Inhibition of thermohaline mixing by a magnetic field in Ap star descendants: Implications for the Galactic evolution of 3He

To reconcile the measurements of 3He/H in Galactic HII regions with high values of 3He in a couple of planetary nebulae, we propose that thermohaline mixing is inhibited by a fossil magnetic field in red giant stars that are descendants of Ap stars. We examine the effect of a magnetic field on the salt-finger instability, using a local analysis. We obtain a threshold for the magnetic field of 10^4 - 10^5 Gauss, above which it inhibits thermohaline mixing in red giant stars located at or above the bump. Fields of that order are expected in the descendants of the Ap stars, taking into account the contraction of their core. We conclude that in a large fraction of the descendants of Ap stars thermohaline mixing does not occur. As a consequence these objects must produce 3He as predicted by the standard theory of stellar evolution and as observed in the planetary nebulae NGC3242 and J320. The relative number of such stars with respect to non-magnetic objects that undergo thermohaline mixing is consistent with the statistical constraint coming from observations of the carbon isotopic ratio in red giant stars. It also satisfies the Galactic requirements for the evolution of the 3He abundance.Comment: Accepted for publication in A&A Letters (Vol.476

The Electron Temperature Gradient in the Galactic Disk

We derive the electron temperature gradient in the Galactic disk using a sample of HII regions that spans Galactocentric distances 0--17 kpc. The electron temperature was calculated using high precision radio recombination line and continuum observations for more than 100 HII regions. Nebular Galactocentric distances were calculated in a consistent manner using the radial velocities measured by our radio recombination line survey. The large number of nebulae widely distributed over the Galactic disk together with the uniformity of our data provide a secure estimate of the present electron temperature gradient in the Milky Way. Because metals are the main coolants in the photoionized gas, the electron temperature along the Galactic disk should be directly related to the distribution of heavy elements in the Milky Way. Our best estimate of the electron temperature gradient is derived from a sample of 76 sources for which we have the highest quality data. The present gradient in electron temperature has a minimum at the Galactic Center and rises at a rate of 287 +/- 46 K/kpc. There are no significant variations in the value of the gradient as a function of Galactocentric radius or azimuth. The scatter we find in the HII region electron temperatures at a given Galactocentric radius is not due to observational error, but rather to intrinsic fluctuations in these temperatures which are almost certainly due to fluctuations in the nebular heavy element abundances. Comparing the HII region gradient with the much steeper gradient found for planetary nebulae suggests that the electron temperature gradient evolves with time, becoming flatter as a consequence of the chemical evolution of the Milky Way's disk.Comment: 43 pages, 9 figures (accepted for publication in the ApJ

Out-Of-Focus Holography at the Green Bank Telescope

We describe phase-retrieval holography measurements of the 100-m diameter Green Bank Telescope using astronomical sources and an astronomical receiver operating at a wavelength of 7 mm. We use the technique with parameterization of the aperture in terms of Zernike polynomials and employing a large defocus, as described by Nikolic, Hills & Richer (2006). Individual measurements take around 25 minutes and from the resulting beam maps (which have peak signal to noise ratios of 200:1) we show that it is possible to produce low-resolution maps of the wavefront errors with accuracy around a hundredth of a wavelength. Using such measurements over a wide range of elevations, we have calculated a model for the wavefront-errors due to the uncompensated gravitational deformation of the telescope. This model produces a significant improvement at low elevations, where these errors are expected to be the largest; after applying the model, the aperture efficiency is largely independent of elevation. We have also demonstrated that the technique can be used to measure and largely correct for thermal deformations of the antenna, which often exceed the uncompensated gravitational deformations during daytime observing. We conclude that the aberrations induced by gravity and thermal effects are large-scale and the technique used here is particularly suitable for measuring such deformations in large millimetre wave radio telescopes.Comment: 10 pages, 7 figures (accepted by Astronomy & Astrophysics

Effects of thermohaline instability and rotation-induced mixing on the evolution of light elements in the Galaxy : D, 3He and 4He

Recent studies of low- and intermediate-mass stars show that the evolution of the chemical elements in these stars is very different from that proposed by standard stellar models. Rotation-induced mixing modifies the internal chemical structure of main sequence stars, although its signatures are revealed only later in the evolution when the first dredge-up occurs. Thermohaline mixing is likely the dominating process that governs the photospheric composition of low-mass red giant branch stars and has been shown to drastically reduce the net 3He production in these stars. The predictions of these new stellar models need to be tested against galaxy evolution. In particular, the resulting evolution of the light elements D, 3He and 4He should be compared with their primordial values inferred from the Wilkinson Microwave Anisotropy Probe data and with the abundances derived from observations of different Galactic regions. We study the effects of thermohaline mixing and rotation-induced mixing on the evolution of the light elements in the Milky Way. We compute Galactic evolutionary models including new yields from stellar models computed with thermohaline instability and rotation-induced mixing. We discuss the effects of these important physical processes acting in stars on the evolution of the light elements D, 3He, and 4He in the Galaxy. Galactic chemical evolution models computed with stellar yields including thermohaline mixing and rotation fit better observations of 3He and 4He in the Galaxy than models computed with standard stellar yields. The inclusion of thermohaline mixing in stellar models provides a solution to the long-standing "3He problem" on a Galactic scale. Stellar models including rotation-induced mixing and thermohaline instability reproduce also the observations of D and 4He.Comment: 12 pages, 9 figures, accepted for publication in A&

Thermohaline Mixing and its Role in the Evolution of Carbon and Nitrogen Abundances in Globular Cluster Red Giants: The Test Case of Messier 3

We review the observational evidence for extra mixing in stars on the red giant branch (RGB) and discuss why thermohaline mixing is a strong candidate mechanism. We recall the simple phenomenological description of thermohaline mixing, and aspects of mixing in stars in general. We use observations of M3 to constrain the form of the thermohaline diffusion coefficient and any associated free parameters. This is done by matching [C/Fe] and [N/Fe] along the RGB of M3. After taking into account a presumed initial primordial bimodality of [C/Fe] in the CN-weak and CN-strong stars our thermohaline mixing models can explain the full spread of [C/Fe]. Thermohaline mixing can produce a significant change in [N/Fe] as a function of absolute magnitude on the RGB for initially CN-weak stars, but not for initially CN-strong stars, which have so much nitrogen to begin with that any extra mixing does not significantly affect the surface nitrogen composition.Comment: 33 Pages, 10 Figures. Accepted for publication in The Astrophysical Journa

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Thermohaline instability and rotation-induced mixing. I - Low- and intermediate-mass solar metallicity stars up to the end of the AGB

(abridged) Numerous spectroscopic observations provide compelling evidence for non-canonical processes that modify the surface abundances of low- and intermediate-mass stars beyond the predictions of standard stellar theory. We study the effects of thermohaline instability and rotation-induced mixing in the 1-4 Msun range at solar metallicity. We present evolutionary models by considering both thermohaline and rotation-induced mixing in stellar interior. We discuss the effects of these processes on the chemical properties of stars from the zero age main sequence up to the end of the second dredge-up on the early-AGB for intermediate-mass stars and up to the AGB tip for low-mass stars. Model predictions are compared to observational data for lithium,12C/13C,[N/C],[Na/Fe],16O/17O, and 16O/18O in Galactic open clusters and in field stars with well-defined evolutionary status,as well as in planetary nebulae. Thermohaline mixing simultaneously accounts for the observed behaviour of 12C/13C,[N/C], and lithium in low-mass stars that are more luminous than the RGB bump, and its efficiency is increasing with decreasing initial stellar mass. On the TP-AGB,thermohaline mixing leads to lithium production, although the 7Li yields remain negative. Although the 3He stellar yields are much reduced thanks to this process, we find that solar-metallicity, low-mass stars remain net 3He producers. Rotation-induced mixing is found to change the stellar structure so that in the mass range between \sim 1.5 and 2.2 Msun the thermohaline instability occurs earlier on the red giant branch than in non-rotating models. Finally rotation accounts for the observed star-to-star abundance variations at a given evolutionary status, and is necessary to explain the features of CN-processed material in intermediate-mass stars.Comment: 18 pages, 22 figures, accepted for publication in A&

Stability conditions and Stokes factors

Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce.Comment: Very minor changes. Final version. To appear in Inventione

Microbial Community Structure of Leaf-Cutter Ant Fungus Gardens and Refuse Dumps

BACKGROUND: Leaf-cutter ants use fresh plant material to grow a mutualistic fungus that serves as the ants' primary food source. Within fungus gardens, various plant compounds are metabolized and transformed into nutrients suitable for ant consumption. This symbiotic association produces a large amount of refuse consisting primarily of partly degraded plant material. A leaf-cutter ant colony is thus divided into two spatially and chemically distinct environments that together represent a plant biomass degradation gradient. Little is known about the microbial community structure in gardens and dumps or variation between lab and field colonies. METHODOLOGY/PRINCIPAL FINDINGS: Using microbial membrane lipid analysis and a variety of community metrics, we assessed and compared the microbiota of fungus gardens and refuse dumps from both laboratory-maintained and field-collected colonies. We found that gardens contained a diverse and consistent community of microbes, dominated by Gram-negative bacteria, particularly gamma-Proteobacteria and Bacteroidetes. These findings were consistent across lab and field gardens, as well as host ant taxa. In contrast, dumps were enriched for Gram-positive and anaerobic bacteria. Broad-scale clustering analyses revealed that community relatedness between samples reflected system component (gardens/dumps) rather than colony source (lab/field). At finer scales samples clustered according to colony source. CONCLUSIONS/SIGNIFICANCE: Here we report the first comparative analysis of the microbiota from leaf-cutter ant colonies. Our work reveals the presence of two distinct communities: one in the fungus garden and the other in the refuse dump. Though we find some effect of colony source on community structure, our data indicate the presence of consistently associated microbes within gardens and dumps. Substrate composition and system component appear to be the most important factor in structuring the microbial communities. These results thus suggest that resident communities are shaped by the plant degradation gradient created by ant behavior, specifically their fungiculture and waste management

Rank rigidity for CAT(0) cube complexes

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits Alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.Comment: 39 pages, 4 figures. Revised version according to referee repor