Spectral Types of Field and Cluster O-Stars

The recent catalog of spectral types of Galactic O-type stars by Mai'z-Apella'niz et al. has been used to study the differences between the frequencies of various subtypes of O-type stars in the field, in OB associations and among runaway stars. At a high level of statistical significance the data show that O-stars in clusters and associations have earlier types (and hence presumably larger masses and/or younger ages) than those that are situated in the general field. Furthermore it is found that the distribution of spectral subtypes among runaway O-stars is indistinguishable from that among field stars, and differs significantly from that of the O-type stars that are situated in clusters and associations. The difference is in the sense that runaway O-stars, on average, have later subtypes than do those that are still located in clusters and associations.Comment: To be published in the October 2004 issue of the Astronomical Journal Included Figure 1, page

Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure

Hochschild cohomology for Lie algebroids

We define the Hochschild (co)homology of a ringed space relative to a locally free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an algebraic variety. We show that our (co)homology groups can be computed using suitable standard complexes. Our formulae depend on certain natural structures on jetbundles over Lie algebroids. In an appendix we explain this by showing that such jetbundles are formal groupoids which serve as the formal exponentiation of the Lie algebroid.Comment: The authors were informed that the fact that jetbundles are formal groupoids is already contained in arXiv:0904.4736 (with a somewhat different proof

The Expansion Center and Dynamical Age of the Galactic Supernova Remnant Cassiopeia A

We present proper motions for 21 bright main shell and 17 faint, higher-velocity, outer ejecta knots in the Cas A supernova remnant and use them to derive new estimates for the remnant's expansion center and age. Our study included 1951 - 1976 Palomar 5 m prime focus plates, 1988 - 1999 CCD images from the KPNO 4 m and MDM 2.4 m telescopes, and 1999 HST WFPC2 images. Measurable positions covered a 23 to 41 yr time span for most knots, with a few outer knots followed for almost 48 yr. We derive an expansion center of alpha = 23h 23m 27s.77 +- 0s.05, delta = 58d 48' 49".4 +- 0".4 (ICRS), with little difference between centers derived using outer or main shell knots. This position is 3.0 arcsec due north of that estimated by van den Bergh and Kamper (1983). It also lies 6.6 +- 1.5 arcsec almost due north (PA = 354 deg) of the remnant's recently-detected central X-ray point source, implying a transverse velocity for the X-ray point source of about 330 km/s at a distance of 3.4 kpc. Using the knots which lie out ahead of the remnant's forward blast wave, we estimate a knot convergent date of A.D. 1671.3 +- 0.9, assuming no deceleration. However, a deceleration of just approximately 1.6 km/(s yr) over a 300 yr time span would produce an explosion date A.D. 1680, consistent with the suspected sighting of the Cas A supernova by J. Flamsteed.Comment: Astron. Journal in press, sched. July 2001. AASTex5, 17 pages, 2 jpeg greyscale figures, 3 postscript figure

The Stellar Mass Spectrum in the Young Populous Cluster NGC 1866

The young populous cluster NGC 1866 in the Large Magellanic Cloud LMC), which is probably one of the most massive object formed in the LMC during the last ~ 3 Gyr, appears to have an unexpectedly high mass-to-light ratio. From its velocity dispersion Fischer et al. (1992) find its mass to be (1.35 " 0.25) x 105 Mu. The luminosity of this cluster is MV = -8.93 " 0.13, corresponding to LV = (3.2 " 0.4) x 105 LV (u). This yields M/LV = 0.42 " 0.09 in solar units. For a cluster of age 0.1 Gyr such a relatively high mass-to-light ratio requires a mass spectrum with an exponent x = 1.72 " 0.09; or x = 1.75 " 0.09 if mass loss by evolving stars is taken into account.Comment: To be published in the October 1999 issue of the Publications of the Astronomical Society of the Pacifi

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.Comment: 9 page

Diameters of Open Star Clusters

The present paper presents a tabulation of data on all 600 Galactic open clusters for which it is presently possible to calculate linear diameters. As expected, the youngest `clusters' with ages < 15 Myr, contain a significant (greater than or equal to 20%) admixture of associations. Among intermediate-age clusters, with ages in the range 15 Myr to 1.5 Gyr, the median cluster diameter is found to increase with age. Small compact clusters are rare among objects with ages > 1.5 Gyr. Open clusters with ages > 1 Gyr appear to form what might be termed a `cluster thick disk', part of which consistst of objects that were probably captured gravitationally by the main body of the Galaxy.Comment: Astronomical Journal, in pres

Spatial Evolution of Social Norms in a Common-Pool Resource Game

We study the conditions for the emergence of cooperation in a spatial common-pool resource game. We consider three types of agents: cooperators, defectors and enforcers. The role of enforcers is to punish defectors for overharvesting the resource. Agents are located around a circle and they only observe the actions of their two nearest neighbors. Their payoffs are determined by both local and global interactions and they modify their actions by imitating the strategy in their neighborhood with the highest payoffs on average. Using theoretical and numerical analysis, we find that a large diversity of equilibria exists in this game. In particular, we derive conditions for the occurrence of equilibria in which the three strategies coexist. We also discuss the stability of these equilibria. Finally, we show that introducing resource dynamics favors the occurrence of cooperative equilibria.Common property, Evolutionary game theory, Local interactions game, Self-organization, Cooperation

Local and Global Interactions in an Evolutionary Resource Game

Conditions for the emergence of cooperation in a spatial common-pool resource game are studied. This combines in a unique way local and global interactions. A fixed number of harvesters are located on a spatial grid. Harvesters choose among three strategies: defection, cooperation, and enforcement. Individual payoffs are affected by both global factors, namely, aggregate harvest and resource stock level, and local factors, such as the imposition of sanctions on neighbors by enforcers. The evolution of strategies in the population is driven by social learning through imitation. Numerous types of equilibria exist in these settings. An important new finding is that clusters of cooperators and enforcers can survive among large groups of defectors. We discuss how the results contrast with the non-spatial, but otherwise similar, game of Sethi and Somanathan (1996).Common property, Cooperation, Evolutionary game theory, Global interactions, Local interactions, Social norms