3D Spectrography IV – The search for supermassive black holes

3D SpectrographyIV – The search for supermassive black holes

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)

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)

DF: an axisymmetric modelfor NGC 3115 Wide field HRCAM WFPC2/HST arcsec V band arcsec Model arcsec arcsec arcsec Emsellem, Dejonghe, Bacon 1999

DF : NGC3115 • Two-Integral model : distribution function f(E, Lz) Disks Black Hole Emsellem, Dejonghe, Bacon 1999

Integral field data: TIGER/CFHT NGC 3115 2I / 3I Dynamical models data : Kormendy et al. (~ 45 pc / arcsec) -- Central FOS LOSVD -- model FOS --Mbh = 6.5 108 Msun Emsellem, Dejonghe, Bacon 1999

Surface density M/L Spatial density Deriving 2 Dark matter Potential NNLS Optimal superposition of orbits Orbital library Schwarzschild modelling Surface brightness Kinematics Observables for each orbit

Jeans’ theorem Orbital initial conditions:The Energy  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

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

Initial conditions : 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

Integration of the orbits IntegratenE 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 …..

Observables and constraints Observables  Orbital matrix Orbital Weights Constraints vector • Photometric: • Mass model integrated over grid cells, normalized by total galaxy mass • Kinematic: • Aperture positions with up to 6 Gauss-Hermite moments

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

3s 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) • Drawχ2 contours, and find best fit M/L Mbh

The compact elliptical galaxy M32

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)

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) STIS V  h3 h4  h3 h4 V

M32: Best fit parameters • Strong constraints on M/L, MBH, i • MBH in agreement with van der Marel et al. 1998 3 level (Verolme, Cappellari et al. 2002)

M32: Importance of 3D spectrography 3 level SAURON + STIS 4 slits + STIS • Model parameters and internal dynamics are strongly constrained (Verolme, Cappellari et al. 2002)

M 32 regularized • Distribution function f(E, Lz, I3)

NGC 821: Schwarzschild model DONNEES MODELE - Velocity field well reproduced RESIDUS Mc Dermid et al. 2002

Dispersion (km/s) Vitesse (km/s) Results for NGC 821 • M / L well constrained • Black holemassnot constrained

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

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) • ????

Degeneracy in models Valluri, Merritt, Emsellem 03

Degeneracy in models:the case of M 32 Which minimum ?? Valluri, Merritt, Emsellem 03

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 IV – The search for supermassive black holes