Filamentary structure in the Orion molecular cloud

A large scale 13CO map (containing 33,000 spectra) of the giant molecular cloud located in the southern part of Orion is presented which contains the Orion Nebula, NGC1977, and the LI641 dark cloud complex. The overall structure of the cloud is filamentary, with individual features having a length up to 40 times their width. This morphology may result from the effects of star formation in the region or embedded magnetic fields in the cloud. We suggest a simple picture for the evolution of the Orion-A cloud and the formation of the major filament. A rotating proto-cloud (counter rotating with respect to the galaxy) contians a b-field aligned with the galaxtic plane. The northern protion of this cloud collapsed first, perhaps triggered by the pressure of the Ori I OB association. The magnetic field combined with the anisotropic pressure produced by the OB-association breaks the symmetry of the pancake instability, a filament rather than a disc is produced. The growth of instabilities in the filament formed sub-condensations which are recent sites of star formation

Model calculations for diffuse molecular clouds

A steady state isobaric cloud model is developed. The pressure, thermal, electrical, and chemical balance equations are solved simultaneously with a simple one dimensional approximation to the equation of radiative transfer appropriate to diffuse clouds. Cooling is mainly by CII fine structure transitions, and a variety of heating mechanisms are considered. Particular attention is given to the abundance variation of H2. Inhomogeneous density distributions are obtained because of the attenuation of the interstellar UV field and the conversion from atomic to molecular hyrodgen. The effects of changing the model parameters are described and the applicability of the model to OAO-3 observations is discussed. Good qualitative agreement with the fractional H2 abundance determinations has been obtained. The observed kinetic temperatures near 80 K can also be achieved by grain photoelectron heating. The problem of the electron density is solved taking special account of the various hydrogen ions as well as heavier ones

The metallicity dependence of envelope inflation in massive stars

Recently it has been found that models of massive stars reach the Eddington limit in their interior, which leads to dilute extended envelopes. We perform a comparative study of the envelope properties of massive stars at different metallicities, with the aim to establish the impact of the stellar metallicity on the effect of envelope inflation. We analyse published grids of core-hydrogen burning massive star models computed with metallicities appropriate for massive stars in the Milky Way, the LMC and the SMC, the very metal poor dwarf galaxy I Zwicky 18, and for metal-free chemical composition. Stellar models of all the investigated metallicities reach and exceed the Eddington limit in their interior, aided by the opacity peaks of iron, helium and hydrogen, and consequently develop inflated envelopes. Envelope inflation leads to a redward bending of the zero-age main sequence and a broadening of the main sequence band in the upper part of the Hertzsprung-Russell diagram. We derive the limiting L/M-values as function of the stellar surface temperature above which inflation occurs, and find them to be larger for lower metallicity. While Galactic models show inflation above ~29 Msun, the corresponding mass limit for Population III stars is ~150 Msun. While the masses of the inflated envelopes are generally small, we find that they can reach 1-100 Msun in models with effective temperatures below ~8000 K, with higher masses reached by models of lower metallicity. Envelope inflation is expected to occur in sufficiently massive stars at all metallicities, and is expected to lead to rapidly growing pulsations, high macroturbulent velocities, and might well be related to the unexplained variability observed in Luminous Blue Variables like S Doradus and Eta Carina.Comment: 16 pages (with Appendix), accepted in A&

Minimum free-energy path of homogenous nucleation from the phase-field equation

The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy path (MFEP) of homogeneous nucleation. We use a simple square-gradient free-energy functional with a quartic local free-energy function as an example and study the time evolution of a single nucleus placed within a metastable environment. The time integration of the phase-field equation is performed using the numerically efficient cell-dynamics method. By monitoring the evolution of the size of the nucleus and the free energy of the system simultaneously, we can easily deduce the free-energy barrier as a function of the size of the sub- and the super-critical nucleus along the MFEP.Comment: 8 pages, 5 figures, Journal of Chemical Physics accepted for publicatio

Electron and ion densities in interstellar clouds

A quantitative theory of ionization in diffuse clouds is developed which includes H(+) charge exchange with O. Dissociative charge exchange of He(+) with H2 plays an important role in the densities of H(+) and He(+). The abundance of HD is also discussed

Hamiltonians for curves

We examine the equilibrium conditions of a curve in space when a local energy penalty is associated with its extrinsic geometrical state characterized by its curvature and torsion. To do this we tailor the theory of deformations to the Frenet-Serret frame of the curve. The Euler-Lagrange equations describing equilibrium are obtained; Noether's theorem is exploited to identify the constants of integration of these equations as the Casimirs of the euclidean group in three dimensions. While this system appears not to be integrable in general, it {\it is} in various limits of interest. Let the energy density be given as some function of the curvature and torsion, $f(\kappa,\tau)$. If $f$ is a linear function of either of its arguments but otherwise arbitrary, we claim that the first integral associated with rotational invariance permits the torsion $\tau$ to be expressed as the solution of an algebraic equation in terms of the bending curvature, $\kappa$. The first integral associated with translational invariance can then be cast as a quadrature for $\kappa$ or for $\tau$.Comment: 17 page

Simply connected projective manifolds in characteristic p>0p>0 have no nontrivial stratified bundles

We show that simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker. The proof uses Hrushovski's theorem on periodic points.Comment: 16 pages. Revised version contains a more general theorem on torsion points on moduli, together with an illustration in rank 2 due to M. Raynaud. Reference added. Last version has some typos corrected. Appears in Invent.math