1. The Masses of Black Holes in Active Galactic Nuclei
Bradley M. Peterson
The Ohio State University
Space Telescope Science Institute 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 hasn’t
(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 > 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 M = f (r V 2 /G) 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
In units of the Schwarzschild radius
RS = 2GM/c2 = 3 × 1013 M8 cm .

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
 = r/c
 = r cos /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
 = 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.
A multiple-ring system

18. Observed Response of an Emission Line
The relationship between the continuum and emission can be taken to be:
Emission-line
light curve
“Velocity-Delay Map”
Continuum
Light Curve
Velocity-delay map is observed line
response to a -function outburst
Simple
velocity-delay map

19. Time after continuum outburst
“Isodelay surface”
Time
delay
20 light days
Broad-line region
as a disk,
2–20 light days
Line profile at
current time delay
Black hole/accretion disk

21. Two Simple Velocity-Delay Maps
Inclined Keplerian
disk
Randomly inclined
circular Keplerian orbits
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
C IV and He II in NGC 4151
(Ulrich & Horne 1996)
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. Optical continuum flux
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

26. How Should the Lag Vary with Luminosity?
  Lopt0.9
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. Mean optical continuum flux
  Lopt0.9
Mean optical continuum flux
H lag
BLR Size vs. Luminosity
UV varies more than optical
  Lopt0.9  (LUV 0.56 ) 0.9  LUV 0.5
Lopt  LUV0.56
UV flux
Optical flux

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
Tremaine slope
Ferrarese slope

33. MBH-*. relationship
Reverberation
Other methods

34. The AGN Mass–Luminosity Relationship

35. The AGN Mass–Luminosity Relationship
Lbol = 9L(5100 Å)

36. SDSS composites, by luminosity
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:
r  L0.69 ± 0.05
Radius-luminosity relationship
from reverberation data
(Peterson et al. 2004)
Same ionization
parameter
Same density
r  L1/2

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)
Narrow [O III] FWHM
M BH (M)
Shields et al. (2003)

40. Estimating AGN Black Hole Masses
Phenomenon:
Quiescent
Galaxies
Type 2
AGNs
Type 1
Primary
Methods:
Stellar, gas
dynamics
Megamasers
1-d RM
2-d
Broad-line width V
& size scaling with
luminosity
R  L0.7
 MBH
Fundamental
Empirical
Relationships:
MBH – *
AGN MBH – *
[O III] line width
V  *  MBH
Fundamental
plane:
e, re  *
 MBH
BL Lac
objects
Secondary
Mass
Indicators:
Low-z AGNs
High-z AGNs
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.