Integrability as a consequence of discrete holomorphicity: the Z_N model

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

HyperGal: hyperspectral scene modeling for supernova typing with the Integral Field Spectrograph SEDmachine

Recent developments in time domain astronomy, like the Zwicky Transient Facility, have made possible a daily scan of the entire visible sky, leading to the discovery of hundreds of new transients every night. Among them, 10 to 15 are supernovae (SNe), which have to be classified prior to cosmological use. The Spectral Energy Distribution machine (SEDm), a low resolution Integral Field Spectrograph, has been designed, built, and operated to spectroscopically classify targets detected by the ZTF main camera. The current Pysedm pipeline is limited by contamination when the transient is too close to its host galaxy core; this can lead to an incorrect typing and ultimately bias the cosmological analyses, and affect the SN sample homogeneity in terms of local environment properties. We present a new scene modeler to extract the transient spectrum from its structured background, aiming at improving the typing efficiency of the SEDm. HyperGal is a fully chromatic scene modeler, which uses pre-transient photometric images to generate a hyperspectral model of the host galaxy; it is based on the CIGALE SED fitter used as a physically-motivated spectral interpolator. The galaxy model, complemented by a point source and a diffuse background component, is projected onto the SEDm spectro-spatial observation space and adjusted to observations. The full procedure is validated on 5000 simulated cubes. We introduce the contrast as the transient-to-total flux ratio at SN location. From estimated contrast distribution of real SEDm observations, we show that HyperGal correctly classifies ~95% of SNe Ia. Compared to the standard extraction method, HyperGal correctly classifies 10% more SNe Ia. The false positive rate is less than 2%, half as much as the standard extraction method. Assuming a similar contrast distribution for core-collapse SNe, HyperGal classifies 14% (11%) additional SNe II (Ibc).Comment: 14 pages, 17 figures, submitted to Astronomy & Astrophysic

Axisymmetric dynamical models for SAURON and OASIS observations of NGC3377

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

SAURON Observations of Disks in Spheroids

The panoramic integral-field spectrograph SAURON is currently being used to map the stellar kinematics, gaseous kinematics, and stellar populations of a large number of early-type galaxies and bulges. Here, we describe SAURON observations of cold stellar disks embedded in spheroids (NGC3384, NGC4459, NGC4526), we illustrate the kinematics and ionization state of large-scale gaseous disks (NGC4278, NGC7742), and we show preliminary comparisons of SAURON data with barred galaxy N-body simulations (NGC3623).Comment: 8 pages including 5 figures. To appear in Galaxies: The Third Dimension, eds. M. Rosado, L. Binnette, & L. Arias (ASP: San Francisco

SAURON: An Innovative Look at Early-Type Galaxies

A summary of the SAURON project and its current status is presented. SAURON is a panoramic integral-field spectrograph designed to study the stellar kinematics, gaseous kinematics, and stellar populations of spheroids. Here, the sample of galaxies and its properties are described. The instrument is detailed and its capabilities illustrated through observational examples. These includes results on the structure of central stellar disks, the kinematics and ionization state of gaseous disks, and the stellar populations of galaxies with decoupled cores.Comment: 10 pages, 6 figures. To appear in "The Dynamics, Structure & History of Galaxies", eds. G. S. Da Costa & E. M. Sadler (San Francisco: ASP). Version with full resolution images available at http://www.strw.leidenuniv.nl/~dynamics/Instruments/Sauron/pub_list.htm

The parafermionic observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE. We provide a definition for a one parameter family of continuum versions of the paraferminonic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of kappa. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which helps illuminate a fundamental property of the discrete observable.Comment: 29 pages, 7 figure