1. Padova 03 3D Spectrography 3D Spectrography IV – The search for supermassive black holes

2. Padova 03 3D Spectrography The search for supermassive black holes Most (present day) galaxies should contain a central massive dark object with a mass M ● of 10 6 to a few 10 9 M sun Ferrarese & Merritt 2000 (see also Gebhardt et al. 2000, 2003)

3. Padova 03 3D Spectrography The search for supermassive black holes The holy grail for dynamicists: The distribution function: f = Density of stars at every (x, y, z, v x, v y, v z, t)

4. Padova 03 3D Spectrography DF: an axisymmetric model for NGC 3115 V band Model Emsellem, Dejonghe, Bacon 1999 Wide field HRCAM WFPC2/HST arcsec

5. Padova 03 3D Spectrography DF : NGC 3115 Two-Integral model : distribution function f(E, L z ) Disks Black Hole Emsellem, Dejonghe, Bacon 1999

6. Padova 03 3D Spectrography NGC 3115 2I / 3I Dynamical models (~ 45 pc / arcsec) Emsellem, Dejonghe, Bacon 1999 data : Kormendy et al. FOS -- M bh = 6.5 10 8 M sun -- Central FOS LOSVD -- model Integral field data: TIGER/CFHT

7. Padova 03 3D Spectrography Surface brightness Kinematics Spatial densityOrbital library Observables for each orbit Surface density M/L Potential Dark matter Deriving  2 NNLS Optimal superposition of orbits Schwarzschild modelling

8. Padova 03 3D Spectrography Orbital initial conditions: The Energy Jeans’ theorem  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

9. Padova 03 3D Spectrography Angular momentum L z Linear grid from the minimum L z (=0, radial orbit) to the maximum L z (circular orbit) at this Energy Orbital initial conditions: The angular momentum

10. Padova 03 3D Spectrography Third integral I 3 Parametrized with starting angle atan(z zvc /R zvc ) on the ZVC, from the minimum I 3 (=0, planar orbit) to maximum I 3 (thin tube orbit) at these E and L z Initial conditions : Cretton et al. 1999 Orbital initial conditions: The Third Integral

11. Padova 03 3D Spectrography Integration of the orbits Integrate n E x n Lz x n I3 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 …..

12. Padova 03 3D Spectrography Observables and constraints  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

13. Padova 03 3D Spectrography Solving the matrix problem Least squares problem: Solve for orbital weights vector  j >0 that gives superposition  i  j O ij closest to D j NNLS or other least-squares methods Quality of fit determined by

14. Padova 03 3D Spectrography To constrain M BH and M/L M bh M/L 33 Derive orbital libraries for different values of M BH and M/L … Solve the matrix problem for each library (NNLS) Draw χ 2 contours, and find best fit

15. Padova 03 3D Spectrography The compact elliptical galaxy M32

16. Padova 03 3D Spectrography 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 – M TR =(3.4 ± 0.7)x10 6 M o – 55 o < i < 90 o STIS/HST data have been published by Joseph et al. (2001)

17. Padova 03 3D Spectrography M 32 : dynamical modeling with SAURON 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  h3h3 h4h4 V  h3h3 h4h4 STIS

18. Padova 03 3D Spectrography M32: Best fit parameters Strong constraints on M/L, M BH, i M BH in agreement with van der Marel et al. 1998 (Verolme, Cappellari et al. 2002) 3  level

19. Padova 03 3D Spectrography M32: Importance of 3D spectrography SAURON + STIS4 slits + STIS Model parameters and internal dynamics are strongly constrained 3  level (Verolme, Cappellari et al. 2002)

20. Padova 03 3D Spectrography M 32 Distribution function f(E, L z, I 3 ) regularized

21. Padova 03 3D Spectrography NGC 821: Schwarzschild model - Velocity field well reproduced DONNEES MODELE RESIDUS Mc Dermid et al. 2002

22. Padova 03 3D Spectrography Results for NGC 821 Vitesse (km/s) Dispersion (km/s)  M / L well constrained  Black hole mass not constrained

23. Padova 03 3D Spectrography 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

24. Padova 03 3D Spectrography Problems of degeneracy Spherical case: – When f(E) : unique solution – General situation: f(E, L 2 ) –  There exists an infinity of models having a given  (r) Axisymmetric case: – When f(E, L z ) : unique even part – General situation: f(E, L z, I 3 ) –  There exists an infinity of models having a given  (R, z) ????

25. Padova 03 3D Spectrography Valluri, Merritt, Emsellem 03 Degeneracy in models

26. Padova 03 3D Spectrography Which minimum ?? Degeneracy in models: the case of M 32 Valluri, Merritt, Emsellem 03

27. Padova 03 3D Spectrography 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