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The Masses of Black Holes in Active Galactic Nuclei

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Title: The Masses of Black Holes in Active Galactic Nuclei


1
The Masses of Black Holes in Active Galactic
Nuclei
Bradley M. Peterson The Ohio State University
Space Telescope Science Institute 12
January 2005
2
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.)

3
Outline
  • How emission-line reverberation works
  • Results what has worked, what hasnt
  • (Brief) implications for the AGN broad-line
    region (BLR)
  • Evidence for a virialized BLR
  • The AGN MBH-?. Relationship
  • The AGN MBH-L Relationship
  • Secondary (scaling) methods
  • Immediate prospects

4
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

5
Driving Force in AGNs
  • UV/optical big blue bump can plausibly be
    identified with accretion-disk emission

Big Blue Bump
6
10 17 cm
7
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?

8
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 gt 3?109 M?
9
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

10
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
11
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?.

12
Gas Motions in M84 Nucleus
13
Reverberation Mapping
  • Kinematics and geometry of the BLR can be tightly
    constrained by measuring the emission-line
    response to continuum variations.

Continuum
Emission line
NGC 5548, the most closely monitored Seyfert 1
galaxy
14
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

The isodelay surface is a parabola
15
Isodelay Surfaces
All points on an isodelay surface have the
same extra light-travel time to the
observer, relative to photons from the
continuum source.
? r/c
16
Velocity-Delay Map for an Edge-On Ring
  • 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.

17
Thick Geometries
  • Generalization to a disk or thick shell is
    trivial.
  • General result is illustrated with simple two
    ring system.

18
Observed Response of an Emission Line
  • The relationship between the continuum and
    emission can be taken to be

Velocity-delay map is observed line response to
a ?-function outburst
Simple velocity-delay map
19
Line profile at current time delay
Black hole/accretion disk
20
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21
Two Simple Velocity-Delay Maps
The profiles and velocity-delay maps are
superficially similar, but can be distinguished
from one other and from other forms.
22
Recovering Velocity-Delay Maps from Real Data
Optical lines in Mrk 110 (Kollatschny 2003)
  • 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!

23
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)

24
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

25
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

26
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
the ionizing flux.
27
BLR Size vs. Luminosity
  • UV varies more than optical
  • ? ? Lopt0.9 ? (LUV 0.56 ) 0.9 ? LUV 0.5

28
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.

29
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.

Ionizing flux
Particle density
Korista et al. (1997)
30
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)
31
Virialized BLR
  • The virial relationship is best seen in the
    variable part of the emission line.

32
Calibration of the Reverberation Mass Scale
  • M f (c?cent? 2 /G)
  • Detemine scale factor f that matches AGNs to the
    quiescent-galaxy MBH-?. relationship
  • Current best estimate f 5.5
    1.8

33
MBH-?. relationship
34
The AGN MassLuminosity Relationship
35
The AGN MassLuminosity Relationship
Lbol 9??L?(5100 Å)
36
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 luminosity Vanden Berk et al.
(2004)
37
BLR Scaling with Luminosity
  • Suppose, to first order, AGN spectra look the
    same
  • Same ionization
  • parameter
  • Same density

38
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 (c?cent? 2 /G) ? L0.7? 2
39
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)
40
Estimating AGN Black Hole Masses
Application
41
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)
42
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)

A program to obtain a velocity-delay map is
not much more difficult than what has been done
already!
43
10 Simulations Based on HST/STIS Performance
Each step increases the experiment duration by
25 days
44
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

45
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.

46
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.

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