Random walk loop soups and conformal loop ensembles

The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a conformally invariant Poissonian ensemble of planar loops with deep connections to conformal loop ensembles (CLEs) and the Schramm-Loewner evolution (SLE). Lawler and Trujillo Ferreras showed that, roughly speaking, in the continuum scaling limit, ``large'' lattice loops from the random walk loop soup converge to ``large'' loops from the Brownian loop soup. Their results, however, do not extend to clusters of loops, which are interesting because the connection between Brownian loop soup and CLE goes via cluster boundaries. In this paper, we study the scaling limit of clusters of ``large'' lattice loops, showing that they converge to Brownian loop soup clusters. In particular, our results imply that the collection of outer boundaries of outermost clusters composed of ``large'' lattice loops converges to CLE.Comment: 30 pages, 7 figures, to appear in Probab. Theory Related Field

Water abundance variations around high-mass protostars: HIFI observations of the DR21 region

Context. Water is a key molecule in the star formation process, but its spatial distribution in star-forming regions is not well known. Aims. We study the distribution of dust continuum and H_(2)O and ^(13)CO line emission in DR21, a luminous star-forming region with a powerful outflow and a compact H ii region. Methods. Herschel-HIFI spectra near 1100 GHz show narrow ^(13)CO 10–9 emission and H_(2)O 1_(11)–0_(00) absorption from the dense core and broad emission from the outflow in both lines. The H_(2)O line also shows absorption by a foreground cloud known from ground-based observations of low-J CO lines. Results. The dust continuum emission is extended over 36” FWHM, while the ^(13)CO and H_(2)O lines are confined to ≈24” or less. The foreground absorption appears to peak further North than the other components. Radiative transfer models indicate very low abundances of ~2×10^(-10) for H_(2)O and ~8×10^(-7) for ^(13)CO in the dense core, and higher H_(2)O abundances of ~4×10^(-9) in the foreground cloud and ~7×10^(-7) in the outflow. Conclusions. The high H_(2)O abundance in the warm outflow is probably due to the evaporation of water-rich icy grain mantles, while the H_(2)O abundance is kept down by freeze-out in the dense core and by photodissociation in the foreground cloud

Water: from clouds to planets

Results from recent space missions, in particular Spitzer and Herschel, have lead to significant progress in our understanding of the formation and transport of water from clouds to disks, planetesimals, and planets. In this review, we provide the underpinnings for the basic molecular physics and chemistry of water and outline these advances in the context of water formation in space, its transport to a forming disk, its evolution in the disk, and finally the delivery to forming terrestrial worlds and accretion by gas giants. Throughout, we pay close attention to the disposition of water as vapor or solid and whether it might be subject to processing at any stage. The context of the water in the solar system and the isotopic ratios (D/H) in various bodies are discussed as grounding data point for this evolution. Additional advances include growing knowledge of the composition of atmospheres of extra-solar gas giants, which may be influenced by the variable phases of water in the protoplanetary disk. Further, the architecture of extra-solar systems leaves strong hints of dynamical interactions, which are important for the delivery of water and subsequent evolution of planetary systems. We conclude with an exploration of water on Earth and note that all of the processes and key parameters identified here should also hold for exoplanetary systems.Comment: 24 pages, 13 figures; updated exoplanet observations references. Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin

An elementary proof of phase transition in the planar XY model

Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fr\"{o}hlich and Spencer and establishes a Berezinskii-Kosterlitz-Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers on delocalisation of integer-valued height functions, and classical correlation inequalities.Comment: 25 pages, statement of main result slightly improve

A Comprehensive Survey of Hydrogen Chloride in the Galaxy

We report new observations of the fundamental $J=1-0$ transition of HCl (at 625.918GHz) toward a sample of 25 galactic star-forming regions, molecular clouds, and evolved stars, carried out using the Caltech Submillimeter Observatory. Fourteen sources in the sample are also observed in the corresponding H\tscl\ $J=1-0$ transition (at 624.978GHz). We have obtained clear detections in all but four of the targets, often in emission. Absorptions against bright background continuum sources are also seen in nine cases, usually involving a delicate balance between emission and absorption features. From RADEX modeling, we derive gas densities and HCl column densities for sources with HCl emission. HCl is found in a wide range of environments, with gas densities ranging from $10^5$ to $10^7$~cm$^{-3}$. The HCl abundance relative to H$_2$ is in the range of $(3-30)\times10^{-10}$. Comparing with the chlorine abundance in the solar neighborhood, this corresponds to a chlorine depletion factor of up to $\sim$400, assuming that HCl accounts for one third of the total chlorine in the gas phase. The [\tfcl]/[\tscl] isotopic ratio is rather varied, from unity to $\sim$5, mostly lower than the terrestrial value of 3.1. Such variation is highly localized, and could be generated by the nucleosynthesis in supernovae, which predicts a \tscl\ deficiency in most models. The lower ratios seen in W3IRS4 and W3IRS5 likely confine the progenitors of the supernovae to stars with relatively large mass (\ga25M_\sun) and high metallicity (Z$\sim$0.02).Comment: 11 pages, 5 figures, accepted by Ap

H2CO and CH3OH maps of the Orion Bar photodissociation region

A previous analysis of methanol and formaldehyde towards the Orion Bar concluded that the two molecular species may trace different physical components, methanol the clumpy material, and formaldehyde the interclump medium. To verify this hypothesis, we performed multi-line mapping observations of the two molecules to study their spatial distributions. The observations were performed with the IRAM-30m telescope at 218 and 241 GHz, with an angular resolution of ~11''. Additional data for H2CO from the Plateau de Bure array are also discussed. The data were analysed using an LVG approach. Both molecules are detected in our single-dish data. Our data show that CH3OH peaks towards the clumps of the Bar, but its intensity decreases below the detection threshold in the interclump material. When averaging over a large region of the interclump medium, the strongest CH3OH line is detected with a peak intensity of ~0.06K. Formaldehyde also peaks on the clumps, but it is also detected in the interclump gas. We verified that the weak intensity of CH3OH in the interclump medium is not caused by the different excitation conditions of the interclump material, but reflects a decrease in the column density of methanol. The abundance of CH3OH relative to H2CO decreases by at least one order of magnitude from the dense clumps to the interclump medium.Comment: 11 pages, accepted for publication in A&

Family size and intergenerational social mobility during the fertility transition: evidence of resource dilution from the city of Antwerp in nineteenth century Belgium

It has been argued in sociology, economics, and evolutionary anthropology that family size limitation enhances the intergenerational upward mobility chances in modernized societies. If parents have a large flock, family resources get diluted and intergenerational mobility is bound to head downwards. Yet, the empirical record supporting this resource dilution hypothesis is limited. This article investigates the empirical association between family size limitation and intergenerational mobility in an urban, late nineteenth century population in Western Europe. It uses life course data from the Belgian city of Antwerp between 1846 and 1920. Findings are consistent with the resource dilution hypothesis: after controlling for confounding factors, people with many children were more likely to end up in the lower classes. Yet, family size limitation was effective as a defensive rather than an offensive strategy: it prevented the next generation from going down rather than helping them to climb up the social ladder. Also, family size appears to have been particularly relevant for the middle classes. Implications for demographic transition theory are discussed

Hydrogen Fluoride in High-Mass Star-forming Regions

Hydrogen fluoride has been established to be an excellent tracer of molecular hydrogen in diffuse clouds. In denser environments, however, the HF abundance has been shown to be approximately two orders of magnitude lower. We present Herschel/HIFI observations of HF J=1-0 toward two high-mass star formation sites, NGC6334 I and AFGL 2591. In NGC6334 I the HF line is seen in absorption in foreground clouds and the source itself, while in AFGL 2591 HF is partially in emission. We find an HF abundance with respect to H2 of 1.5e-8 in the diffuse foreground clouds, whereas in the denser parts of NGC6334 I, we derive a lower limit on the HF abundance of 5e-10. Lower HF abundances in dense clouds are most likely caused by freeze out of HF molecules onto dust grains in high-density gas. In AFGL 2591, the view of the hot core is obstructed by absorption in the massive outflow, in which HF is also very abundant 3.6e-8) due to the desorption by sputtering. These observations provide further evidence that the chemistry of interstellar fluorine is controlled by freeze out onto gas grains.Comment: accepted in Ap