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The Masses of Black Holes in Active Galactic Nuclei

Space Telescope Science Institute 12 January 2005

Bradley M. PetersonThe Ohio State University

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Principal Collaborators• M. Bentz, C.A. Onken, R.W. Pogge (Ohio State) • L. Ferrarese (Herzberg Inst., Victoria)• K.M. Gilbert (Lick Obs.)• K. Horne (St. Andrews)• S. Kaspi, D. Maoz, H. Netzer (Tel-Aviv Univ.)• M.A. Malkan (UCLA)• D. Merritt (RIT) • S.G. Sergeev (Crimean Astrophys. Obs.) • M. Vestergaard (Steward Obs.)• A. Wandel (Hebrew Univ.)

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Outline

1. How emission-line reverberation works2. Results: what has worked, what hasn’t3. (Brief) implications for the AGN broad-line

region (BLR) 4. Evidence for a virialized BLR

5. The AGN MBH-*. Relationship

6. The AGN MBH-L Relationship7. Secondary (scaling) methods8. Immediate prospects

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Driving Force in AGNs• Simple arguments suggest AGNs

are powered by supermassive black holes– Eddington limit requires M 106 M

• Requirement is that self-gravity exceeds radiation pressure

– Deep gravitational potential leads to accretion disk that radiates across entire spectrum

• Accretion disk around a 106 – 108 M black hole emits a thermal spectrum that peaks in the UV

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Driving Force in AGNs

• UV/optical “big blue bump” can plausibly be identified with accretion-disk emission

“Big Blue Bump”

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~10 17 cm

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Quasars

• Very luminous AGNs were much more common in the past.

• The “quasar era” occurred when the Universe was 10-20% its current age.

• Where are they now?

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Supermassive Black Holes Are Common• Supermassive black

holes are found in galaxies with large central bulge components.

• These are almost certainly remnant black holes from the quasar era.

• To understand accretion history, we need to determine black-hole demographics. M 87, a giant elliptical

SMBH > 3109 M

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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

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NGC 4258• The first and still

most reliable measurement of a black-hole mass in an AGN is due to megamaser motions in NGC 4258.

• Radial velocities and proper motions give a mass 4 ×107M.

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Gas Motions in M84 Nucleus

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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,) is = (1 + cos )r / c

= r/c

The isodelay surface isa parabola:

θcos1

τ

cr

= r cos /c

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= r/c

“Isodelay Surfaces”

All pointson an “isodelaysurface” have the same extralight-travel timeto the observer,relative to photonsfrom the continuumsource.

= r/c

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• Clouds at intersection of isodelay surface and orbit have line-of-sight velocities V = ±Vorb sin.

• Response time is = (1 + cos )r/c

• Circular orbit projects to an ellipse in the (V, ) 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:

Emission-linelight curve

“Velocity-Delay Map”

ContinuumLight Curve

d t C V t V L) ( ) , ( ) , (

Simple velocity-delay map

Velocity-delay map is observed line response to a -function outburst

Broad-line regionas a disk,

2–20 light daysBlack hole/accretion disk

Time after continuum outburst

Timedelay

Line profile atcurrent time delay

“Isodelay surface”

20 light days

C:\Program Files\QuickTime\QuickTimePlayer.exe C:\Movies\TimeDelay.mov

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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

d t t) ( ACF ) ( ) ( CCF

• 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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Time-Variable Lags

• 14 years of observing the H response in NGC 5548 shows that lags increase with the mean continuum flux.

• Measured lags range from 6 to 26 days

• Best fit is Lopt0.9

Lopt0.9

Optical continuum flux

H

lag

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How Should the Lag Vary with Luminosity?

• Responsivity of a line depends primarily on ionizing flux and particle density.

• Assuming wide range of densities at all radii implies that the radius of peak responsivity should depend primarily on geometrical dilution: L1/2

Hidden in this argument is that the flux must be theionizing flux.

L1/2

Lopt0.9

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BLR Size vs. Luminosity

• UV varies more than optical

Lopt0.9 (LUV

0.56 ) 0.9 LUV

0.5

Lopt LUV0.56

UV flux

Opt

ical

flu

x

L1/2

Lopt0.9

Mean optical continuum flux

H

lag

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What Fine -Tunes the BLR?

• Why are the ionization parameter and electron density the same for all AGNs?

• How does the BLR know precisely where to be?

• Answer: gas is everywhere in the nuclear regions. We see emission lines emitted under optimal conditions.

Locally optimally-emitting cloud (LOC) model

• The flux variations in each line are responsivity-weighted.– Determined by where

physical conditions (mainly flux and particle density) give the largest response for given continuum increase.

• Emission in a particular line comes predominantly from clouds with optimal conditions for that line. Korista et al. (1997)

Ioni

zing

flu

x

Particle density

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Evidence for a Virialized BLR• Gravity is important

– Broad-lines show virial relationship between size of line-emitting region and line width, r 2

– Yields measurement of black-hole mass

Peterson et al. (2004)

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Virialized BLR• The virial relationship

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

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M = f (ccent 2 /G)• Detemine scale

factor f that matches AGNs to the quiescent-galaxy MBH-*. relationship

• Current best estimate: f = 5.5 ± 1.8

Calibration of the Reverberation Mass Scale

Tremaine slope

Ferrarese slope

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MBH-*. relationship

Reverberation

Other methods

The AGN Mass–Luminosity Relationship

The AGN Mass–Luminosity Relationship

Lbol = 9L(5100 Å)

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Luminosity Effects• Average line spectra

of AGNs are amazingly similar over a wide range of luminosity.

• Exception: Baldwin Effect– Relative to continuum,

C IV 1549 is weaker in more luminous objects

– Origin unknown

SDSS composites, by luminosityVanden Berk et al. (2004)

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BLR Scaling with Luminosity

2HH

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)H(

rn

L

cnr

QU

• Suppose, to first order, AGN spectra look the same:

Same ionization

parameter Same density

r L1/2

r L0.69 ± 0.05

Radius-luminosity relationshipfrom reverberation data

(Peterson et al. 2004)

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Secondary Mass Indicators

• Reverberation masses serve as an anchor for related AGN mass determinations (e.g., based on photoionization modeling)– Will allow exploration of

AGN black hole demographics over the history of the Universe.

Vestergaard (2002)based on scaling relationship r L0.7

and C IV line width

M = f (ccent 2 /G) L0.7 2

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Narrow-Line Widths as a Surrogate for *

• Narrow-line widths and * are correlated– The narrow-line

widths have been used to estimate black-hole mass, based on the MBH- *

correlation– Limitations imposed

by angular resolution, non-virial component (jets)

Shields et al. (2003)

Narrow [O III] FWHM

M B

H (

M)

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 L0.7 MBH

Application:High-z AGNsLow-z AGNs

BL Lac objects

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 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!

10 Simulations Based on HST/STIS Performance

Each step increases the experiment duration by 25 days

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Accuracy of Reverberation Masses• Without knowledge of the

BLR kinematics and geometry, it is not even possible to estimate how large the systematic errors might be (e.g., low-inclination disk could have a huge projection correction).– However, superluminal jet

implies that 3C 120 is nearly face-on

– Simple disks alone do not work

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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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Summary• 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 ~1 dex at this time

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