Transcript Document

Methods and Uncertainties in
Super massive Black Hole mass
determination
Miguel Charcos Llorens
January 27th 2006
Super Massive Black
Holes
• Black holes as a Mathematical
curiosity
• End of evolution of massive stars
• Discover of quasar in 1963
• Model of SMBH in AGN’s
General Description
• Definition: M>10^5Msun
• Sphere of influence: rh = GMBH / σ 2
– D ~ 1" (M / 2 × 108 M )( / 200 km s-1)-2(D/5 Mpc).
– Seeing
– Hubble Space Telescope (HST) and radio VLBI
• Good examples: Milky Way and Local cluster
• Review papers (Kormendy & Richstone 1995;
Rees 1998; Richstone 1998; Ford et al. 1998; van
der Marel 1999).
Photometry
• The central density: non isothermal core
following a cuspy profile ρ(r) r-3/2
• More luminous, more
massive galaxies tend to
have more massive
central BHs but they also
have larger, more diffuse
cores (flattened cores)
Techniques
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Continuum Spectral Fitting
Variability
Stellar Kinematic
Gas Kinematic
Spectral Fitting
• Disk emission model
• Thin disk:
• Black Hole:
Uncertainties
• Very complex models
• Too many free parameters because little
constraints
Variability
• Variability time scale sets size of emission
region
• High energy emission region is close to
black hole (several black hole radii)
• Derive black hole mass
Uncertainties
• Inaccurate distance of the X-ray emission
• BH size-mass relation is model dependent
This method only gives upper limit
Stellar Kinematics I
• Velocity dispersion:  (r)r-1/2
• the radial variation in mass
• Simplifications:
– Spherically symmetric mass distribution;
– Circular mean rotation;
– And L  M/L does not vary with radius.
Stellar Kinematic II
• line-of-sight velocity distribution (LOSVD)
of the absorption lines
• dynamical models with two-integral phasespace distribution functions, f (E, Lz), E
being the total energy and Lz the angular
momentum in the symmetry axis
• axisymmetric three-integral models
Stellar Kinematics III
Uncertainties
• Technical challenge:
observed I (r), V(r) and σ (r) range of
intrinsic values
• Maximum entropy dynamical models:
sensitivity to the anisotropy
• Line profiles in spectroscopy
Gas Kinematics I
Gas Kinematics II
• Assume virial motion for emission line
clouds: M~2R/G
• Spectroscopy: Broad lines
NGC3079
• Photoinoization models
• Line or Masers
Uncertainties
• Complex lines (Spatial distribution, width,
double-picked, …)
• Uncertain models: heavy disk, edge on-disk
model
• Most parameters are not directly observable
and can only estimate a range for them.
Reverberating Model I
• Gravitational forces and dynamical model
• Radial distance of emitting region: time lag
• Velocity of emission line
Uncertainties
• Kinematic model: Virial Theorem
• Choice of the emission line
• Redshift determination
Example: M87
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Macchetto et al (1997)
b=0.08“
Mbh=3.2e9 Msun
zeta=-9°
i=51°
Vsys=1290 km/s
Example:
NGC 4258
Example: SDSS J1148+5251
(z~6.4)
• Willott et al (2003)
• Redshift:
MgII vs CIV
• Mbh = 3e9 Msun
• Accuracy: 2.5(1σ)
Stellar and Gas Kinematics Table
Stellar Kinematics vs Gas Kinematics
Reverberating Model Table
Gas and Stellar Kinematics vs
Reverberating Model
THE END