1. 1 The Masses of Black Holes in Active Galactic Nuclei The Central Engine of Active Galactic Nuclei 16 October 2006 Bradley M. Peterson The Ohio State University

2. 2 Principal Current Collaborators on 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

3. 3 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

4. 4 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

5. 5 Evidence That Reverberation- Based Masses Are Reliable 1.Virial relationship for emission-line lags (BLR radius) and line widths 2.The M BH –  * relationship 3.Direct comparisons with other methods –Stellar dynamical masses in the cases of NGC 3227 and NGC 4151

6. 6 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.

7. 7 Characterizing Line Widths FWHM:  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 2.452.833.462.35 Some trivial profiles:

8. 8 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

9. 9 M = f (c  cent  line 2 /G) Determine scale factor f that matches AGNs to the quiescent- galaxy M BH -  *. relationship Onken et al. calibration: f = 5.5 ± 1.8 Scatter around M BH -  * indicates that reverberation masses are accurate to better than 0.5 dex. The AGN M BH –  * Relationship: Calibration of the Reverberation Mass Scale Tremaine slope Ferrarese slope

10. 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 * = GM BH /  * 2 with diffraction-limited telescopes.

11. 11 Direct Comparison: NGC 3227 Stellar dynamical mass in range (7 – 20)  10 6 M  (Davies et al. 2006) Reverberation-based mass is (42 ± 21)  10 6 M  (Peterson et al. 2004) Davies et al. (2006) M rev

12. 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  10 6 M  Reverberation: (46 ± 5)  10 6 M  from Bentz et al. 2006) Minimum at 3  10 7 M  for this model

13. 13 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

14. 14 Estimating Black Hole Masses from Individual Spectra Correlation between BLR radius R (= c  cent ) and luminosity L allows estimate of black hole mass by measuring line width and luminosity only: M = f (c  cent  line 2 /G)  f L 1/2  line 2 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!

15. 15 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

16. 16 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

17. 17 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 lowFWHM/  line high

18. 18 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 

19. 19 Pop A Pop B similar to Sulentic et al. Pop 1 Pop 2 Collin et al. From Collin et al. (2006) Mean spectra RMS spectra

20. 20 Pop 1 Pop 2 Pop A Pop B similar to Sulentic et al. Collin et al. From Collin et al. (2006) Mean spectra RMS spectra f = 5.7  1.5 f = 5.4  2.7 f = 6.2  3.5 f = 4.7  1.1  line -based calibration

21. 21 Pop 1 Pop 2 Pop A Pop B similar to Sulentic et al. Collin et al. From Collin et al. (2006) Mean spectra RMS spectra f = 0.9  0.3 f = 2.2  1.2 FWHM-based f = 2.5  1.5 f = 0.8  0.2

22. 22 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

23. 23 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 II triplet VLT spectra Dasyra et al. (2006)

24. 24 Can We Determine Inclination? Suggestion (Wu & Han 2001; Zhang & Wu 2002; McLure & Dunlop 2001): Use prediction of M BH –  *  M  * (assumed isotropic) –Compare to reverberation measurement M rev –Expect that small M rev / M  *  low (face-on) inclination –Similarly, expect that some NLS1s or other likely low inclination to have small M rev / M  *

25. 25 Can We Determine Inclination? Even if M rev / 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.

26. 26 Test Case 1: 3C 120 Superluminal jet implies that 3C 120 is nearly face-on (i < 20 o ) Does not stand out in M BH –  *

27. 27 Test Case 2: Mrk 110 An NLS1 with an independent mass estimate from gravitational redshift of emission lines (Kollatschny 2003): M  * = 4.8  10 6 M  M rev = 25 (±6)  10 6 M  M grav = 14 (±3)  10 6 M 

28. 28 Other Ways to Determine Inclination Radio jets Spectropolarimetry (P. Lira, this meeting) Reverberation mapping (full velocity- delay map)

29. 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)

30. 30 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) A program to obtain a velocity-delay map is not much more difficult than what has been done already!

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

32. 32 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.

34. 34 Backup Slides

35. 35 What does FWHM/  line actually measure? Not just Eddington rate. All data Subset correctable for starlight Corrected for starlight: big symbols are NGC 5548 Collin et al. (2006)

36. 36 What does FWHM/  line actually measure? Not just inclination (NGC 5548). Extreme examples NLS1 + I Zw 1-type NGC 5548 H 

37. 37 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

38. 38 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

39. 39 Virial Estimators In units of the Schwarzschild radius R S = 2GM/c 2 = 3 × 10 13 M 8 cm. 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

40. 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):

41. 41 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

42. 42 Accuracy of Reverberation Masses AGNs masses follow same M BH -  * relationship as normal galaxies Scatter around M BH -  * indicates that reverberation masses are accurate to better than 0.5 dex.

43. 43 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 M BH -  * relationship as normal galaxies Reverberation masses are accurate to better than 0.5 dex