Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph $G$ and the dimer model defined on a decorated version \GD of this graph \cite{Fisher}. In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain \GD_1. Our main result consists in explicitly constructing CRSFs of \GD_1 counted by the dimer characteristic polynomial, from CRSFs of $G_1$ where edges are assigned Kenyon's critical weight function \cite{Kenyon3}; thus proving a relation on the level of configurations between two well known 2-dimensional critical models.Comment: 51 pages, 24 figures. To appear, Comm. Math. Phys. Revised version: title has changed. The terminology `correspondence' has been changed to that of `explicit construction' and `mapping

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

Limit shapes for the asymmetric five vertex model

We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a positive weight. We give a variational principle for limit shapes in this setting, and show that the resulting Euler-Lagrange equation can be integrated, giving explicit limit shapes parameterized by analytic functions.Comment: 37 pages, 21 figure

Wind-accretion disks in wide binaries, second generation protoplanetary disks and accretion onto white dwarfs

Mass transfer from an evolved donor star to its binary companion is a standard feature of stellar evolution in binaries. In wide binaries, the companion star captures some of the mass ejected in a wind by the primary star. The captured material forms an accretion disk. Here, we study the evolution of wind-accretion disks, using a numerical approach which allows us to follow the long term evolution. For a broad range of initial conditions, we derive the radial density and temperature profiles of the disk. In most cases, wind-accretion leads to long-lived stable disks over the lifetime of the AGB donor star. The disks have masses of a few times 10^{-5}-10^{-3} M_sun, with surface density and temperature profiles that follow broken power-laws. The total mass in the disk scales approximately linearly with the viscosity parameter used. Roughly 50% to 80% of the mass falling into the disk accretes onto the central star; the rest flows out through the outer edge of the disk into the stellar wind of the primary. For systems with large accretion rates, the secondary accretes as much as 0.1 M_sun. When the secondary is a white dwarf, accretion naturally leads to nova and supernova eruptions. For all types of secondary star, the surface density and temperature profiles of massive disks resemble structures observed in protoplanetary disks, suggesting that coordinated observational programs might improve our understanding of uncertain disk physics.Comment: ApJ, in press. Some discussion on thermal instabilities, and different viscosities adde

An Outer Planet Beyond Pluto and Origin of the Trans-Neptunian Belt Architecture

Trans-Neptunian objects (TNOs) are remnants of a collisionally and dynamically evolved planetesimal disk in the outer solar system. This complex structure, known as the trans-Neptunian belt (or Edgeworth-Kuiper belt), can reveal important clues about disk properties, planet formation, and other evolutionary processes. In contrast to the predictions of accretion theory, TNOs exhibit surprisingly large eccentricities, e, and inclinations, i, which can be grouped into distinct dynamical classes. Several models have addressed the origin and orbital evolution of TNOs, but none have reproduced detailed observations, e.g., all dynamical classes and peculiar objects, or provided insightful predictions. Based on extensive simulations of planetesimal disks with the presence of the four giant planets and massive planetesimals, we propose that the orbital history of an outer planet with tenths of Earth's mass can explain the trans-Neptunian belt orbital structure. This massive body was likely scattered by one of the giant planets, which then stirred the primordial planetesimal disk to the levels observed at 40-50 AU and truncated it at about 48 AU before planet migration. The outer planet later acquired an inclined stable orbit (>100 AU; 20-40 deg) because of a resonant interaction with Neptune (an r:1 or r:2 resonance possibly coupled with the Kozai mechanism), guaranteeing the stability of the trans-Neptunian belt. Our model consistently reproduces the main features of each dynamical class with unprecedented detail; it also satisfies other constraints such as the current small total mass of the trans-Neptunian belt and Neptune's current orbit at 30.1 AU. We also provide observationally testable predictions.Comment: 80 pages, 24 figures, 7 tables. Accepted for publication in The Astronomical Journa

Distances on Rhombus Tilings

The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected space (a flip is the elementary operation on rhombus tilings which rotates 180{\deg} a hexagon made of three rhombi). Motivated by the study of a quasicrystal growth model, we are here interested in better understanding how "tight" rhombus tiling spaces are flip-connected. We introduce a lower bound (Hamming-distance) on the minimal number of flips to link two tilings (flip-distance), and we investigate whether it is sharp. The answer depends on the number n of different edge directions in the tiling: positive for n=3 (dimer tilings) or n=4 (octogonal tilings), but possibly negative for n=5 (decagonal tilings) or greater values of n. A standard proof is provided for the n=3 and n=4 cases, while the complexity of the n=5 case led to a computer-assisted proof (whose main result can however be easily checked by hand).Comment: 18 pages, 9 figures, submitted to Theoretical Computer Science (special issue of DGCI'09

Progress towards ultra sensitive KIDs for future far-infrared missions: a focus on recombination times

Future generations of far-infrared (FIR) telescopes will need detectors with noise-equivalent powers on the order of 5 x 10^(-20) W/Hz^(1/2) in order to be photon background limited by astrophysical sources. One such mission concept in development is the Galaxy Evolution Probe (GEP), which will characterize galaxy formation and evolution from z=0 to beyond z=4. Kinetic inductance detectors (KIDs) have been baselined for the GEP for spectroscopy and imaging science between 10 μm and 400 μm due to their intrinsic frequency multiplexability and simple readout schemes. We focus on quasiparticle recombination times as a strategy for increasing detector responsivities to move towards the NEP requirements of the GEP. We present a new model for quantifying time constants from the responses of detectors to pulses of light, and test this model on a 40 nm thick ¼ λ Al coplanar waveguide KID. We intend to use this measurement scheme to quantify the dependence of the quasiparticle recombination time on Al thickness

UV and X-Ray Monitoring of AG Draconis During the 1994/1995 Outbursts

The recent 1994-1995 active phase of AG Draconis has given us for the first time the opportunity to follow the full X-ray behaviour of a symbiotic star during two successive outbursts and to compare with its quiescence X-ray emission. With \ros observations we have discovered a remarkable decrease of the X-ray flux during both optical maxima, followed by a gradual recovering to the pre-outburst flux. In the UV the events were characterized by a large increase of the emission line and continuum fluxes, comparable to the behaviour of AG Dra during the 1980-81 active phase. The anticorrelation of X-ray/UV flux and optical brightness evolution is shown to very likely be due to a temperature decrease of the hot component. Such a temperature decrease could be produced by an increased mass transfer to the burning compact object, causing it to slowly expand to about twice its original size.Comment: 12 pages postscript incl. figures, Proc. of Workshop on Supersoft X-Ray Sources, to appear in Lecture Notes in Physics vol. 472 (1996

Castor A and Castor B resolved in a simultaneous Chandra and XMM-Newton observation

We present a simultaneous Chandra and XMM-Newton observation of the Castor sextett, focusing on Castor A and Castor B, two spectroscopic binaries with early-type primaries. Of the present day X-ray instruments only Chandra can isolate the X-ray lightcurves and spectra of A and B. We compare the Chandra observation with XMM-Newton data obtained simultaneously. Albeit not able to resolve Castor A and Castor B from each other, the higher sensitivity of XMM-Newton allows for a quantitative analysis of their combined high-resolution spectrum. He-like line triplets are used to examine the temperature and the density in the corona of Castor AB. The temporal variability of Castor AB is studied using data collected with the European Photon Imaging Camera onboard XMM-Newton. Strong flare activity is observed, and combining the data acquired simultaneously with Chandra and XMM-Newton each flare can be assigned to its host. Our comparison with the conditions of the coronal plasma of other stars shows that Castor AB behave like typical late-type coronal X-ray emitters supporting the common notion that the late-type secondaries within each spectroscopic binary are the sites of the X-ray production.Comment: accepted for publication in A&