission...

Systematic Effects in Measurement of BH Masses by Emission-Line

Reverberation of AGN

Dan Li University of Florida

April 4, 2008

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)

Reverberation Mapping

VP: Virial Product

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)

MBH-σ* Relationship

 In addition, AGNs show a similar MBH-σ* relationship as observed in quiescent galaxies.

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 ?

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.

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

The Scale Factor f

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

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)

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)

The Scale Factor f

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

The Scale Factor f

The Scale Factor f  FWHM/ σline is not correlated with BH mass, or with luminosity.

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


 The BLR as a Flared Disk


 The BLR as a Warped Disk


 A Two-Component BLR:A Disk and a Wind


 A Simple Parameterization (zeroth approximation of the three cases above)

 Thus, in these “thick disk” models:


 The ratio of the VP in the thick disk model to the VP in the general case (isotropic case):


 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)

Influence of BLR Inclination Cumulative fraction of real observations:

Influence of BLR Inclination Cumulative fraction of Population 1 & 2:

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 …

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