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Black Hole Masses from Reverberation Mapping

STScI Spring Symposium: Black Holes 24 April 2007

Bradley M. Peterson and Misty C. BentzThe Ohio State University

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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.)

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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

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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

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Thick Geometries• Generalization to a disk or

thick shell is trivial. • General result is illustrated

with simple two ring system.

A multiple-ring system

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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.

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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

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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

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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.

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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)

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)

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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

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n

Wandel (2002)compilation of

AGNs

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Overlap betweenWandel and RM/ACS

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Overlap betweenWandel and RM/ACS

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Corrected Massesand Bulge Luminosities

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Corrected Massesand Bulge Luminosities

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All reverberation-mappedAGNs in ACS sample

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All reverberation-mappedAGNs in ACS sample

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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

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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

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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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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)

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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)

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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.

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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)

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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)

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!

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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)

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!

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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.

• Full potential of reverberation mapping has not yet been realized.– Significant improvements in quality of results are within

reach.