Wind bubbles within H II regions around slowly moving stars

Interstellar bubbles around O stars are driven by a combination of the star's wind and ionizing radiation output. The wind contribution is uncertain because the boundary between the wind and interstellar medium is difficult to observe. Mid-infrared observations (e.g., of the H II region RCW 120) show arcs of dust emission around O stars, contained well within the H II region bubble. These arcs could indicate the edge of an asymmetric stellar wind bubble, distorted by density gradients and/or stellar motion. We present two-dimensional, radiation-hydrodynamics simulations investigating the evolution of wind bubbles and H II regions around massive stars moving through a dense (n=3000 cm^{-3}), uniform medium with velocities ranging from 4 to 16 km/s. The H II region morphology is strongly affected by stellar motion, as expected, but the wind bubble is also very aspherical from birth, even for the lowest space velocity considered. Wind bubbles do not fill their H II regions (we find filling factors of 10-20%), at least for a main sequence star with mass M~30 Msun. Furthermore, even for supersonic velocities the wind bow shock does not significantly trap the ionization front. X-ray emission from the wind bubble is soft, faint, and comes mainly from the turbulent mixing layer between the wind bubble and the H II region. The wind bubble radiates <1 per cent of its energy in X-rays; it loses most of its energy by turbulent mixing with cooler photoionized gas. Comparison of the simulations with the H II region RCW 120 shows that its dynamical age is <=0.4 Myr and that stellar motion <=4 km/s is allowed, implying that the ionizing source is unlikely to be a runaway star but more likely formed in situ. The region's youth, and apparent isolation from other O or B stars, makes it very interesting for studies of massive star formation and of initial mass functions.Comment: 14 pages, 11 figures, accepted for publication in Astronomy and Astrophysics (new version corrects an error in the simulation postprocessing, figs 6,7,11 are modified slightly, conclusions unchanged

Three results on representations of Mackey Lie algebras

I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\otimes V\to\mathbb C$ of vector spaces, the Lie algebra $\mathfrak{gl}^M=\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\subseteq V^*$. In their work, the category $\mathbb{T}_{\mathfrak{gl}^M}$ of $\mathfrak{gl}^M$-modules which are finite length subquotients of the tensor algebra $T(W\otimes V)$ is singled out and studied. In this note we solve three problems posed by these authors concerning the categories $\mathbb{T}_{\mathfrak{gl}^M}$. Denoting by $\mathbb{T}_{V\otimes W}$ the category with the same objects as $\mathbb{T}_{\mathfrak{gl}^M}$ but regarded as $V\otimes W$-modules, we first show that when $W$ and $V$ are paired by dual bases, the functor $\mathbb{T}_{\mathfrak{gl}^M}\to \mathbb{T}_{V\otimes W}$ taking a module to its largest weight submodule with respect to a sufficiently nice Cartan subalgebra of $V\otimes W$ is a tensor equivalence. Secondly, we prove that when $W$ and $V$ are countable-dimensional, the objects of $\mathbb{T}_{\mathrm{End}(V)}$ have finite length as $\mathfrak{gl}^M$-modules. Finally, under the same hypotheses, we compute the socle filtration of a simple object in $\mathbb{T}_{\mathrm{End}(V)}$ as a $\mathfrak{gl}^M$-module.Comment: 9 page

On the stability of bow shocks generated by red supergiants: the case of IRC-10414

In this Letter, we explore the hypothesis that the smooth appearance of bow shocks around some red supergiants (RSGs) might be caused by the ionization of their winds by external sources of radiation. Our numerical simulations of the bow shock generated by IRC-10414 (the first-ever RSG with an optically detected bow shock) show that the ionization of the wind results in its acceleration by a factor of two, which reduces the difference between the wind and space velocities of the star and makes the contact discontinuity of the bow shock stable for a range of stellar space velocities and mass-loss rates. Our best fit model reproduces the overall shape and surface brightness of the observed bow shock and suggests that the space velocity and mass-loss rate of IRC-10414 are $\approx$50 ${\rm km} \, {\rm s}^{-1}$ and $\approx$$10^{-6}$ $M_\odot \, {\rm yr}^{-1}$, respectively, and that the number density of the local ISM is $\approx$3 ${\rm cm}^{-3}$. It also shows that the bow shock emission comes mainly from the shocked stellar wind. This naturally explains the enhanced nitrogen abundance in the line-emitting material, derived from the spectroscopy of the bow shock. We found that photoionized bow shocks are $\approx$15$-$50 times brighter in optical line emission than their neutral counterparts, from which we conclude that the bow shock of IRC-10414 must be photoionized.Comment: 5 pages, 5 figures. Accepted for publication in MNRAS Letter

Models of the circumstellar medium of evolving, massive runaway stars moving through the Galactic plane

At least 5 per cent of the massive stars are moving supersonically through the interstellar medium (ISM) and are expected to produce a stellar wind bow shock. We explore how the mass loss and space velocity of massive runaway stars affect the morphology of their bow shocks. We run two-dimensional axisymmetric hydrodynamical simulations following the evolution of the circumstellar medium of these stars in the Galactic plane from the main sequence to the red supergiant phase. We find that thermal conduction is an important process governing the shape, size and structure of the bow shocks around hot stars, and that they have an optical luminosity mainly produced by forbidden lines, e.g. [OIII]. The Ha emission of the bow shocks around hot stars originates from near their contact discontinuity. The H$\alpha$ emission of bow shocks around cool stars originates from their forward shock, and is too faint to be observed for the bow shocks that we simulate. The emission of optically-thin radiation mainly comes from the shocked ISM material. All bow shock models are brighter in the infrared, i.e. the infrared is the most appropriate waveband to search for bow shocks. Our study suggests that the infrared emission comes from near the contact discontinuity for bow shocks of hot stars and from the inner region of shocked wind for bow shocks around cool stars. We predict that, in the Galactic plane, the brightest, i.e. the most easily detectable bow shocks are produced by high-mass stars moving with small space velocities.Comment: 22 pages, 24 figure

Evidence of the inhomogeneity of the stellar population in the differentially reddened globular cluster NGC 3201

We report on evidence of the inhomogeneity (multiplicity) of the stellar population in the Galactic globular cluster (GC) NGC 3201, which is irregularly reddened across its face. We carried out a more detailed and careful analysis of our recently published new multi-color photometry in a wide field of the cluster with particular emphasis on the U band. Using the photometric data corrected for differential reddening, we found for the first time two key signs of the inhomogeneity in the cluster's stellar population and of its radial variation in the GC. These are (1) an obvious trend in the color-position diagram, based on the (U-B) color-index, of red giant branch (RGB) stars, which shows that the farther from the cluster's center, the bluer on average the (U-B) color of the stars is; and (2) the dependence of the radial distribution of sub-giant branch (SGB) stars in the cluster on their U magnitude, where brighter stars are less centrally concentrated than their fainter counterparts at a confidence level varying between 99.2% and 99.9% depending on the color-index used to select the stars. The same effects were recently found by us in the GC NGC 1261. However, contrary to NGC 1261, we are not able to unambiguously suggest which of the sub-populations of SGB/RGB stars can be the progenitor of blue and red horizontal branch stars of the cluster. Apart from M4, NGC 3201 is another GC very probably with an inhomogeneous stellar population, which has essentially lower mass than the most massive Galactic GCs where multiple stellar populations were unambiguously detected for the first timeComment: 5 pages, 4 figure

Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes

This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the peculiar algebraic role played by the degrees of Taylor jet expansions, especially the notion of minimal subtraction and oversubtractions.Comment: revised versio