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

The central mass and mass-to-light profile of the Galactic globular cluster M15

We analyze line-of-sight velocity and proper motion data of stars in the Galactic globular cluster M15 using a new method to fit dynamical models to discrete kinematic data. Our fitting method maximizes the likelihood for individual stars and, as such, does not suffer the same loss of spatial and velocity information incurred when spatially binning data or measuring velocity moments. In this paper, we show that the radial variation in M15 of the mass-to-light ratio is consistent with previous estimates and theoretical predictions, which verifies our method. Our best-fitting axisymmetric Jeans models do include a central dark mass of $\sim2 \pm 1\cdot 10^3M_\odot$, which can be explained by a high concentration of stellar remnants at the cluster center. This paper shows that, from a technical point of view and with current computing power, spatial binning of data is no longer necessary. This not only leads to more accurate fits, but also avoids biased mass estimates due to the loss of resolution. Furthermore, we find that the mass concentration in M15 is significantly higher than previously measured, and is in close agreement with theoretical predictions for core-collapsed globular clusters without a central intermediate-mass black hole.Comment: Accepted by MNRAS; 8 pages, 7 figure

MRK 1216 & NGC 1277 - An orbit-based dynamical analysis of compact, high velocity dispersion galaxies

We present a dynamical analysis to infer the structural parameters and properties of the two nearby, compact, high velocity dispersion galaxies MRK1216 & NGC1277. Combining deep HST imaging, wide-field IFU stellar kinematics, and complementary long-slit spectroscopic data out to 3 R_e, we construct orbit-based models to constrain their black hole masses, dark matter content and stellar mass-to-light ratios. We obtain a black hole mass of log(Mbh/Msun) = 10.1(+0.1/-0.2) for NGC1277 and an upper limit of log(Mbh/Msun) = 10.0 for MRK1216, within 99.7 per cent confidence. The stellar mass-to-light ratios span a range of Upsilon_V = 6.5(+1.5/-1.5) in NGC1277 and Upsilon_H = 1.8(+0.5/-0.8) in MRK1216 and are in good agreement with SSP models of a single power-law Salpeter IMF. Even though our models do not place strong constraints on the dark halo parameters, they suggest that dark matter is a necessary ingredient in MRK1216, with a dark matter contribution of 22(+30/-20) per cent to the total mass budget within 1 R_e. NGC1277, on the other hand, can be reproduced without the need for a dark halo, and a maximal dark matter fraction of 13 per cent within the same radial extent. In addition, we investigate the orbital structures of both galaxies, which are rotationally supported and consistent with photometric multi-S\'ersic decompositions, indicating that these compact objects do not host classical, non-rotating bulges formed during recent (z <= 2) dissipative events or through violent relaxation. Finally, both MRK 1216 and NGC 1277 are anisotropic, with a global anisotropy parameter delta of 0.33 and 0.58, respectively. While MRK 1216 follows the trend of fast-rotating, oblate galaxies with a flattened velocity dispersion tensor in the meridional plane of the order of beta_z = delta, NGC 1277 is highly tangentially anisotropic and seems to belong kinematically to a distinct class of objects.Comment: 27 pages, 15 figures and 4 tables. Accepted for publication in MNRA

Strategies for autonomy used by people with cervical spinal cord injury:A qualitative study

Purpose. To identify strategies used by people with high cervical spinal cord injury (SCI) to function autonomously. A multidimensional concept of autonomy was used, with four dimensions: independence, self-determination, participation and identification. Methods. Qualitative methods were used, involving literature study and semi-structured interviews with eight individuals with high SCI who had been discharged from the rehabilitation centre for several years and were members of a sports club. Results. Strategies for independence included making independent functioning a personal challenge and learning from others with SCI. Strategies for self-determination included keeping oneself informed, setting personal goals and being assertive. Strategies for participation were making challenges out of barriers, planning and organizing, asking and accepting help, and dealing with reactions from others. Strategies for identification involved taking life as it comes and focussing on positive aspects of life. Conclusions. Different strategies are necessary for different dimensions of autonomy. Some strategies seem contradictory in terms of their effects on different dimensions of autonomy. Patients can be made aware of strategies for autonomy during the rehabilitation phase

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 1kpc is 8.5\times10^(7\pm0.05) M\odot, 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.Comment: 2 pages, 4 figures, to appear in the proceedings of "Assembling the Puzzle of the Milky Way", Le Grand Bornand (Apr. 17-22, 2011

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

The structural and dynamical properties of compact elliptical galaxies

Dedicated photometric and spectroscopic surveys have provided unambiguous evidence for a strong stellar mass-size evolution of galaxies within the last 10 Gyr. The likely progenitors of today's most massive galaxies are remarkably small, disky, passive and have already assembled much of their stellar mass at redshift z=2. An in-depth analysis of these objects, however, is currently not feasible due to the lack of high-quality, spatially-resolved photometric and spectroscopic data. In this paper, we present a sample of nearby compact elliptical galaxies (CEGs), which bear resemblance to the massive and quiescent galaxy population at earlier times. Hubble Space Telescope (HST) and wide-field integral field unit (IFU) data have been obtained, and are used to constrain orbit-based dynamical models and stellar population synthesis (SPS) fits, to unravel their structural and dynamical properties. We first show that our galaxies are outliers in the present-day stellar mass-size relation. They are, however, consistent with the mass-size relation of compact, massive and quiescent galaxies at redshift z=2. The compact sizes of our nearby galaxies imply high central stellar mass surface densities, which are also in agreement with the massive galaxy population at higher redshift, hinting at strong dissipational processes during their formation. Corroborating evidence for a largely passive evolution within the last 10 Gyr is provided by their orbital distribution as well as their stellar populations, which are difficult to reconcile with a very active (major) merging history. This all supports that we can use nearby CEGs as local analogues of the high-redshift, massive and quiescent galaxy population, thus providing additional constraints for models of galaxy formation and evolution.Comment: 33 pages, 27 figures and 20 tables (with most of the tables provided as online-only supporting information). Accepted for publication in MNRA