Methods and Uncertainties in Super massive Black Hole mass determination

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Methods and Uncertainties in Super massive Black
Hole mass determination

• Miguel Charcos Llorens
• January 27th 2006

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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 AGNs

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General Description

• Definition Mgt105Msun
• Sphere of influence rh GMBH / s 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).

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Photometry

• The central density non isothermal core
  following a cuspy profile ?(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)

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Techniques

• Continuum Spectral Fitting
• Variability
• Stellar Kinematic
• Gas Kinematic

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Spectral Fitting

• Disk emission model
• Thin disk
• Black Hole

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Uncertainties

• Very complex models
• Too many free parameters because little
  constraints

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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

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Uncertainties

• Inaccurate distance of the X-ray emission
• BH size-mass relation is model dependent
• This method only gives upper limit

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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.

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Stellar Kinematic II

• line-of-sight velocity distribution (LOSVD) of
  the absorption lines
• dynamical models with two-integral phase-space
  distribution functions, f (E, Lz), E being the
  total energy and Lz the angular momentum in the
  symmetry axis
• axisymmetric three-integral models

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Stellar Kinematics III
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Uncertainties

• Technical challenge observed I (r), V(r) and s
  (r) ?range of intrinsic values
• Maximum entropy dynamical models sensitivity to
  the anisotropy
• Line profiles in spectroscopy

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Gas Kinematics I
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Gas Kinematics II

• Assume virial motion for emission line clouds
  M?2R/G
• Spectroscopy Broad lines
• Photoinoization models
• Line or Masers

NGC3079
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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.

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Reverberating Model I

• Gravitational forces and dynamical model
• Radial distance of emitting region time lag
• Velocity of emission line

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Uncertainties

• Kinematic model Virial Theorem
• Choice of the emission line
• Redshift determination

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Example M87

• Macchetto et al (1997)
• b0.08
• Mbh3.2e9 Msun
• zeta-9
• i51
• Vsys1290 km/s

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Example NGC 4258
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Example SDSS J11485251 (z6.4)

• Willott et al (2003)
• Redshift MgII vs CIV
• Mbh 3e9 Msun
• Accuracy 2.5(1s)

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Stellar and Gas Kinematics Table
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Stellar Kinematics vs Gas Kinematics
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Reverberating Model Table
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Gas and Stellar Kinematics vs Reverberating Model
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THE END