R. C. E. van den Bosch

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

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster ω 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 bring the kinematic measurements onto a common coordinate system, and select on cluster membership and on measurement error. This provides a homogeneous data-set of 2295 stars with proper motions accurate to 0.20 mas yr -1 and 2163 stars with line-of-sight velocities accurate to 2 km s -1 , covering a radial range out to about half the tidal radius. 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 (caused by relative rotation of the photographic plates from which they were derived) can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on I) tan i. The corrected mean velocity fields are consistent with regular rotation, and the velocity dispersion fields display significant deviations from isotropy. We model ω Cen with an axisymmetric implementation of Schwarzschilds orbit superposition method, which accurately fits the surface brightness distribution, makes no assumptions about the degree of velocity anisotropy in the cluster, and allows for radial variations in M/L. We bin the individual measurements on the plane of the sky to search efficiently through the parameter space of the models. Tests on an analytic model demonstrate that this approach is capable of measuring the cluster distance to an accuracy of about 6 per cent. Application to w Cen reveals no dynamical evidence for a significant radial dependence of M/L, in harmony with the relatively long relaxation time of the cluster. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L V = 2.5 ±0.1 M ○. /L ○. and an inclination i = 50° ± 4°, 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 ○. . 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.

Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365

We present a flexible and efficient method to construct triaxial dynamical models of galaxies with a central black hole, using Schwarzschilds orbital superposition approach. Our method is general and can deal with realistic luminosity distributions, which project to surface brightness distributions that may show position angle twists and ellipticity variations. The models are fit to measurements of the full line-of-sight velocity distribution (wherever available). We verify that our method is able to reproduce theoretical predictions of a three-integral triaxial Abel model. In a companion paper by Ven, de Zeeuw & van den Bosch, we demonstrate that the method recovers the phase-space distribution function. We apply our method to two-dimensional observations of the E3 galaxy NGC 4365, obtained with the integral-field spectrograph SAURON, and study its internal structure, showing that the observed kinematically decoupled core is not physically distinct from the main body and the inner region is close to oblate axisymmetric.

The SAURON project – XIX. Optical and near-infrared scaling relations of nearby elliptical, lenticular and Sa galaxies

We present ground-based MDM Observatory V-band and Spitzer/InfraRed Array Camera 3.6-mu m-band photometric observations of the 72 representative galaxies of the SAURON survey. Galaxies in our sample probe the elliptical E, lenticular S0 and spiral Sa populations in the nearby Universe, both in field and cluster environments. We perform aperture photometry to derive homogeneous structural quantities. In combination with the SAURON stellar velocity dispersion measured within an effective radius (sigma(e)), this allows us to explore the location of our galaxies in the colour-magnitude, colour-sigma(e), Kormendy, Faber-Jackson and Fundamental Plane scaling relations. We investigate the dependence of these relations on our recent kinematical classification of early-type galaxies (i.e. slow/fast rotators) and the stellar populations. Slow rotator and fast rotator E/S0 galaxies do not populate distinct locations in the scaling relations, although slow rotators display a smaller intrinsic scatter. We find that Sa galaxies deviate from the colour-magnitude and colour-sigma(e) relations due to the presence of dust, while the E/S0 galaxies define tight relations. Surprisingly, extremely young objects do not display the bluest (V - [3.6]) colours in our sample, as is usually the case in optical colours. This can be understood in the context of the large contribution of thermally pulsing asymptotic giant branch stars to the infrared, even for young populations, resulting in a very tight (V - [3.6])-sigma(e) relation that in turn allows us to define a strong correlation between metallicity and se. Many Sa galaxies appear to follow the Fundamental Plane defined by E/S0 galaxies. Galaxies that appear offset from the relations correspond mostly to objects with extremely young populations, with signs of ongoing, extended star formation. We correct for this effect in the Fundamental Plane, by replacing luminosity with stellar mass using an estimate of the stellar mass-to-light ratio, so that all galaxies are part of a tight, single relation. The new estimated coefficients are consistent in both photometric bands and suggest that differences in stellar populations account for about half of the observed tilt with respect to the virial prediction. After these corrections, the slow rotator family shows almost no intrinsic scatter around the best-fitting Fundamental Plane. The use of a velocity dispersion within a small aperture (e. g. R-e/8) in the Fundamental Plane results in an increase of around 15 per cent in the intrinsic scatter and an average 10 per cent decrease in the tilt away from the virial relation.

Orbit-based dynamical models of the Sculptor dSph galaxy

We have developed spherically symmetric dynamical models of dwarf spheroidal (dSph) galaxies using Schwarzschilds orbit superposition method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) and on the orbital structure of the system (e.g. velocity anisotropy). This method is thus less prone to biases introduced by assumptions in comparison to the more commonly used Jeans modelling, and it allows us to put reliable constraints on their dark matter content. Here we present our results for the Sculptor dSph galaxy, after testing our methods on mock data sets. We fit both the second and fourth velocity moment profiles to break the mass-anisotropy degeneracy. For an Navarro, Frenk & White (NFW) dark matter halo profile, we find that the mass of Sculptor within 1 kpc is M-1 kpc = (1.03 +/- 0.07) x 10(8) M-circle dot, and that its velocity anisotropy profile is tangentially biased and nearly constant for radii beyond similar to 100 pc. The preferred concentration (c similar to 15) is low for its dark matter mass but consistent within the scatter found in N-body cosmological simulations. When we let the value of the central logarithmic slope alpha vary, we find that the best-fitting model has alpha = 0, although an NFW cusp or shallower is consistent at the 1 Sigma confidence level. On the other hand, very cuspy density profiles with logarithmic central slopes alpha <-1.5 are strongly disfavoured for Sculptor.

Stellar kinematics across the Hubble sequence in the CALIFA survey : general properties and aperture corrections

We present the stellar kinematic maps of a large sample of galaxies from the integral-field spectroscopic survey CALIFA. The sample comprises 300 galaxies displaying a wide range of morphologies across the Hubble sequence, from ellipticals to late-type spirals. This dataset allows us to homogeneously extract stellar kinematics up to several effective radii. In this paper, we describe the level of completeness of this subset of galaxies withrespect to the full CALIFA sample, as well as the virtues and limitations of the kinematic extraction compared to other well-known integral-field surveys. In addition, we provide averaged integrated velocity dispersion radial profiles for different galaxy types, which are particularly useful to apply aperture corrections for single aperture measurements or poorly resolved stellar kinematics of high-redshift sources. The work presented in this paper sets the basis for the study of more general properties of galaxies that will be explored in subsequent papers of the survey.

IMF shape constraints from stellar populations and dynamics from CALIFA

In this Paper, we describe how we use stellar dynamics information to constrain the shape of the stellar initial mass function (IMF) in a sample of 27 early-type galaxies from the CALIFA survey. We obtain dynamical and stellar mass-to-light ratios, Υdyn and Υ*, over a homogenous aperture of 0.5 Re. We use the constraint Υdyn≥Υ* to test two IMF shapes within the framework of the extended MILES stellar population models. We rule out a single power-law IMF shape for 75 per cent of the galaxies in our sample. Conversely, we find that a double power-law IMF shape with a varying high-mass end slope is compatible (within 1σ) with 95 per cent of the galaxies. We also show that dynamical and stellar IMF mismatch factors give consistent results for the systematic variation of the IMF in these galaxies.

Recovery of the internal orbital structure of galaxies

We construct axisymmetric and triaxial galaxy models with a phase-space distribution function that depends on linear combinations of the three exact integrals of motion for a separable potential. These Abel models, first introduced by Dejonghe & Laurent and subsequently extended by Mathieu & Dejonghe, are the axisymmetric and triaxial generalizations of the well-known spherical Osipkov-Merritt models. We show that the density and higher order velocity moments, as well as the line-of-sight velocity distribution of these models can be calculated efficiently and that they capture much of the rich internal dynamics of early-type galaxies. We build a triaxial and oblate axisymmetric galaxy model with projected kinematics that mimic the two-dimensional kinematic observations that are obtained with integral-field spectrographs such as SAURON. We fit the simulated observations with axisymmetric and triaxial dynamical models constructed with our numerical implementation of Schwarzschild orbit-superposition method. We find that Schwarzschild method is able to recover the internal dynamics and three-integral distribution function of realistic models of early-type galaxies.

Scaling relations in early-type galaxies from integral-field stellar kinematics

Early-type galaxies (ETGs) satisfy a now classic scaling relation Re ∝ σ1.2eI-0.8e, the Fundamental Plane (FP; Djorgovski & Davis 1987; Dressler et al. 1987), between their size, stellar velocity dispersion and mean surface brightness. A significant effort has been devoted in the past twenty years to try to understand why the coefficients of the relation are not the ones predicted by the virial theorem Re ∝ σ2eI-1e.

The stellar structure of early-type galaxies: a wide-field Mitchell Spectrograph view

N. F. Boardman1†, A. Weijmans1, R. C. E. van den Bosch2, L. Zhu2, A. Yildirim2, G. van de Ven2, M. Cappellari3, P. T. de Zeeuw4,5, E. Emsellem4, D. Krajnović6 and T. Naab7 School of Physics and Astronomy, University of St Andrews, KY16 9SS UK Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany Sub-department of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Sterrewacht Leiden, Leiden University, Postbus 9513, 2300 RA, Leiden, The Netherlands Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

Schwarzschild models of the Sculptor dSph galaxy

We have developed a spherically symmetric dynamical model of a dwarf spheroidal galaxy using the Schwarzschild method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) as well as on the orbital structure of the system modelled (e.g. velocity anisotropy). Therefore not only can we derive the dark matter content of these systems, but also explore possible formation scenarios. Here we present preliminary results for the Sculptor dSph. We find that the mass of Sculptor within 1 kpc is 8.5 × 107±0.05 M๏, its anisotropy profile is tangentially biased and slightly more isotropic near the center. For an NFW profile, the preferred concentration (~15) is compatible with cosmological models. Very cuspy density profiles (steeper than NFW) are strongly disfavoured for Sculptor.