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

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.)

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

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

Driving Force in AGNs UV/optical “big blue bump” can plausibly be identified with accretion-disk emission “Big Blue Bump”

~10 17 cm

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?

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

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

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 .

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.

Gas Motions in M84 Nucleus

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

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:

“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

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.

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

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

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

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.

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!

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):

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

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

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.

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

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. Ionizing flux Particle density Korista et al. (1997)

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)

Virialized BLR The virial relationship is best seen in the variable part of the emission line.

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

MBH-*. relationship Reverberation Other methods

The AGN Mass–Luminosity Relationship

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

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)

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

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

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)

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:

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)

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!

10 Simulations Based on HST/STIS Performance Each step increases the experiment duration by 25 days

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

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.

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.