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The Masses of Black Holes in Active Galactic Nuclei

The Central Engine of Active Galactic Nuclei 16 October 2006

Bradley M. PetersonThe Ohio State University

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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

1. Virial relationship for emission-line lags (BLR radius) and line widths

2. The MBH – * relationship

3. 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 WidthsFWHM: 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

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220

2line / dPdP

line

FWHM

6 2/1)2ln2(2 32 22

2.45 2.833.462.35

Sometrivial

profiles:

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Virialized BLR• The virial relationship

is best seen in the variable part of the emission line.

Three contributing factors account for additional scatter:

(1) Failure to account for narrow component(2) Use of mean rather than rms spectrum

(3) Use of FWHM instead of line

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M = f (ccent 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.

The AGN MBH – * Relationship: Calibration of the Reverberation Mass Scale

Tremaine slope

Ferrarese slope

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/*

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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.,

in preparation

Stellar dynamics: ≤ 70 106 M

Reverberation: (46 ± 5) 106 M from Bentz et al. 2006)

Minimum at3 107 M

for this model

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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 (= ccent) and luminosity L allows estimate of black hole mass by measuring line width and luminosity only:

M = f (ccent line2 /G) f L1/2 line

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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 that’s 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)

NLS1 + I Zw 1-type

NGC 5548 H 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

Boroson (2001)

PC1: low

PC1: high

FWHM/line low FWHM/line high

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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.

NLS1 + I Zw 1-type

NGC 5548 H

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Pop A Pop Bsimilar to Sulentic et al.

Pop 1

Pop 2

Col

lin e

t al

.

From Collin et al. (2006)

Mean spectraRMSspectra

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Pop 1

Pop 2

Pop A Pop Bsimilar to Sulentic et al.

Col

lin e

t al

.

From Collin et al. (2006)

Mean spectraRMSspectra f = 5.7 1.5

f = 5.4 2.7

f = 6.2 3.5f = 4.7 1.1

line-based calibration

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Pop 1

Pop 2

Pop A Pop Bsimilar to Sulentic et al.

Col

lin e

t al

.

From Collin et al. (2006)

Mean spectraRMSspectra f = 0.9 0.3

f = 2.2 1.2

FWHM-based

f = 2.5 1.5f = 0.8 0.2

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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 *

• Requires observations of CO bandhead in near IR.

• Preliminary results with VLT/ISAAC.

• Upcoming SV program on Gemini North with NIFS/Altair/LGS system

All Ca IItriplet

VLT spectraDasyra 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 < 20 o)

• Does not stand out in MBH

– *

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Test Case 2: Mrk 110An 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)

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)

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!

Phenomenon: QuiescentGalaxies

Type 2AGNs

Type 1AGNs

Estimating AGN Black Hole Masses

PrimaryMethods:

Stellar, gasdynamics

Stellar, gasdynamics

MegamasersMegamasers 1-dRM1-dRM

2-dRM2-dRM

FundamentalEmpiricalRelationships:

MBH – *AGN MBH – *

SecondaryMassIndicators:

Fundamentalplane:

e, re *

MBH

[O III] line widthV * MBH

Broad-line width V & size scaling with

luminosity R L1/2 MBH

Application:High-z AGNsLow-z AGNs

BL Lac objects

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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?

• Not just Eddington rate.

All data

Subset correctable for starlight

Correctedfor starlight:big symbolsare NGC 5548

Collin et al. (2006)

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What does FWHM/line actually measure?

Not just inclination (NGC 5548).

Extreme examples

NLS1 + I Zw 1-type

NGC 5548 H

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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 > 0.5: Mean FWHM = 6464 km s-1

radio < 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

Source Distance from central source

X-Ray Fe K 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 V 2 /G)

wherer = scale length of regionV = velocity dispersionf = a factor of order unity, depends on details of geometry and kinematics

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