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

Triaxial orbit-based modelling of the Milky Way Nuclear Star Cluster

We construct triaxial dynamical models for the Milky Way nuclear star cluster using Schwarzschild's orbit superposition technique. We fit the stellar kinematic maps presented in Feldmeier et al. (2014). The models are used to constrain the supermassive black hole mass M_BH, dynamical mass-to-light ratio M/L, and the intrinsic shape of the cluster. Our best-fitting model has M_BH = (3.0 +1.1 -1.3)x10^6 M_sun, M/L = (0.90 +0.76 -0.08) M_sun/L_{sun,4.5micron}, and a compression of the cluster along the line-of-sight. Our results are in agreement with the direct measurement of the supermassive black hole mass using the motion of stars on Keplerian orbits. The mass-to-light ratio is consistent with stellar population studies of other galaxies in the mid-infrared. It is possible that we underestimate M_BH and overestimate the cluster's triaxiality due to observational effects. The spatially semi-resolved kinematic data and extinction within the nuclear star cluster bias the observations to the near side of the cluster, and may appear as a compression of the nuclear star cluster along the line-of-sight. We derive a total dynamical mass for the Milky Way nuclear star cluster of M_MWNSC = (2.1 +-0.7)x10^7 M_sun within a sphere with radius r = 2 x r_eff = 8.4 pc. The best-fitting model is tangentially anisotropic in the central r = 0.5-2 pc of the nuclear star cluster, but close to isotropic at larger radii. Our triaxial models are able to recover complex kinematic substructures in the velocity map.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

Three flow regimes of viscous jet falling onto a moving surface

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied, both theoretically and experimentally. We distinguish three flow regimes and classify them by the convexity of the jet shape (concave, vertical and convex). The fluid is modeled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. We make a comparison between the model and experiments, and obtain qualitative agreement

Falling of a viscous jet onto a moving surface

We analyze the stationary flow of a jet of Newtonian fluid that is drawn by gravity onto a moving surface. The situation is modeled by a third-order ODE on a domain of unknown length and with an additional integral condition; by solving part of the equation explicitly we can reformulate the problem as a first-order ODE, again with an integral constraint. We show that there are two flow regimes, and characterize the associated regions in the three-dimensional parameter space in terms of an easily calculable quantity. In a qualitative sense the results from the model are found to correspond with experimental observations.Comment: 16 pages, 11 figure

When opportunities backfire:Alternatives reduce perseverance and success in task completion

We consider an agent who needs to finish one task under a time constraint. Would she benefit from having several alternatives of which she only needs to complete one, or is it better not to have options? We conjecture that agents will be worse off when having several options. In our experiment, the control group receives a single task to work on, while the treated group has two optional tasks to choose from. We find that having two alternatives negatively affects performance. Even when the additional task is substantially easier than the original one, having more options does not help. We discuss potential mechanisms and present evidence showing that many managers do not anticipate the negative effects.</p