Transcript
Page 1: 3D Spectrography IV – The search for supermassive  black holes

Padova 033D Spectrography

3D Spectrography3D Spectrography

IV – The search for supermassive IV – The search for supermassive

black holesblack holes

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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)

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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)

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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

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Padova 033D Spectrography

DF : NGCDF : NGC 31153115

Two-Integral model : distribution function f(E, Lz)

Disks

Black Hole

Emsellem, Dejonghe, Bacon 1999

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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

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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

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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

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• 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

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• 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

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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 …..

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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

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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

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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

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The compact elliptical galaxy M32The compact elliptical galaxy M32

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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)

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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

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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

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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)

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M 32 M 32

Distribution function f(E, Lz, I3)

regularized

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NGC 821: Schwarzschild modelNGC 821: Schwarzschild model

- Velocity field well reproduced

DONN

EES

MOD

ELE

RESI

DUS

Mc Dermid et al. 2002

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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

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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

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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)

????

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Padova 033D SpectrographyValluri, Merritt, Emsellem 03

Degeneracy in modelsDegeneracy in models

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Padova 033D Spectrography

Which minimum ??

Degeneracy in models:Degeneracy in models:the case of M 32the case of M 32

Valluri, Merritt, Emsellem 03

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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


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