Post on 25-Feb-2016
description
Padova 033D Spectrography
3D Spectrography3D Spectrography
IV – The search for supermassive IV – The search for supermassive
black holesblack holes
Padova 033D Spectrography
The search for supermassive The search for supermassive black holesblack 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)
Padova 033D Spectrography
The search for supermassive The search for supermassive black holesblack holes
The holy grail for dynamicists:
The distribution function: f
=
Density of stars at every(x, y, z, vx, vy, vz, t)
Padova 033D Spectrography
DF: an axisymmetric modelDF: an axisymmetric modelfor NGC 3115for NGC 3115
V band
Model
Emsellem, Dejonghe, Bacon 1999
Wide field HRCAM WFPC2/HST
arcsec arcsecarcsec
arcs
ecar
csec
Padova 033D Spectrography
DF : NGCDF : NGC 31153115
Two-Integral model : distribution function f(E, Lz)
Disks
Black Hole
Emsellem, Dejonghe, Bacon 1999
Padova 033D Spectrography
NGC 3115 NGC 3115 2I / 3I Dynamical models2I / 3I Dynamical models
(~ 45 pc / arcsec)
Emsellem, Dejonghe, Bacon 1999
data : Kormendy et al.
FOS
-- Mbh = 6.5 108 Msun
-- Central FOS LOSVD
-- model
Integral field data: TIGER/CFHT
Padova 033D Spectrography
Surface brightnessKinematics
Spatial density
Orbital library
Observables for each orbit
Surface densityM/L
Potential
Dark matterDeriving 2
NNLS
Optimal superposition of orbits
Schwarzschild Schwarzschild modellingmodelling
Padova 033D Spectrography
Orbital initial conditions:Orbital initial conditions:The EnergyThe Energy
Jeans’ theorem ),,(),( DF DF 03
00 ILEII z
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
Padova 033D Spectrography
• Angular momentum Lz
Linear grid from the minimum Lz (=0, radial orbit) to the maximum Lz (circular orbit) at this Energy
Orbital initial conditions:Orbital initial conditions:The angular momentumThe angular momentum
Padova 033D Spectrography
• 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
0
),(
0
0,0,0
v
zRx ZVCZVC
Initial conditions :
Cretton et al. 1999
Orbital initial conditions:Orbital initial conditions:The Third IntegralThe Third Integral
Padova 033D Spectrography
Integration of the orbits 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 …..
Padova 033D Spectrography
Observables and constraintsObservables and constraints
CO
OCC
O
nnnnn
n
D
D
OOOO
11
,1,
,11,1
...
...
Orbital matrix
Constraints vector• Photometric:
Mass model integrated over grid cells, normalized by total galaxy mass• Kinematic:
Aperture positions with up to 6 Gauss-Hermite moments
Orbital Weights
Observables
Padova 033D Spectrography
Solving the matrix problemSolving the matrix problem
2
2 ),,(
j j
iijjj
BH D
ODiLMM
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
Padova 033D Spectrography
To constrain MTo constrain MBHBH and M/L and M/L
Mbh
M/L 3
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
Padova 033D Spectrography
The compact elliptical galaxy M32The compact elliptical galaxy M32
Padova 033D Spectrography
M 32M 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)
Padova 033D Spectrography
M 32 : dynamical modeling with M 32 : dynamical modeling with SAURON dataSAURON data
New dataset:– SAURON maps in the central 9”x11” (de Zeeuw et al. 2001)– STIS data along the major-axis (Joseph et al. 2001)
V h3 h4
V
h3
h4
STIS
Padova 033D Spectrography
M32: Best fit parametersM32: Best fit parameters
Strong constraints on M/L, MBH, i
MBH in agreement with van der Marel et al. 1998
(Verolme, Cappellari et al. 2002)
3 level
Padova 033D Spectrography
M32: M32: Importance of 3D spectrographyImportance of 3D spectrography
SAURON + STIS 4 slits + STIS Model parameters and internal
dynamics are strongly constrained
3
level
(Verolme, Cappellari et al. 2002)
Padova 033D Spectrography
M 32 M 32
Distribution function f(E, Lz, I3)
regularized
Padova 033D Spectrography
NGC 821: Schwarzschild modelNGC 821: Schwarzschild model
- Velocity field well reproduced
DONN
EES
MOD
ELE
RESI
DUS
Mc Dermid et al. 2002
Padova 033D Spectrography
Results for NGC 821Results for NGC 821Vi
tess
e (k
m/s
)D
ispe
rsio
n (k
m/s
)
M / L well constrained Black hole mass not constrained
Padova 033D Spectrography
Integral-Space Distribution of NGC Integral-Space Distribution of NGC 821821
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
Padova 033D Spectrography
Problems of degeneracyProblems of degeneracy
Spherical case:– When f(E) : unique solution– General situation: f(E, L2)– There exists an infinity of models having a given (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 (R, z)
????
Padova 033D SpectrographyValluri, Merritt, Emsellem 03
Degeneracy in modelsDegeneracy in models
Padova 033D Spectrography
Which minimum ??
Degeneracy in models:Degeneracy in models:the case of M 32the case of M 32
Valluri, Merritt, Emsellem 03
Padova 033D Spectrography
Summary - ConclusionsSummary - 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