1,937 research outputs found

    A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

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    Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is 2+2.\sqrt{2+\sqrt{2}}. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference

    Disk Heating, Galactoseismology, and the Formation of Stellar Halos

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    Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope

    CATS: The Hubble Constant from Standardized TRGB and Type Ia Supernova Measurements

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    The Tip of the Red Giant Branch (TRGB) provides a luminous standard candle for constructing distance ladders to measure the Hubble constant. In practice its measurements via edge-detection response (EDR) are complicated by the apparent fuzziness of the tip and the multi-peak landscape of the EDR. As a result, it can be difficult to replicate due to a case-by-case measurement process. Previously we optimized an unsupervised algorithm, Comparative Analysis of TRGBs (CATs), to minimize the variance among multiple halo fields per host without reliance on individualized choices, achieving state-of-the-art ∼\sim << 0.05 mag distance measures for optimal data. Further, we found an empirical correlation at 5σ\sigma confidence in the GHOSTS halo survey between our measurements of the tip and their contrast ratios (ratio of stars 0.5 mag just below and above the tip), useful for standardizing the apparent tips at different host locations. Here, we apply this algorithm to an expanded sample of SN Ia hosts to standardize these to multiple fields in the geometric anchor, NGC 4258. In concert with the Pantheon++ SN Ia sample, this analysis produces a (baseline) result of H0=73.22±2.06H_0= 73.22 \pm 2.06 km/s/Mpc. The largest difference in H0H_0 between this and similar studies employing the TRGB derives from corrections for SN survey differences and local flows used in most recent SN Ia compilations but which were absent in earlier studies. SN-related differences total ∼\sim 2.0 km/s/Mpc. A smaller share, ∼\sim 1.4 km/s/Mpc, results from the inhomogeneity of the TRGB calibration across the distance ladder. We employ a grid of 108 variants around the optimal TRGB algorithm and find the median of variants is 72.94±1.9872.94\pm1.98 km/s/Mpc with an additional uncertainty due to algorithm choices of 0.83 km/s/Mpc. None of these TRGB variants result in H0H_0 less than 71.6 km/s/Mpc.Comment: Submitted to ApJL, comments welcom

    Exploring Halo Substructure with Giant Stars. XV. Discovery of a Connection between the Monoceros Ring and the Triangulum-Andromeda Overdensity?

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    Thanks to modern sky surveys, over twenty stellar streams and overdensity structures have been discovered in the halo of the Milky Way. In this paper, we present an analysis of spectroscopic observations of individual stars from one such structure, "A13", first identified as an overdensity using the M giant catalog from the Two Micron All-Sky Survey. Our spectroscopic observations show that stars identified with A13 have a velocity dispersion of ≲\lesssim 40 km s−1\mathrm{km~s^{-1}}, implying that it is a genuine coherent structure rather than a chance super-position of random halo stars. From its position on the sky, distance (∼\sim15~kpc heliocentric), and kinematical properties, A13 is likely to be an extension of another low Galactic latitude substructure -- the Galactic Anticenter Stellar Structure (also known as the Monoceros Ring) -- towards smaller Galactic longitude and farther distance. Furthermore, the kinematics of A13 also connect it with another structure in the southern Galactic hemisphere -- the Triangulum-Andromeda overdensity. We discuss these three connected structures within the context of a previously proposed scenario that one or all of these features originate from the disk of the Milky Way.Comment: 12 pages, 9 figures. Accepted for publication in Ap

    Extinction Maps Toward The Milky Way Bulge: Two-Dimensional And Three-Dimensional Tests With APOGEE

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    Galactic interstellar extinction maps are powerful and necessary tools for Milky Way structure and stellar population analyses, particularly toward the heavily reddened bulge and in the midplane. However, due to the difficulty of obtaining reliable extinction measures and distances for a large number of stars that are independent of these maps, tests of their accuracy and systematics have been limited. Our goal is to assess a variety of photometric stellar extinction estimates, including both two-dimensional and three-dimensional extinction maps, using independent extinction measures based on a large spectroscopic sample of stars toward the Milky Way bulge. We employ stellar atmospheric parameters derived from high-resolution H-band Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectra, combined with theoretical stellar isochrones, to calculate line-of-sight extinction and distances for a sample of more than 2400 giants toward the Milky Way bulge. We compare these extinction values to those predicted by individual near-IR and near+mid-IR stellar colors, two-dimensional bulge extinction maps, and three-dimensional extinction maps. The long baseline, near+mid-IR stellar colors are, on average, the most accurate predictors of the APOGEE extinction estimates, and the two-dimensional and three-dimensional extinction maps derived from different stellar populations along different sightlines show varying degrees of reliability. We present the results of all of the comparisons and discuss reasons for the observed discrepancies. We also demonstrate how the particular stellar atmospheric models adopted can have a strong impact on this type of analysis, and discuss related caveats.NSF Astronomy & Astrophysics Postdoctoral Fellowship AST-1203017Physics Frontier Center/Joint Institute for Nuclear Astrophysics (JINA) PHY 08-22648U.S. National Science FoundationAlfred P. Sloan FoundationParticipating InstitutionsU.S. Department of Energy Office of Science ANR-12-BS05-0015-01Astronom

    Integrability as a consequence of discrete holomorphicity: the Z_N model

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    It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star-triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde

    The UT 7/8 February 2013 Sila-Nunam Mutual Event and Future Predictions

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    A superior mutual event of the Kuiper Belt binary system (79360) Sila-Nunam was observed over 15.47 h on UT 7/8 February 2013 by a coordinated effort at four different telescope facilities; it started approximately 1.5 h earlier than anticipated, the duration was approximately 9.5 h (about 10% longer than predicted), and was slightly less deep than predicted. It is the first full event observed for a comparably sized binary Kuiper Belt object. We provide predictions for future events refined by this and other partial mutual event observations obtained since the mutual event season began
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