Orbital structure of triaxial galaxies

We have developed a method to construct realistic triaxial dynamical models for elliptical galaxies, allowing us to derive best-fitting parameters, such as the mass-to-light ratio and the black hole mass, and to study the orbital structure. We use triaxial theoretical Abel models to investigate the robustness of the method.Comment: 2 pages (1 figure), to appear in the proceedings of the IAU Symposium 220 "Dark matter in galaxies", eds. S. Ryder, D.J. Pisano, M. Walker and K. Freema

The dynamical distance and intrinsic structure of the globular cluster omega Centauri

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster omega Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on D tan i. Application of our axisymmetric implementation of Schwarzschild's orbit superposition method to omega Cen reveals no dynamical evidence for a significant radial dependence of M/L. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3 kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6 M_sun. The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.Comment: 37 pages (23 figures), accepted for publication in A&A, abstract abridged, for PS and PDF file with full resolution figures, see http://www.strw.leidenuniv.nl/~vdven/oc

A SAURON view of galaxies

We have measured the two-dimensional kinematics and line-strength distributions of 72 representative nearby early-type galaxies, out to approximately one effective radius, with our panoramic integral-field spectrograph SAURON. The resulting maps reveal a rich variety in kinematical structures and linestrength distributions, indicating that early-type galaxies are more complex systems than often assumed. We are building detailed dynamical models for these galaxies, to derive their intrinsic shape and dynamical structure, and to determine the mass of the supermassive central black hole. Here we focus on two examples, the compact elliptical M32 and the E3 galaxy NGC4365. These objects represent two extreme cases: M32 has very regular kinematics which can be represented accurately by an axisymmetric model in which all stars rotate around the short axis, while NGC4365 is a triaxial galaxy with a prominent kinematically decoupled core, with an inner core that rotates about an axis that is nearly perpendicular to the rotation axis of the main body of the galaxy. Our dynamical models for these objects demonstrate that two-dimensional observations are essential for deriving the intrinsic orbital structure and dark matter content of galaxies.Comment: 7 pages (3 figures, full resolution Fig. 1 available at http://www.strw.leidenuniv.nl/~verolme/M32.ps). Contributed talk to the Athens Workshop on Galaxies and Chaos, Theory and Observations; Proceedings to appear in "Galaxies and Chaos", eds. G. Contopoulos and N. Vogli

Probing the stellar populations of early-type galaxies: the SAURON survey

The SAURON project will deliver two-dimensional spectroscopic data of a sample of nearby early-type galaxies with unprecedented quality. In this paper, we focus on the mapping of their stellar populations using the SAURON data, and present some preliminary results on a few prototypical cases.Comment: 12 pages, 6 figures. ASP Conference, Galaxies: the Third Dimension, Cozumel. Version with higher resolution figures available at http://www-obs.univ-lyon1.fr/eric.emsellem/papers/cozumel_emsellem.ps.g

A Log-Quadratic Relation Between the Nuclear Black-Hole Masses and Velocity Dispersions of Galaxies

We demonstrate that a log-linear relation does not provide an adequate description of the correlation between the masses of Super-Massive Black-Holes (SMBH, M_bh) and the velocity dispersions of their host spheroid (sigma). An unknown relation between log(M_bh) and log(sigma) may be expanded to second order to obtain a log-quadratic relation of the form log(M_bh)=alpha+beta log(sigma/200) + beta_2[log(sigma/200)]^2. We perform a Bayesian analysis using the Nuker sample, and solve for beta, beta_2 and alpha, in addition to the intrinsic scatter (delta). We find unbiased parameter estimates of beta=4.2+/-0.37, beta_2=1.6+/-1.3 and delta=0.275+/-0.05. At the 80% level the M_bh-sigma relation does not follow a uniform power-law. Indeed, over the velocity range 70km/s<sigma<380km/s the logarithmic slope of the best fit relation varies between 2.7 and 5.1, which should be compared with a power-law estimate of 4.02+/-0.33. Assuming no systematic offset, single epoch virial SMBH masses estimated for AGN follow the same log-quadratic M_bh-sigma relation as the Nuker sample, but extend it downward in mass by an order of magnitude. The log-quadratic term in the M_bh-sigma relation has a significant effect on estimates of the local SMBH mass function at M_bh>10^9 solar masses, leading to densities of SMBHs with M_bh>10^10 solar masses that are several orders of magnitude larger than inferred from a log-linear relation. We also estimate unbiased parameters for the SMBH-bulge mass relation. With a parameterisation log(M_bh)=alpha_b + beta_b log(M_b/10^{11}) + beta_2b[log(M_b/10^{11})]^2, we find beta_b=1.15+/-0.18 and beta_2b=0.12+/-0.14. We determined an intrinsic scatter delta_b=0.41+/-0.07 which is ~50% larger than the scatter in the M_bh-sigma relation.Comment: 21 pages, 14 figures. Replaced to correct errors in published versio

Dynamical Modeling of SAURON Galaxies

We describe our program for the dynamical modeling of early-type galaxies observed with the panoramic integral-field spectrograph SAURON. We are using Schwarzschild's numerical orbit superposition method to reproduce in detail all kinematical and photometric observables, and recover the intrinsic orbital structure of the galaxies. Since catastrophes are the most prominent features in the orbital observables, two-dimensional kinematical coverage is essential to constrain the dynamical models.Comment: 5 pages, 4 figures, LaTeX. Published in 2003, Carnegie Observatories Astrophysics Series, Vol. 1: Coevolution of Black Holes and Galaxies, ed. L. C. Ho (Pasadena: Carnegie Observatories, http://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.html

Estimating Black Hole Masses in Triaxial Galaxies

Most of the super massive black hole mass estimates based on stellar kinematics use the assumption that galaxies are axisymmetric oblate spheroids or spherical. Here we use fully general triaxial orbit-based models to explore the effect of relaxing the axisymmetric assumption on the previously studied galaxies M32 and NGC 3379. We find that M32 can only be modeled accurately using an axisymmetric shape viewed nearly edge-on and our black hole mass estimate is identical to previous studies. When the observed 5 degrees kinematical twist is included in our model of NGC 3379, the best shape is mildly triaxial and we find that our best-fitting black hole mass estimate doubles with respect to the axisymmetric model. This particular black hole mass estimate is still within the errors of that of the axisymmetric model and consistent with the M-sigma relationship. However, this effect may have a pronounced impact on black hole demography, since roughly a third of the most massive galaxies are strongly triaxial.Comment: Accepted for publication in MNRAS. 11 pages, 9 figures. PDFlate

A completely analytical family of dynamical models for spherical galaxies and bulges with a central black hole

We present a family of spherical models for elliptical galaxies and bulges consisting of a stellar component and a central black hole. All models in this family share the same stellar density profile, which has a steep central cusp. The gravitational potential of each models is a linear combination of the potential generated selfconsistently by the stars and the potential of a central black hole. The relative importance of these two contributions is a free parameter in the models. Assuming an isotropic dynamical structure, almost all kinematical properties of these models can be calculated analytically. In particular, they form the first simple dynamical models for galaxies with a central black hole where the distribution function and differential energy distribution can be written completely in terms of elementary functions only. We also present various extensions of this family to models with anisotropic orbital structures. Also for these dynamical models, the distribution function and its moments can be expressed completely in terms of elementary functions. This family is useful for a large range of applications, in particular to generate initial conditions for N-body and hydrodynamical simulations to model galactic nuclei with a central black hole.Comment: 13 pages, 1 figure, accepted for publication in MNRA

The non-evolving internal structure of early-type galaxies: the case study SDSS J0728+3835 at z = 0.206

We study the internal dynamical structure of the early-type lens galaxy SDSS J0728+3835 at z = 0.206. The analysis is based on two-dimensional kinematic maps extending out to 1.7 effective radii obtained from Keck spectroscopy, on lensing geometry and on stellar mass estimates obtained from multiband Hubble Space Telescope imaging. The data are modelled under the assumptions of axial symmetry supported by a two-integral distribution function (DF), by applying the combined gravitational lensing and stellar dynamics code CAULDRON, and yielding high-quality constraints for an early-type galaxy at cosmological redshifts. Modelling the total density profile as a power-law of the form rho_tot ~ 1/r^{gamma}, we find that it is nearly isothermal (logarithmic slope gamma = 2.08^{+0.04}_{-0.02}), and quite flattened (axial ratio q = 0.60^{+0.08}_{-0.03}). The galaxy is mildly anisotropic (delta = 0.08 +/- 0.02) and shows a fair amount of rotational support, in particular towards the outer regions. We determine a dark matter fraction lower limit of 28 per cent within the effective radius. The stellar contribution to the total mass distribution is close to maximal for a Chabrier initial mass function (IMF), whereas for a Salpeter IMF the stellar mass exceeds the total mass within the galaxy inner regions. We find that the combination of a NFW dark matter halo with the maximally rescaled luminous profile provides a remarkably good fit to the total mass distribution over a broad radial range. Our results confirm and expand the findings of the SLACS survey for early-type galaxies of comparable velocity dispersion (sigma_SDSS = 214 +/- 11 km/s). The internal structure of J0728 is consistent with that of local early-type galaxies of comparable velocity dispersion as measured by the SAURON project, suggesting lack of evolution in the past two billion years.Comment: 13 pages, 10 figures. MNRAS in press. Revised to match accepted versio

Recovering the intrinsic shape of early-type galaxies

We investigate how well the intrinsic shape of early-type galaxies can be recovered when both photometric and two-dimensional stellar kinematic observations are available. We simulate these observations with galaxy models that are representative of observed oblate fast-rotator to triaxial slow-rotator early-type galaxies. By fitting realistic triaxial dynamical models to these simulated observations, we recover the intrinsic shape (and mass-to-light ratio), without making additional (ad-hoc) assumptions on the orientation. For (near) axisymmetric galaxies the dynamical modelling can strongly exclude triaxiality, but the regular kinematics do not further tighten the constraint on the intrinsic flattening significantly, so that the inclination is nearly unconstrained above the photometric lower limit even with two-dimensional stellar kinematics. Triaxial galaxies can have additional complexity in both the observed photometry and kinematics, such as twists and (central) kinematically decoupled components, which allows the intrinsic shape to be accurately recovered. For galaxies that are very round or show no significant rotation, recovery of the shape is degenerate, unless additional constraints such as from a thin disk are available.Comment: 12 pages, 7 figures, PDFLaTeX, accepted to MNRAS, minor revision