The Economics of Shallow Lakes

non-linear differential games;ecological systems

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

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

A Hipparcos census of the nearby OB associations

A comprehensive census of the stellar content of the nearby OB associations is presented, based on Hipparcos positions, proper motions, and parallaxes. Moving groups are identified by combining de Bruijne's refurbished convergent point method with the `Spaghetti method' of Hoogerwerf & Aguilar. Monte Carlo simulations are used to estimate the expected number of interloper field stars. Astrometric members are listed for 12 young stellar groups, out to a distance of ~650 pc. These are the 3 subgroups Upper Scorpius, Upper Centaurus Lupus and Lower Centaurus Crux of Sco OB2, as well as Vel OB2, Tr 10, Col 121, Per OB2, alpha Persei (Per OB3), Cas-Tau, Lac OB1, Cep OB2, and a new group designated as Cep OB6. The selection procedure corrects the list of previously known astrometric and photometric B- and A-type members, and identifies many new members, including a significant number of F stars, as well as evolved stars, e.g., the Wolf-Rayet stars gamma^2 Vel (Vel OB2) and EZ CMa (Col 121), and the classical Cepheid delta Cep in Cep OB6. In the nearest associations the later-type members include T Tauri objects and other pre-main sequence stars. Astrometric evidence for moving groups in the fields of R CrA, CMa OB1, Mon OB1, Ori OB1, Cam OB1, Cep OB3, Cep OB4, Cyg OB4, Cyg OB7, and Sct OB2, is inconclusive, due to their large distance or unfavorable kinematics. The mean distances of the well-established groups are systematically smaller than previous estimates. The mean motions display a systematic pattern, which is discussed in relation to the Gould Belt. Six of the 12 detected moving groups do not appear in the classical list of nearby OB associations. The number of unbound young stellar groups in the Solar neighbourhood may be significantly larger than thought previously.Comment: 51 pages, 30 PostScript figures, 6 tables in PostScript format, default LaTeX using psfig.sty; accepted for publication in the Astronomical Journal, scheduled for January 1999 issue. Abbreviated abstrac

OB Associations

Since the previous (1990) edition of this meeting enormous progress in the field of OB associations has been made. Data from X-ray satellites have greatly advanced the study of the low-mass stellar content of associations, while astrometric data from the Hipparcos satellite allow for a characterization of the higher-mass content of associations with unprecedented accuracy. We review recent work on the OB associations located within 1.5 kpc from the Sun, discuss the Hipparcos results at length, and point out directions for future research.Comment: To appear in The Physics of Star Formation and Early Stellar Evolution II, eds C.J. Lada & N. Kylafis (Kluwer Academic), 30 pages, 9 EPS-figures, LaTeX using crckapb.sty, epsfig.sty, amssymb.st

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