Three-integral oblate galaxy models

A simple numerical scheme is presented for the construction of three-integral phase-space distribution functions for oblate galaxy models with a gravitational potential of St\"{a}ckel form, and an arbitrary axisymmetric luminous density distribution. The intrinsic velocity moments can be obtained simultaneously with little extra effort. The distribution of the inner and outer turning points of the short-axis tube orbits that are populated can be specified freely, and is chosen in advance. The entire distribution function is then derived from the density by an iterative scheme that starts from the explicitly known distribution function of the thin-orbit (maximum streaming) model, in which only the tubes with equal inner and outer turning points are populated. The versatility and limitations of this scheme are illustrated by the construction of a number of self-consistent three-integral flattened isochrone models of Kuzmin--Kutuzov type, and by investigation of special cases where the scheme is tractable analytically. This includes the behaviour of the distribution functions in the outer regions of the models. The scheme converges rapidly for models containing orbits with ratios of the outer to inner turning point as large as ten, and is particularly suited for the construction of tangentially anisotropic flattened models, self-consistent as well as non-consistent. The algorithm simplifies in the disk and spherical limit, and can be generalized to triaxial models.Comment: uuencoded gziped PostScript, 21 pages without figures. PostScript with figures available from http://www.strw.leidenuniv.nl/dynamics/Papers/ or ftp://ftp.strw.leidenuniv.nl/pub/dynamics/Papers/RobijnDeZeeuw95.tar.Z Accepted by MNRA

Two-integral Schwarzschild models

We describe a practical method for constructing axisymmetric two-integral galaxy models (with distribution functions of the form f(E,L_z), in which E is the orbital energy, and L_z is the vertical component of the angular momentum), based on Schwarzschild's orbit superposition method. Other f(E,L_z)-methods are mostly based on solving the Jeans equations or on finding the distribution function directly from the density, which often places restrictions on the shape of the galaxy. Here, no assumptions are made and any axisymmetric density distribution is possible. The observables are calculated (semi-)analytically, so that our method is faster than most previous, fully numerical implementations. Various aspects are tested extensively, the results of which apply directly to three-integral Schwarzschild methods. We show that a given distribution function can be reproduced with high accuracy and investigate the behaviour of the parameter that is used to measure the goodness-of-fit. Furthermore, we show that the method correctly identifies the range of cusp clopes for which axisymmetric two-integral models with a central black hole do not exist.Comment: 10 pages, 9 figures, Accepted for publication in MNRA

Mapping young stellar populations towards Orion with Gaia DR1

We use the first data release of the Gaia mission to explore the three dimensional arrangement and the age ordering of the many stellar groups towards the Orion OB association, aiming at a new classification and characterization of the stellar population. We make use of the parallaxes and proper motions provided in the Tycho Gaia Astrometric Solution (TGAS) sub-set of the Gaia catalogue, and of the combination of Gaia and 2MASS photometry. In TGAS we find evidence for the presence of a young population, at a parallax $\varpi \sim 2.65 \, \mathrm{mas}$, loosely distributed around some known clusters: 25 Ori, $\epsilon$ Ori and $\sigma$ Ori, and NGC 1980 ($\iota$ Ori). The low mass counterpart of this population is visible in the color-magnitude diagrams constructed by combining Gaia and 2MASS photometry. We study the density distribution of the young sources in the sky. We find the same groups as in TGAS, and also some other density enhancements that might be related to the recently discovered Orion X group, the Orion dust ring, and to the $\lambda$ Ori complex. We estimate the ages of this population and we infer the presence of an age gradient going from 25 Ori (13-15 Myr) to the ONC (1-2 Myr). We confirm this age ordering by repeating the Bayesian fit using the Pan-STARRS1 data. The estimated ages towards the NGC 1980 cluster span a broad range of values. This can either be due to the presence of two populations coming from two different episodes of star formation or to a large spread along the line of sight of the same population. Our results form the first step towards using the Gaia data to unravel the complex star formation history of the Orion region in terms of the different star formation episodes, their duration, and their effects on the surrounding interstellar medium.Comment: 17 pages, 17 figure

3D mapping of young stars in the solar neighbourhood with Gaia DR2

We study the three dimensional arrangement of young stars in the solar neighbourhood using the second release of the Gaia mission (Gaia DR2) and we provide a new, original view of the spatial configuration of the star forming regions within 500 pc from the Sun. By smoothing the star distribution through a gaussian filter, we construct three dimensional density maps for early-type stars (upper-main sequence, UMS) and pre-main sequence (PMS) sources. The PMS and the UMS samples are selected through a combination of photometric and astrometric criteria. A side product of the analysis is a three dimensional, G-band extinction map, which we use to correct our colour-magnitude diagram for extinction and reddening. Both density maps show three prominent structures, Scorpius-Centaurus, Orion, and Vela. The PMS map shows a plethora of lower mass star forming regions, such as Taurus, Perseus, Cepheus, Cassiopeia, and Lacerta, which are less visible in the UMS map, due to the lack of large numbers of bright, early-type stars. We report the finding of a candidate new open cluster towards $l, b \sim 218.5^{\circ}, -2^{\circ}$, which could be related to the Orion star forming complex. We estimate ages for the PMS sample and we study the distribution of PMS stars as a function of their age. We find that younger stars cluster in dense, compact clumps, and are surrounded by older sources, whose distribution is instead more diffuse. The youngest groups that we find are mainly located in Scorpius-Centaurus, Orion, Vela, and Taurus. Cepheus, Cassiopeia, and Lacerta are instead more evolved and less numerous. Finally, we find that the three dimensional density maps show no evidence for the existence of the ring-like structure which is usually referred to as the Gould Belt.Comment: 17 pages, 17 figures, 6 appendixes; accepted for publication in A&A; image quality decreased to comply with the arXiv.org rules on file siz

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