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

The Size of Stable International Environmental Agreements in the case of Stock Pollution

Most of the literature on stability of International Environmental Agreements is essen- tially static and can therefore not identify changes in the size of the stable coalition in connection with changes in the stock of pollutants. This is a relevant issue because most global pollution problems are dynamic with stock externalities. This paper shows that the incentives for membership indeed change with changes in the stock of pollutants and that technology choice is an important factor when considering the consequences.

Optimal Management with Potential Regime Shifts

We analyze how the threat of a potential future regime shift affects optimal management. We use a simple general growth model to analyze four cases that involve combinations of stock collapse versus changes in system dynamics, and exogenous versus endogenous probabilities of regime shift. Prior work has focused on stock collapse with endogenous probabilities and reaches ambiguous conclusions about the effect of potential regime shift on optimal management. We show that all other cases yield unambiguous results. In particular, with endogenous probability of regime shift that affects system dynamics the potential for regime shift causes optimal management to become precautionary.

The Economics of Shallow Lakes

non-linear differential games;ecological systems

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

Simultaneous Arithmetic Progressions on Algebraic Curves

A simultaneous arithmetic progression (s.a.p.) of length k consists of k points (x_i, y_\sigma(i)), where x_i and y_i are arithmetic progressions and \sigma is a permutation. Garcia-Selfa and Tornero asked whether there is a bound on the length of an s.a.p. on an elliptic curve in Weierstrass form over Q. We show that 4319 is such a bound for curves over R. This is done by considering translates of the curve in a grid as a graph. A simple upper bound is found for the number of crossings and the 'crossing inequality' gives a lower bound. Together these bound the length of an s.a.p. on the curve. We then use a similar method to extend the result to arbitrary real algebraic curves. Instead of considering s.a.p.'s we consider k^2/3 points in a grid. The number of crossings is bounded by Bezout's Theorem. We then give another proof using a result of Jarnik bounding the number of grid points on a convex curve. This result applies as any real algebraic curve can be broken up into convex and concave parts, the number of which depend on the degree. Lastly, these results are extended to complex algebraic curves.Comment: 11 pages, 6 figures, order of email addresses corrected 12 pages, closing remarks, a reference and an acknowledgment adde

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 Effect of Varying the Causes of Environmental Problems on Stated WTP Values: Evidence from a Field Study

Standard applications of utility theory assume that utility depends solely on outcomes and not on causes. This study uses a field experiment conducted in the Netherlands to determine if alternative causes of an environmental problem affect willingness to pay to ameliorate it. We find evidence supporting the hypothesis that people are willing to pay significantly more to correct problems caused by humans than by nature (the ""outrage effect""), but find no support for the hypothesis that ""moral responsibility"" matters. We also find support for the hypothesis that stated willingness to pay values obtained via ""cheap talk"" and ""consequential"" treatments are lower than without inclusion of these protocols.Field experiment, endangered species, non-market valuation