3D Spectrography
IV – The search for supermassive
black holes
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The search for supermassive black
holes

Most (present day) galaxies should contain a
central massive dark object with a mass M● of 106
to a few 109 Msun
Ferrarese & Merritt 2000 (see also Gebhardt et al. 2000, 2003)
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The search for supermassive black
holes

The holy grail for dynamicists:
The distribution function: f
=
Density of stars at every
(x, y, z, vx, vy, vz, t)
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DF: an axisymmetric model
for NGC 3115
HRCAM
WFPC2/HST
arcsec
Wide field
arcsec
V band
Model
arcsec
arcsec
arcsec
Emsellem, Dejonghe, Bacon 1999
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DF : NGC 3115

Two-Integral model : distribution function f(E, Lz)
Disks
Black
Hole
Emsellem, Dejonghe, Bacon 1999
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NGC 3115
2I / 3I Dynamical models
Integral field data: TIGER/CFHT
data : Kormendy et al.
(~ 45 pc / arcsec)
-- Central FOS LOSVD
-- model
FOS
-- Mbh = 6.5 108 Msun
Emsellem, Dejonghe, Bacon 1999
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Schwarzschild modelling
Surface brightness
Kinematics
Surface density
M/L
Spatial density
Deriving 2
NNLS
Optimal superposition of orbits
Dark
matter
Potential
Orbital library
Observables for each orbit
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Orbital initial conditions:
The Energy
Jeans’ theorem
 
DF  DF ( I ), I  ( E0 , L0z , I 30 )
 Sample orbits through their integrals
• Energy E
Logarithmic grid of circular radii defines energy grid
Radial range large enough to include all of the mass
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Orbital initial conditions:
The angular momentum
• Angular momentum Lz
Linear grid from the minimum
Lz (=0, radial orbit) to the
maximum Lz (circular orbit) at
this Energy
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Orbital initial conditions:
The Third Integral
Cretton et al. 1999
• Third integral I3
Parametrized with starting angle
atan(zzvc/Rzvc) on the ZVC, from
the minimum I3 (=0, planar orbit) to
maximum I3 (thin tube orbit) at
these E and Lz
Initial conditions :
3D Spectrography

x0  ( RZVC , 0 , z ZVC , 0 )

v0  0
Padova 03
Integration of the orbits
Integrate nE x nLz x nI3 orbits and store on
• Intrinsic, polar grid:
Density (r,) , velocity moments
• Projected, polar grid:
Density (r’,’)
• Projected, cartesian grid:
Density (x’,y’) , velocity profile VP(x’,y’,v’)
Store fractional contributions in …..
3D Spectrography
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Observables and constraints
Observables
 O1,1
 Orbital matrix  O
 nC ,1
Constraints vector
  1   D1 

... O1,nO    
      
... OnC ,nO    


D
 nO   nC 
Orbital
Weights
• Photometric:
Mass model integrated over grid cells, normalized by
total galaxy mass
• Kinematic:
Aperture positions with up to 6 Gauss-Hermite
moments
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Solving the matrix problem
Least squares problem:
• Solve for orbital weights vector j>0 that gives
superposition i j Oij closest to Dj
• NNLS or other least-squares methods
• Quality of fit determined by
 D j    j Oij 


2
i
 ( M BH , M L , i)   


D
j 
j



3D Spectrography
2
Padova 03
To constrain MBH and M/L

Derive orbital libraries for different values of
MBH and M/L …

Solve the matrix problem for each library
(NNLS)
Draw χ2 contours, and find best fit
3s
M/L

Mbh
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The compact elliptical galaxy M32
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M 32

Small - inactive - companion of the Andromeda galaxy
(M31)

Evidences for the presence of a massive black hole

Best study so far?: Schwarzschild model on long-slit
data and HST/FOS spectrography (van der Marel et al.
1997, 1998)
 Results:
– (M/L)V=2.0 ± 0.3
– MTR=(3.4 ± 0.7)x106 Mo
– 55o < i < 90o

STIS/HST data have been published by Joseph et al.
(2001)
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M 32 : dynamical modeling with
SAURON data
STIS
V
s
h3
s
V

h3
h4
h4
New dataset:
–
–
SAURON maps in the central 9”x11” (de Zeeuw et al. 2001)
STIS data along the major-axis (Joseph et al. 2001)
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M32: Best fit parameters


Strong constraints on
M/L, MBH, i
MBH in agreement with
van der Marel et al.
1998
3s level
(Verolme, Cappellari et al. 2002)
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M32:
Importance of 3D spectrography
3s
level
SAURON + STIS
4 slits + STIS
 Model parameters and internal
dynamics are strongly constrained
(Verolme, Cappellari et al. 2002)
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M 32
regularized

Distribution function f(E, Lz, I3)
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RESIDUS
MODELE
DONNEES
NGC 821: Schwarzschild model
- Velocity field well reproduced
Mc Dermid et al. 2002
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Vitesse (km/s) Dispersion (km/s)
Results for NGC 821
 M / L well constrained
 Black hole mass not constrained
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Integral-Space Distribution of NGC 821




Distinct component around
R~10’’
Consistent with photometric
disk
Comparison of Ca / Hb
kinematics implies that disk
> 6 Gyrs old
Slow rotator
=1:3 dissipationless merger?
Mc Dermid et al. 2002
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Problems of degeneracy

Spherical case:
– When f(E) : unique solution
– General situation: f(E, L2)
–  There exists an infinity of models having a given F(r)

Axisymmetric case:
– When f(E, Lz) : unique even part
– General situation: f(E, Lz, I3)
–  There exists an infinity of models having a given F(R, z)

????
3D Spectrography
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Degeneracy in models
Valluri, Merritt, Emsellem 03
3D Spectrography
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Degeneracy in models:
the case of M 32
Which minimum ??
Valluri, Merritt, Emsellem 03
3D Spectrography
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Summary - Conclusions
•
3D spectrography is required to probe the morphology and
dynamics of nearby galaxies :
•
•
•
•
Mapping of the gas/stellar kinematics and populations
Probing the full complexity of these objects
•
•
Internal structures
Estimates of black hole masses
More specifically :
• Should we believe present black hole mass estimates?
• What structures should we expect at the 10 pc scale ?
• Need for a general tool to model the dynamics of galaxies
• Need to break the degeneracy which may exists in models
In the future: need for 3D spectrographs on large telescopes
delivering high spatial resolution
3D Spectrography
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