Dynamical Models for Galaxies Observed with SAURON Michele Cappellari Leiden Observatory

Outline Extraction of kinematics: 2D-binning Why Integral Field Spectroscopy is important? SAURON example Next steps

Adaptive 2D-binning: The SAURON Data of NGC 2273 Reconstructed image S/N map Barred Sa galaxy The basic adaptive 2D-binning problem: partition the data into bins having a minimum S/N

2D-binning Requirements Topological: partition the plane without holes or overlapping bins Morphological: bins as compact or “round” as possible Uniformity: minimal S/N scatter

2D-binning by QuadTree Decomposition 2x Regular cells but: large S/N scatter border problems Satisfies Topological and Morphological requirements ONLY

Voronoi Tessellation Definition: each point in a bin is closer to its generator than to any other point Satisfies Topological requirement ONLY

Centroidal Voronoi Tessellation Cappellari & Copin 2002, astro-ph/0202379 All Topological, Morphological and Uniformity requirements satisfied!

NGC 2273 Stellar Mean Velocity Field Not binned 2D-binned velocity

NGC 2273 Stellar Velocity Dispersion Field Not binned 2D-binned and interpolated

SAURON Dynamical Modeling Requirements no restriction on form of potential arbitrary geometry multiple components no restriction on distribution function [but f(r,v)0] full range of velocity anisotropy no need to know analytic integrals of motion This can be done with Schwarzschild’s orbit superposition method including all kinematic observables (V,,VP shapes)

Galaxy Orbits box short-axis tube inner long-axis tube Axisymmetric potential e.g. Cretton et al. (1999) Triaxial Stäckel potential e.g. Statler (1987) inner long-axis tube outer long-axis tube

Catastrophe Theory cusp fold   |x|-2/3   |x|-1/2 no inverse images two inverse images cusp   |x|-2/3 fold   |x|-1/2 When a smooth surface is projected onto a plane only these two singularities appear (Whitney 1955)

Orbital Tori Projection Regular orbits in 3-dim can be reduced to translations on a 3-torus in 6-dim phase space (x,v)(J,) Orbital density is constant on the torus surface folds Projection 2D Torus cusps

Catastrophe in the Orbital Surface Brightness i=80o i=60o Symmetry axis Symmetry axis Regular orbits! In an axisymmetric potential fold   |x|-1/2 cusp   |x|-2/3

Orbital Surface Brightness i=80o i=60o Lz I3 E Same orbit as before, but with a different colormap

Orbital Mean Velocity i=80o (x',y') V(x',y') No observable contribution on the major/minor axis (x',y') V(x',y')

Orbital Velocity Dispersion (x',y') (x',y')

Consequences The localized contribution of regular orbits to the observables implies: Integral Field Spectroscopy is needed to constrain the internal dynamics We can understand some known facts: Easy to construct self-consistent models (fit the density with the orbital components) Easy to reproduce any velocity field: higher order moments are needed to constrain the internal dynamics The DF has to be smooth, otherwise cusps and folds would appear in the galaxy surface brightness

The E3 Galaxy M32 Small, inactive companion of Andromeda nebula Many studies suggest presence of central BH Best previous study ground-based long-slit data and HST/FOS aperture together with Schwarzschild axisymmetric dynamical models (van der Marel et al. 1998) Results: (M/L)I=2.0 ± 0.3 MBH=(3.4 ± 0.7)x106 Mo 55o < i < 90o

M32: Dynamical Modeling with SAURON Stellar Kinematics STIS V  h3 h4 V  h3 h4 We use new data: SAURON high resolution map of inner 9”x11” (de Zeeuw et al. 2002, MNRAS) STIS major axis kinematics (Joseph et al. 2001, ApJ)

M32: Best-fitting Parameters Stringent constraints for M/L, MBH, i MBH in perfect agreement with van der Marel et al. (1998) 3 level Verolme, Cappellari et al. 2002, MNRAS, in press (astro-ph/0201086)

M32: Importance of 2D Kinematics Four slits + STIS SAURON + STIS 3 level Model parameters and internal structure strongly constrained

Next Steps Get a deeper understanding on how our models compare to the real galaxies Construct axisymmetric dynamical models: 26 of the 48 E/S0 in the SAURON survey, are consistent with axisymmetry Construct triaxial dynamical models

Expected Results As a function of morphological type and luminosity Orbital structure, including decoupled components Intrinsic shapes, mass distribution Rate of occurrence of gaseous and stellar disks Star formation history and its connection with dynamical structure Black hole demographics Importance of BHs for shaping galaxies