1	Black Hole Masses in Active Galactic Nuclei Michael Brotherton University of Wyoming
2	Measuring Black Hole Masses in “Nearby” Galaxies SgrA* in the Milky Way Water Masers in NGC 4258, a few others Spatially Resolved Gas or Stellar Dynamics Using the Hubble Space Telescope (HST)
3	Max Planck Institute’s Galactic Core Group
4	Water Masers in NGC 4258 Based on Greenhill et al. (1995) Warped Disk Model Radial Velocities and Proper Motions Measure a Mass of 4x10⁷ solar masses (20 times more massive than SgrA*)
5	Spatially Resolved Spectroscopy from Space Shows BH Signatures HST STIS shows evidence for a super massive black hole in M84 based on spatially resolved gas dynamics (Bower et al 1997). Can also be done by examining spatially resolved stellar absorption line profiles, plus complex 3D orbital modeling.
6	The “M-sigma” Relation Black Hole Masses are about 0.1% of the central galactic bulge mass (a big surprise to theorists) and tightest correlation is with the stellar velocity dispersion (after Gebhardt et al. 2000).
7	What of Black Holes in AGNs? HST image of NGC 7742, a “Seyfert” Galaxy. While stellar and gas dynamical measurements work in normal, nearby galaxies, AGNs are typically too far away to resolve the black hole “sphere of influence” and the AGN itself overpowers the central starlight.
8	Virial Mass Estimates M = f (r ΔV²/ G) r = scale length of region ΔV is the velocity dispersion f is a factor of order unity dependent upon geometry and kinematics Estimates therefore require size scales and velocities, and verification to avoid pitfalls (eg. radiative acceleration).
9	Potential Virial AGN Mass Estimators Source Radius X-ray Fe Kα 3-10 R_s Broad-Line Region 600 R_s Megamasers 4x10⁴ R_s Gas Dynamics 8x10⁵ R_s Stellar Dynamics 10⁶ R_s Where Schwarzschild radius R_s = 2GM/c² = 3x10¹³ M₈ cm
10	Composite Quasar Spectrum Brotherton et al. (2001) – Note Broad Lines, CIV, Hβ
11	Reverberation Mapping (RM) Broad lines are photoionized by the central continuum, which varies. The line flux follows the continuum with a time lag t which is set by the size of the broad-line emitting region and the speed of light. Recombination timescales are very short, BLR stable, and continuum source small and central.
12	Does the BLR obey the Virial Theorem? Four well studied AGNs, RM of multiple emission lines shows the expected relationship (slope = -2) between time lags and velocities (note each of the three will have different central black hole masses). NGC7469: 8.4x10⁶ M_☼ NGC3783: 8.7x10⁶ M_☼ NGC5548: 5.9x10⁷ M_☼ 3C 390.3: 3.2x10⁸ M_☼
13	Does the BLR obey the Virial Theorem? RM-derived masses follow the same M-sigma relationship as seen for normal galaxies that have black hole masses measured from HST spatially resolved gas or stellar dynamics. Not more points since obtaining sigma for AGN is difficult (the AGN dilutes the stellar absorption line EWs). Good to 0.5 dex
14	Empirically BLR Scales With Luminosity Mentioned previously the Kaspi et al. (2000) result how R ~ L^0.7 (above). This permits the possibility of using single-epoch measurements to estimate black hole masses – much easier!
15	Vestergaard (2002) Single epoch FWHM vs. rms FWHM for Hβ Single epoch L vs. mean L
16	Vestergaard (2002) Single epoch BH Mass vs. RM BH mass
17	From Peterson (2002)