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1
Black Hole Masses from Reverberation Mapping
STScI Spring Symposium: Black Holes 24 April 2007
Bradley M. Peterson and Misty C. BentzThe Ohio State University
2
Principal Current Collaborators• M. Bentz, K. Denney, M. Dietrich, R.W. Pogge
(Ohio State)• S. Collin (Meudon) • L. Ferrarese, C.A. Onken, (Herzberg Inst.)• K. Horne (St. Andrews)• S. Kaspi, D. Maoz, H. Netzer (Tel-Aviv Univ.)• T. Kawaguchi (NAOJ)• M.A. Malkan (UCLA)• D. Merritt (RIT) • S.G. Sergeev (Crimean Astrophys. Obs.) • M. Valluri (Chicago)• M. Vestergaard (Steward Obs.)• A. Wandel (Hebrew Univ.)
3
Measuring the Masses of Supermassive Black Holes in Galaxies
• Virial mass measurements based on motions of stars and gas in nucleus.– Stellar dynamics
• Advantage: gravitational forces only• Disadvantage: requires high spatial resolution
– larger distance from nucleus ⇒ less critical test
– Gas dynamics• Advantage: can be found very close to nucleus• Disadvantage: possible role of non-gravitational
forces
4
Virial EstimatorsFor Active
Galactic Nuclei
Source Distance from central source
X-Ray Fe Kα 3-10 RS Broad-Line Region 200−104 RS Megamasers 4 ×104 RS Gas Dynamics 8 ×105 RS Stellar Dynamics 106 RS
In units of the Schwarzschild radius RS = 2GM/c2 = 3 × 1013 M8 cm .
Mass estimates from thevirial theorem:
M = f (r ΔV 2 /G)wherer = scale length of
regionΔV = velocity dispersion
(emission-line width)f = a factor of order
unity, depends ondetails of geometryand kinematics
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Reverberation Mapping• Kinematics and
geometry of the BLR can be tightly constrained by measuring the emission-line response to continuum variations.
NGC 5548, the most closely monitored Seyfert 1 galaxy
Continuum
Emission line
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Reverberation Mapping Concepts: Response of an Edge-On Ring
• Suppose line-emitting clouds are on a circular orbit around the central source.
• Compared to the signal from the central source, the signal from anywhere on the ring is delayed by light-travel time.
• Time delay at position (r,θ) is τ = (1 + cos θ)r/c
τ = r/c
The isodelay surface isa parabola:
θτ
cos1+=
cr
τ = r cosθ /c
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τ = r/c
“Isodelay Surfaces”All pointson an “isodelaysurface” have the same extralight-travel timeto the observer,relative to photonsfrom the continuumsource.
τ = r/c
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• Clouds at intersection of isodelay surface and orbit have line-of-sight velocities V = ±Vorb sinθ.
• Response time is τ = (1 + cos θ)r/c
• Circular orbit projects to an ellipse in the (V, τ) plane.
Velocity-Delay Map for an Edge-On Ring
9
Thick Geometries• Generalization to a disk or
thick shell is trivial. • General result is illustrated
with simple two ring system.
A multiple-ring system
10
Observed Response of an Emission Line
The relationship between the continuum and emission can be taken to be:
Velocity-resolved emission-line
light curve
“Velocity-delay map”
Continuumlight curve
Simple velocity-delay map
Velocity-delay map is observed line response to a δ-function outburst
( , ) ( , ) ( )L V t V C t dτ τ τ= Ψ −∫
Broad-line regionas a disk,
2–20 light daysBlack hole/accretion disk
Time after continuum outburst
Timedelay
“Isodelay surface”
Line profile atcurrent time delay
20 light days
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Two Simple Velocity-Delay Maps
Inclined Kepleriandisk
Randomly inclinedcircular Keplerian orbits
The profiles and velocity-delay maps are superficially similar,but can be distinguished from one other and from other forms.
14
Recovering Velocity-Delay Maps from
Real Data
• Existing velocity-delay maps are noisy and ambiguous• In no case has recovery of the velocity-delay map been
a design goal for an experiment!
C IV and He II in NGC 4151(Ulrich & Horne 1996)
Optical lines in Mrk 110(Kollatschny 2003)
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):
CCF( ) = ( ) ACF( - ) dτ τ τ τ τ′ ′ ′Ψ∫
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Reverberation Mapping Results
• Reverberation lags have been measured for 36 AGNs, mostly for Hβ, but in some cases for multiple lines.
• AGNs with lags for multiple lines show that highest ionization emission lines respond most rapidly ⇒ ionization stratification
17
A Virialized BLR• ΔV ∝ 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 WidthsFWHM:
Trivial to measureLess sensitive to blending and extended wings
Line dispersion σline:Well definedLess sensitive to narrow-line componentsMore accurate for low-contrast lines
( ) 20
220
2line / λλλλλλσ λλ −=−= ∫∫ dPdP
=line
FWHMσ
6 2/1)2ln2(2 32 222.45 2.833.462.35
Sometrivial
profiles:
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• FWHM/σline 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)• σline appears to be a less biased mass estimator than FWHM
NLS1 + I Zw 1-typeNGC 5548 HβExtreme examples
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M = f (cτcent σline2 /G)
• Determine scale factor f that matches AGNs to the quiescent-galaxy MBH-σ*. relationship
• Onken et al. calibration: f = 5.5 ± 1.8
• Scatter around MBH-σ*indicates that reverberation masses are accurate to better than 0.5 dex.
The AGN MBH – σ* Relationship:Calibration of the Reverberation Mass Scale
Tremaine slope
Ferrarese slope
21
Measuring σ*
• For z > 0.06, requires observations of CO bandhead in H-band (1.6 μm).
• Preliminary results with VLT/ISAAC.
• Beginning to acquire Gemini North H-band spectra with NIFS/Altair/LGS system.
All Ca IItriplet
VLT spectraDasyra et al. (2007)
Tremaine et al.Reverberation, Ca IIReverberation, CO H-band
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/σ*
2 with diffraction-limited telescopes.
23
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)
Mrev
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).
Onken, Valluri, et al.,submitted to ApJ
Stellar dynamics: ≤ 70 × 106 MReverberation: (46 ± 5) × 106 M from Bentz et al. 2006)
Minimum at3 × 107 Mfor this model
NGC 4051z = 0.00234
log Lopt = 41.2
Mrk 335z =0.0256
log Lopt = 43.8
PG 0953+414z = 0.234
log Lopt = 45.1
Measurement of host-galaxy properties is difficult even for low-z AGNs• Bulge velocity dispersion σ*• Starlight contribution to optical luminosity
• Radius-luminosity relationship (Vestergaard talk later today)
26
27
Additional Check on Masses:MBH vs. Lbulge
• Modeling the surface brightness distributions of AGNs in our ACS sample give Lbulge.
• Is there a correlation between black hole mass and bulge luminosity (or mass)?
• Is it the same as that for quiescent galaxies?
Magorrian et al. (1998)
Wandel (2002)
Bulge luminosity
MBH
28
n
Wandel (2002)compilation of
AGNs
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Overlap betweenWandel and RM/ACS
30
Overlap betweenWandel and RM/ACS
31
Corrected Massesand Bulge Luminosities
32
Corrected Massesand Bulge Luminosities
33
All reverberation-mappedAGNs in ACS sample
34
All reverberation-mappedAGNs in ACS sample
35
MBH vs. Lbulge
• There is a clear correlation, but more work is necessary to improve slope determination and to compare zero-points with quiescent galaxies.
• At this point, no inconsistency with quiescent galaxies.
Bentz et al., in preparation
Bulge luminosity
MBH
36
Evidence That Reverberation-Based Masses Are Reliable
1. Virial relationship foremission-line lags (BLR radius) and line widths
2. MBH – σ* relationship
3. MBH – Lbulge relationship
4. Direct comparisons with other methods:
– Stellar dynamical masses In the cases of NGC 3227 and NGC 4151
37
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
38
Limitations: Systematic Effects• Unknown geometry
and kinematics of the BLR limit the accuracy of masses.– Lags are unaffected
if axial symmetry and isotropic emission
– Line widths can be severely affected by inclination
A plausible disk-wind conceptbased on Elvis (2000)
39
Evidence Inclination Matters• Relationship between R
(core/lobe) and FWHM (Wills & Browne 1986)– Core-dominant are more face-on
so lines are narrower
• Correlation between αradio and FWHM (Jarvis & McLure 2006)– Flat spectrum sources are closer
to face-on and have smaller line widths
• αradio > 0.5: Mean FWHM = 6464 km s-1
• αradio < 0.5: Mean FWHM = 4990 km s-1
• Width distribution for radio-quiets like flat spectrum sources (i.e., closer to face-on)
40
Can We Determine Inclination?• Suggestion (Wu & Han 2001; Zhang &
Wu 2002; McLure & Dunlop 2001): Use prediction of MBH – σ* ⇒ Mσ* (assumed isotropic)– Seems to be statistically plausible, but fails
for individual cases.
41
Other Ways to Determine (or Constrain) Inclination
• Radio jets– Superluminal expansion requires low
inclination• Spectropolarimetry
– Some AGNs have an equatorial scattering component that precludes low inclination
• Reverberation mapping (fully resolved velocity-delay map)
Next Crucial Step
• Obtain a high-fidelity velocity-delay map for at least one linein one AGN.– 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)
43
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)
Program OSUCTIO/OSU LAG
Wise 1988
Wise/SO PG
IUE 89 HST 93 Opt IUE Opt IUE Opt IUE Opt Opt Opt Opt Opt OptNo. Sources 1 1 1 1 1 1 1 3 5 8 2 5 3 15Time ResolutionDurationSpectral ResolutionHomogeneitySignal/Noise Ratio
AGN Watch NGC 5548
AGN Watch NGC 4151
AGN Watch NGC 7469
AGN Watch (other)
A program to obtain a velocity-delay map is notmuch more difficult than what has been done already!
44
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)
Program OSUCTIO/OSU LAG
Wise 1988
Wise/SO PG
IUE 89 HST 93 Opt IUE Opt IUE Opt IUE Opt Opt Opt Opt Opt OptNo. Sources 1 1 1 1 1 1 1 3 5 8 2 5 3 15Time ResolutionDurationSpectral ResolutionHomogeneitySignal/Noise Ratio
AGN Watch NGC 5548
AGN Watch NGC 4151
AGN Watch NGC 7469
AGN Watch (other)
A program to obtain a velocity-delay map is notmuch more difficult than what has been done already!
45
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.
• Full potential of reverberation mapping has not yet been realized.– Significant improvements in quality of results are within
reach.