The star cluster survivability after gas expulsion is independent of the impact of the Galactic tidal field

We study the impact of the tidal field on the survivability of star clusters following instantaneous gas expulsion. Our model clusters are formed with a centrally-peaked star-formation efficiency profile as a result of star-formation taking place with a constant efficiency per free-fall time. We define the impact of the tidal field as the ratio of the cluster half-mass radius to its Jacobi radius immediately after gas expulsion, $\lambda = r_{h}/R_{J}$. We vary $\lambda$ by varying either the Galactocentric distance, or the size (hence volume density) of star clusters. We propose a new method to measure the violent relaxation duration, in which we compare the total mass-loss rate of star clusters with their stellar evolutionary mass-loss rate. That way, we can robustly estimate the bound mass fraction of our model clusters at the end of violent relaxation. The duration of violent relaxation correlates linearly with the Jacobi radius, when considering identical clusters at different Galactocentric distances. In contrast, it is nearly constant for the solar neighbourhood clusters, slightly decreasing with $\lambda$. The violent relaxation does not last longer than 50 Myr in our simulations. Identical model clusters placed at different Galactocentric distances have the same final bound fraction, despite experiencing different impacts of the tidal field. The solar neighbourhood clusters with different densities experience only limited variations of their final bound fraction. In general, we conclude that the cluster survivability after instantaneous gas expulsion, as measured by their bound mass fraction at the end of violent relaxation, $F_{bound}$, is independent of the impact of the tidal field, $\lambda$.Comment: accepted for publication in MNRAS, 8 pages, 5 figures,3 table

Two Program Packages for Deriving Multistate-Multiregion Life Tables and Two-Sex (Female Dominant) Population Projections

This paper describes two program packages for carrying out multistate/multiregion life table analyses and a female dominant two-sex projection by states and regions. The computer programs are adaptations of those published earlier for multistate life tables (Willekens 1979b) and for multiregional population projections (Willekens and Rogers 1978). Users not familiar with all the details of the theory of multistate demography nevertheless should be able to analyze populations disaggregated by age, sex, states, and regions, using these computer programs

Effects of galaxy--satellite interactions on bar formation

Aims. We aim to show how encounters with low-mass satellite galaxies may alter the bar formation in a Milky Way-like disc galaxy. Methods. We use high-resolution N-body simulations of a disc galaxy prone to mild bar instability. For realistic initial conditions of satellites, we take advantage of cosmological simulations of Milky Way-like dark matter haloes. Results. The satellites may have a significant impact on the time of bar formation. Some runs with satellites demonstrate a delay, while others show an advancement in bar formation compared to the isolated run, with such time differences reaching $\sim$ 1 Gyr. Meanwhile, the final bar configuration, including its very appearance and the bar characteristics such as the pattern speed and the exponential growth rate of its amplitude are independent of the number of encounters and their orbits. The contribution of satellites with masses below $10^9 M_{\odot}$ is insignificant, unless their pericentre distances are small. We suggest that the encounters act indirectly via inducing perturbations across the disc that evolve to delayed waves in the central part and interfere with an emerging seed bar. The predicted effect for the present-day host galaxy is expected to be even more significant at redshifts $z \gtrsim 0.5$.Comment: 16 pages, 14 figures and 4 table

Metropolitan Growth and Population Development at a National Level

This paper demonstrates the importance of treating urban populations as heterogeneous when making national population projections. Large metropolitan areas are shown to exhibit specific patterns of migration, age composition, and fertility when compared with urban areas as a whole. It is argued that the path of demographic change at a national scale is not independent of the urbanization scenario selected, i.e., one emphasizing the expansion of large cities or, alternatively, a balanced settlement hierarchy

On the degenerated soft-mode instability

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general equation of motion the full amplitude equation is derived systematically and formulas for the dependence of the coefficients on the system parameters are obtained. We emphasise the importance of nonlinear derivative terms in the amplitude equation for the behaviour in the vicinity of the bifurcation point. Especially the numerical values of the corresponding coefficients determine the region of coexistence between the stable trivial solution and stable spatially periodic patterns. Our approach clearly shows that similar considerations fail for the case of oscillatory instabilities.Comment: 16 pages, uses iop style files, manuscript also available at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/jpa_97/ or at http://athene.fkp.physik.th-darmstadt.de/public/wolfram_publ.html. J. Phys. A in pres

Global Prospects for Population Growth and Distribution

Accurate estimates of future populations are out of reach of present techniques; the methods actually used, however they are described, are extrapolations of past trends and cannot anticipate turning points in births or other components. The present paper is no exception. It summarizes the errors of past work in the expectation that these will indicate the accuracy of the figures here contained. The method used in this paper is to suppose some year in which each country will attain bare replacement (an average of about 2.3 children per fertile couple) along with a smooth transition to that condition, and a continuance of replacement until the age distribution stabilizes and the population becomes stationary. For most countries we took the turn of the century as about the time when replacement would be reached. Estimates of population and labor force are shown by age and sex at 25 year intervals for 150 countries; groupings are given by continent and degree of development. Printouts are available showing much more detail than we have been able to publish in this working paper

Calibration of radii and masses of open clusters with a simulation

Context: A recent new approach to apply a simple dynamical mass estimate of tidally limited star clusters is based on the identification of the tidal radius in a King profile with the dynamical Jacobi radius. The application to an unbiased open cluster catalogue yields significantly higher cluster masses compared to the classical methods. Aims: We quantify the bias in the mass determination as function of projection direction and cluster age by analysing a simulated star cluster. Methods: We use direct $N$-body simulations of a star cluster including stellar evolution in an analytic Milky Way potential and apply a best fit to the projected number density of cluster stars. Results: We obtain significantly overestimated star cluster masses which depend strongly on the viewing direction. The overestimation is typically in the range of 10-50 percent and reaches a factor of 3.5 for young clusters. Mass segregation reduces the derived limiting radii systematically.Comment: 9 pages, 10+1 figures, accepted by Astronomy and Astrophysic

An Improved Method of Computing Multistate Survivorship Proportions for the Terminal Age Groups

The aging of populations is a phenomenon which has become an important research topic. Demographers, however, have given inadequate attention to the projection of the number of old people and their future age composition. This paper shows that the conventional method for estimating the survivorship proportions of the very old tends to produce misleading results with respect to the size and composition of the aged. Several alternatives are suggested here to overcome these problems. An empirical example is used to point out the problems of the conventional approach and to evaluate the suggested improvements