The Masses of Black Holes in Active Galactic Nuclei

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The Masses of Black Holes in Active Galactic
Nuclei
Bradley M. Peterson The Ohio State University
The Central Engine of Active Galactic Nuclei
16 October 2006
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Principal Current Collaboratorson Work Discussed
Here

• D. Axon, M. Bentz, K. Dasyra, K. Denney,
• M. Dietrich, S. Collin, M. Elvis, L. Ferrarese,
• R. Genzel, K. Horne, S. Kaspi, T. Kawaguchi,
• M. Kishimoto, A. Laor, A. Lawrence, P. Lira,
• D. Maoz, M.A. Malkan, D. Merritt, H. Netzer,
• C.A. Onken, R.W. Pogge, A. Robinson,
• S.G. Sergeev, L. Tacconi, M. Valluri,
• M. Vestergaard, A. Wandel, M. Ward, S. Young

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Notation

• ? Bulge stellar velocity dispersion
• ?line RMS width of an emission line (based on
  second moment of line profile)
• Does not assume Gaussian profile
• Mean and rms spectra are formed from all the
  spectra in a reverberation experiment
• ?line and FWHM can be measured in either

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Main Focus

• Refine measurement and calibration of
  reverberation-based black hole masses
• New reverberation programs on sources with poor
  (or suspicious or no) reverberation measurements
• See K. Denney poster on NGC 4593
• Identify and correct for systematic effects in
  determination of various parameters
• M. Bentz talk on radius-luminosity relationship
• P. Lira contribution on spectropolarimetry

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Evidence That Reverberation-Based Masses Are
Reliable

• Virial relationship for emission-line lags (BLR
  radius) and line widths
• The MBH ? relationship
• Direct comparisons with other methods
• Stellar dynamical masses in the cases of NGC 3227
  and NGC 4151

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A Virialized BLR

• ?V ? R 1/2 for every AGN in which it is
  testable.
• Suggests that gravity is the principal dynamical
  force in the BLR.

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Characterizing Line Widths

• FWHM
• Trivial to measure
• Less sensitive to blending and extended wings

• Line dispersion ?line
• Well defined
• Less sensitive to narrow-line components
• More accurate for low-contrast lines

Some trivial profiles
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Virialized BLR

• The virial relationship is best seen in the
  variable part of the emission line.

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The AGN MBH ? Relationship Calibration of the
Reverberation Mass Scale

• M f (c?cent ?line2 /G)
• Determine scale factor f that matches AGNs to
  the quiescent-galaxy MBH-?. relationship
• Onken et al. calibration f
  5.5 1.8
• Scatter around MBH-? indicates that
  reverberation masses are accurate to better than
  0.5 dex.

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Measuring AGN Black Hole Masses from Stellar
Dynamics

• Only two reverberation-mapped AGNs are close
  enough to resolve their black hole radius of
  influence r GMBH/?2 with diffraction-limited
  telescopes.

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Direct Comparison NGC 3227

• Stellar dynamical mass in range (7 20) ? 106 M?
• (Davies et al. 2006)
• Reverberation-based mass is (42 21) ? 106 M?
• (Peterson et al. 2004)

Davies et al. (2006)
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Direct Comparison NGC 4151

• The reverberation-based mass is consistent with
  the (highly uncertain) stellar dynamical mass
  based on long-slit spectra of the Ca II triplet.
• Non-axisymmetric system will require observations
  with integral field unit (IFU) and adaptive
  optics (AO).

Minimum at 3 ? 107 M? for this model
Onken, Valluri, et al., in preparation
Stellar dynamics 70 ? 106 M? Reverberation
(46 5) ? 106 M? from Bentz et al. 2006)
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Mass-Luminosity Relationship

• All are sub-Eddington
• NLS1s have high Eddington rates
• At least some outliers are heavily reddened
• These 36 AGNs anchor the black hole mass scale

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Estimating Black Hole Masses from Individual
Spectra

• Correlation between BLR radius R ( c?cent) and
  luminosity L allows estimate of black hole mass
  by measuring line width and luminosity only
• M f (c?cent ?line2 /G) ? f L1/2 ?line2
• Dangers
• blending (incl. narrow lines)
• using inappropriate f
• Typically, the variable part of H? is 20
  narrower than the whole line

Radius luminosity relationship Bentz talk on
Thursday!
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Important Point(H? primarily, but can be
generalized)

• FWHM and ?line cannot be used interchangeably
• Bad news Use of FWHM introduces a bias that
  depends on profile
• Good news Bias can be calibrated out so you can
  use FWHM if thats all you have
• You must remove NL component, unless it is weak

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• Reverberation-mapped AGNs show broad range of
  FWHM/?line, which is a simple profile
  parameterization.
• Mass calibration is sensitive to which line-width
  measure is used!
• There is a bias with respect to AGN type (as
  reflected in the profiles)

Extreme examples
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Eigenvector 1

• Principal component analysis reveals a set of
  correlated properties called Eigenvector 1 or
  PC1
• FWHM/?line also correlates with PC1
• Both show some correlation with Eddington rate
• Some indications inclination matters

PC1 high
PC1 low
Boroson (2001)
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• Example if you use FWHM ? 2 and a
  ?line-based mass calibration, you will
  underestimate the masses of NLS1s (and thus
  overestimate their Eddington rates).
• Example by using FWHM instead of ?line, you
  change the mass ratio of the most extreme cases
  by an order of magnitude.

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Mean spectra
RMS spectra
From Collin et al. (2006)
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Mean spectra
Pop 2
?line-based calibration
RMS spectra
Collin et al.
Pop 1
Pop A
Pop B
similar to Sulentic et al.
From Collin et al. (2006)
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Mean spectra
Pop 2
FWHM-based
RMS spectra
Collin et al.
Pop 1
Pop A
Pop B
similar to Sulentic et al.
From Collin et al. (2006)
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Eliminating Bias from the Mass Scale

• Collin et al. (2006) provide a crude empirical
  correction that corrects for different values of
  FWHM/?line (or just FWHM)
• Like all work on f thus far, the correction is
  statistical in nature and does not necessarily
  apply to individual sources

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Next Urgent Need More Measurements of ?
All Ca II triplet

• Requires observations of CO bandhead in near IR.
• Preliminary results with VLT/ISAAC.
• Upcoming SV program on Gemini North with
  NIFS/Altair/LGS system

VLT spectra Dasyra et al. (2006)
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Can We Determine Inclination?

• Suggestion (Wu Han 2001 Zhang Wu 2002
  McLure Dunlop 2001) Use prediction of MBH ?
  ? M? (assumed isotropic)
• Compare to reverberation measurement Mrev
• Expect that small Mrev / M? ? low (face-on)
  inclination
• Similarly, expect that some NLS1s or other likely
  low inclination to have small Mrev / M?

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Can We Determine Inclination?

• Even if Mrev / M? is a poor inclination
  predictor for specific sources, Collin et al.
  (2006) make a statistical argument that some
  objects with low FWHM/?line values are low
  inclination.

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Test Case 1 3C 120

• Superluminal jet implies that 3C 120 is nearly
  face-on (i lt 20 o)
• Does not stand out in MBH ?

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Test Case 2 Mrk 110

• An NLS1 with an independent mass estimate from
  gravitational redshift of emission lines
  (Kollatschny 2003)
• M? 4.8 ? 106 M?
• Mrev 25 (6) ? 106 M?
• Mgrav 14 (3) ? 106 M?

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Other Ways to Determine Inclination

• Radio jets
• Spectropolarimetry (P. Lira, this meeting)
• Reverberation mapping (full velocity-delay map)

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Next Crucial Step

• Obtain a high-fidelity velocity-delay map for at
  least one line in one AGN.
• Cannot assess systematic uncertainties without
  knowing geometry/kinematics of BLR.
• Even one success would constitute proof of
  concept.

BLR with a spiral wave and its velocity-delay
map in three emission lines (Horne et al. 2004)
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Requirements to Map the BLR

• Extensive simulations based on realistic
  behavior.
• Accurate mapping requires a number of
  characteristics (nominal values follow for
  typical Seyfert 1 galaxies)
• High time resolution (? 0.2 1 day)
• Long duration (several months)
• Moderate spectral resolution (? 600 km s-1)
• High homogeneity and signal-to-noise (100)

A program to obtain a velocity-delay map is
not much more difficult than what has been done
already!
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Estimating AGN Black Hole Masses
Application
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Concluding Points

• Good progress has been made in using
  reverberation mapping to measure BLR radii and
  corresponding black hole mases.
• 36 AGNs, some in multiple emission lines
• Reverberation-based masses appear to be accurate
  to a factor of about 3.
• Direct tests and additional statistical tests are
  in progress.
• Scaling relationships allow masses of many
  quasars to be estimated easily
• Uncertainties typically 4 at this time
• Full potential of reverberation mapping has not
  yet been realized.
• Significant improvements in quality of results
  are within reach.

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Backup Slides
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What does FWHM/?line actually measure?
All data

• Not just Eddington rate.

Subset correctable for starlight
Corrected for starlight big symbols are NGC 5548
Collin et al. (2006)
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What does FWHM/?line actually measure?

• Not just inclination (NGC 5548).

Extreme examples
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Evidence Inclination Matters

• Inverse correlation between R (core/lobe) and
  FWHM (Wills Browne 1986)
• Core-dominant are more face-on so lines are
  narrower
• Correlation between ?radio and FWHM (Jarvis
  McLure 2006)
• Flat spectrum sources are closer to face-on and
  have smaller widths
• ?radio gt 0.5 Mean FWHM 6464 km s-1
• ?radio lt 0.5 Mean FWHM 4990 km s-1
• Width distribution for radio-quiets like flat
  spectrum sources (i.e., closer to face-on)
• Width of C IV base is larger for smaller R
  (Vestergaard, Wilkes, Barthel 2000)
• Line base is broader for edge-on sources

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How Can We Measure Black-Hole Masses?

• Virial mass measurements based on motions of
  stars and gas in nucleus.
• Stars
• Advantage gravitational forces only
• Disadvantage requires high spatial resolution
• larger distance from nucleus ? less critical test
• Gas
• Advantage can be found very close to nucleus
• Disadvantage possible role of non-gravitational
  forces

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Virial Estimators
Mass estimates from the virial theorem M f (r
?V 2 /G) where r scale length of
region ?V velocity dispersion f a factor
of order unity, depends on
details of geometry and kinematics
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Emission-Line Lags

• Because the data requirements are relatively
  modest,
• it is most common to determine the
  cross-correlation
• function and obtain the lag (mean response
  time)

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Reverberation Mapping Results

• Reverberation lags have been measured for 36
  AGNs, mostly for H?, but in some cases for
  multiple lines.
• AGNs with lags for multiple lines show that
  highest ionization emission lines respond most
  rapidly ? ionization stratification

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Accuracy of Reverberation Masses

• AGNs masses follow same MBH-? relationship as
  normal galaxies
• Scatter around MBH-? indicates that
  reverberation masses are accurate to better than
  0.5 dex.

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Accuracy of Reverberation Masses

• AGN black-hole masses can be measured by line
  reverberation
• Multiple lines in individual AGNs show a virial
  relationship between lag and line width (? ? V
  ?2)
• AGNs masses follow same MBH-? relationship as
  normal galaxies
• Reverberation masses are accurate to better than
  0.5 dex