Searching for chemical inhomogeneities in Open Clusters: Analysis of the CN and CH Molecular Band Strengths in NGC 2158, NGC 2420, NGC 2682, NGC 7789 and Berkeley 29

Context: The total mass of a cluster, being the main parameter determining its ability to host more than one stellar generation, may constitute a threshold below which the cluster is able to form only a single stellar population. AIms: Our goal is to investigate the existence of star-to-star variations of CN and CH band strengths, related to the N and C abundances, respectively, among the stars in five open cluster (NGC 2158, NGC 2420, NGC 2682, NGC 7789 and Berkeley 29) similar to those observed in globular clusters and linked with the existence of multiple populations therein. Since these systems are less massive than globulars, our results may allow us to constrain the lower mass necessary to form more than one stellar population. Methods: We measured the strength of the CN and CH bands, which correlate with the C and N abundances, using four molecular indices in low-resolution SDSS/SEGUE spectra. Results: We found that for four of the open clusters (NGC 2158, NGC 2420, NGC 2682 and Berkeley 29) all the stars studied in each of them have similar CN and CH band strengths within the uncertainties since neither anomalous spreads nor bimodalities have been detected in their CN and CH distributions. In contrast, for NGC 7789 we found an anomalous spread in the strength of the CN molecular band at 3839 \AA which is larger than the uncertainties. However, the small number of stars studied in this cluster implies that further analysis is needed to confirm the existence of chemical inhomogeneities in this cluster.Comment: 11 pages, 9 figures, Accepted for publication in A&A, Tables 7, 8 and 9 will be publish onlin

A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation

We present results from two-dimensional numerical simulations of a supersonic turbulent flow in the plane of the galactic disk, incorporating shear, thresholded and discrete star formation (SF), self-gravity, rotation and magnetic fields. A test of the model in the linear regime supports the results of the linear theory of Elmegreen (1991). In the fully nonlinear turbulent regime, while some results of the linear theory persist, new effects also emerge. Some exclusively nonlinear effects are: a) Even though there is no dynamo in 2D, the simulations are able to maintain or increase their net magnetic energy in the presence of a seed uniform azimuthal component. b) A well-defined power-law magnetic spectrum and an inverse magnetic cascade are observed in the simulations, indicating full MHD turbulence. Thus, magnetic field energy is generated in regions of SF and cascades up to the largest scales. c) The field has a slight but noticeable tendency to be aligned with density features. d) The magnetic field prevents HII regions from expanding freely, as in the recent results of Slavin \& Cox (1993). e) A tendency to exhibit {\it less} filamentary structures at stronger values of the uniform component of the magnetic field is present in several magnetic runs. f) For fiducial values of the parameters, the flow in general appears to be in rough equipartition between magnetic and kinetic energy. There is no clear domination of either the magnetic or the inertial forces. g) A median value of the magnetic field strength within clouds is $\sim 12\mu$G, while for the intercloud medium a value of $\sim 3\mu$G is found. Maximum contrasts of up to a factor of $\sim 10$ are observed.Comment: Plain TeX file, 25 pages. Gzipped, tarred set of Tex file plus 17 figures and 3 tables (Postscript) available at ftp://kepler.astroscu.unam.mx/incoming/enro/papers/mhdgturb.tar.g

Highly Compressible MHD Turbulence and Gravitational Collapse

We investigate the properties of highly compressible turbulence and its ability to produce self-gravitating structures. The compressibility is parameterized by an effective polytropic exponent gama-eff. In the limit of small gama-eff, the density jump at shocks is shown to be of the order of e^{M^2}, and the production of vorticity by the nonlinear terms appears to be negligible. In the presence of self-gravity, we suggest that turbulence can produce bound structures for gama-eff < 2(1-1/n), where 'n' is the typical dimensionality of the turbulent compressions. We show, by means of numerical simulations, that, for sufficiently small gama-eff, small-scale turbulent density fluctuations eventually collapse even though the medium is globally stable. This result is preserved in the presence of a magnetic field for supercritical mass-to-flux ratios.Comment: 4 pages, 3 postscript figures. Latex, uses aipproc.sty Contribution to the Conference Proc. of the 7th Annual Astrophysics Conference in Maryland, STAR FORMATION, NEAR AND FAR, eds. Stephen S. Holt and Lee G. Mund

Perturbation theory in a pure exchange non-equilibrium economy

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the non-equilibrium theory. In particular, it is completely determined in terms of the initial conditions, and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.non-equilibrium economics; perturbation theory