On geometry of fronts in wave propagations

We give a geometric description of (wave) fronts in wave propagation processes. The concrete form of the defining function of a wave front issuing from the initial algebraic variety is obtained with the aid of the Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagation on the plane, we get restrictions on the types of possible cusps that can appear on the wave front

Period integrals associated to an affine Delsarte type hypersurface

We calculate the period integrals for a special class of affine hypersurfaces (deformed Delsarte hypersurfaces) in an algebraic torus by the aid of their Mellin transforms. A description of the relation between poles of Mellin transforms of period integrals and the mixed Hodge structure of the cohomology of the hypersurface is given. By interpreting the period integrals as solutions to Pochhammer hypergeometric differential equation, we calculate concretely the irreducible monodromy group of period integrals that correspond to the compactification of the affine hypersurface in a complete simplicial toric variety. As an application of the equivalence between oscillating integral for Delsarte polynomial and quantum cohomology of a weighted projective space $\mathbb{P}_{\bf B}$, we establish an equality between its Stokes matrix and the Gram matrix of the full exceptional collection on $\mathbb{P}_{\bf B}$

Stokes matrices for the quantum differential equations of some Fano varieties

The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's conjecture for projective spaces. The same method yields explicit formulas for the Stokes matrices of the quantum differential equations of smooth Fano hypersurfaces in projective n-space and for weighted projective spaces.Comment: 20 pages. Introduction has been changed. Small corrections in the tex

The AKARI/IRC Mid-Infrared All-Sky Survey

Context : AKARI is the first Japanese astronomical satellite dedicated to infrar ed astronomy. One of the main purposes of AKARI is the all-sky survey performed with six infrared bands between 9 and 200um during the period from 2006 May 6 to 2007 August 28. In this paper, we present the mid-infrared part (9um and 18um b ands) of the survey carried out with one of the on-board instruments, the Infrar ed Camera (IRC). Aims : We present unprecedented observational results of the 9 and 18um AKARI al l-sky survey and detail the operation and data processing leading to the point s ource detection and measurements. Methods : The raw data are processed to produce small images for every scan and point sources candidates, above the 5-sigma noise level per single scan, are der ived. The celestial coordinates and fluxes of the events are determined statisti cally and the reliability of their detections is secured through multiple detect ions of the same source within milli-seconds, hours, and months from each other. Results : The sky coverage is more than 90% for both bands. A total of 877,091 s ources (851,189 for 9um, 195,893 for 18um) are confirmed and included in the cur rent release of the point source catalogue. The detection limit for point source s is 50mJy and 90mJy for the 9um and 18um bands, respectively. The position accu racy is estimated to be better than 2". Uncertainties in the in-flight absolute flux calibration are estimated to be 3% for the 9um band and 4% for the 18um ban d. The coordinates and fluxes of detected sources in this survey are also compar ed with those of the IRAS survey and found to be statistically consistent.Comment: Accepted for publication in AandA AKARI special issu

AKARI's infrared view on nearby stars : Using AKARI Infrared Camera All-Sky Survey, 2MASS, and Hipparcos catalog

--Results-- We found that the (B-V) v.s. (V-S9W) color-color diagram is useful to identify the stars with infrared excess emerged from circumstellar envelopes/disks. Be stars with infrared excess are well separated from other types of stars in this diagram. Whereas (J-L18W) v.s. (S9W-L18W) diagram is a powerful tool to classify several object-types. Carbon-rich asymptotic giant branch (AGB) stars and OH/IR stars form distinct sequences in this color-color diagram. Young stellar objects (YSOs), pre-main sequence (PMS) stars, post-AGB stars and planetary nebulae (PNe) have largest mid-infrared color-excess, and can be identified in infrared catalog. Finally, we plot L18W v.s. (S9W-L18W) color-magnitude diagram, using the AKARI data together with Hipparcos parallaxes. This diagram can be used to identify low-mass YSOs, as well as AGB stars. We found that this diagram is comparable to the [24] vs ([8.0]-[24]) diagram of Large Magellanic Cloud sources using the Spitzer Space Telescope data. Our understanding of Galactic objects will be used to interpret color-magnitude diagram of stellar populations in nearby galaxies which Spitzer Space Telescope has observed. --Conclusions-- Our study of the AKARI color-color and color-magnitude will be used to explore properties of unknown objects in future. In addition, our analysis highlights a future key project to understand stellar evolution with circumstellar envelope, once the forthcoming astronometrical data with GAIA are available.Comment: 14 pages, 11 figures, accepted for publication in A&A. High resolution version is available at: http://www.ir.isas.jaxa.jp/%7Eyita/allsky20100302.pdf (26Mb

The Peculiar Type Ib Supernova 2006jc: A WCO Wolf-Rayet Star Explosion

We present a theoretical model for Type Ib supernova (SN) 2006jc. We calculate the evolution of the progenitor star, hydrodynamics and nucleosynthesis of the SN explosion, and the SN bolometric light curve (LC). The synthetic bolometric LC is compared with the observed bolometric LC constructed by integrating the UV, optical, near-infrared (NIR), and mid-infrared (MIR) fluxes. The progenitor is assumed to be as massive as $40M_\odot$ on the zero-age main-sequence. The star undergoes extensive mass loss to reduce its mass down to as small as $6.9M_\odot$, thus becoming a WCO Wolf-Rayet star. The WCO star model has a thick carbon-rich layer, in which amorphous carbon grains can be formed. This could explain the NIR brightening and the dust feature seen in the MIR spectrum. We suggest that the progenitor of SN 2006jc is a WCO Wolf-Rayet star having undergone strong mass loss and such massive stars are the important sites of dust formation. We derive the parameters of the explosion model in order to reproduce the bolometric LC of SN 2006jc by the radioactive decays: the ejecta mass $4.9M_\odot$, hypernova-like explosion energy $10^{52}$ ergs, and ejected $^{56}$Ni mass $0.22M_\odot$. We also calculate the circumstellar interaction and find that a CSM with a flat density structure is required to reproduce the X-ray LC of SN 2006jc. This suggests a drastic change of the mass-loss rate and/or the wind velocity that is consistent with the past luminous blue variable (LBV)-like event.Comment: 12 pages, 11 figures. Accepted for publication in the Astrophysical Journa

Star-galaxy separation in the AKARI NEP Deep Field

Context: It is crucial to develop a method for classifying objects detected in deep surveys at infrared wavelengths. We specifically need a method to separate galaxies from stars using only the infrared information to study the properties of galaxies, e.g., to estimate the angular correlation function, without introducing any additional bias. Aims. We aim to separate stars and galaxies in the data from the AKARI North Ecliptic Pole (NEP) Deep survey collected in nine AKARI / IRC bands from 2 to 24 {\mu}m that cover the near- and mid-infrared wavelengths (hereafter NIR and MIR). We plan to estimate the correlation function for NIR and MIR galaxies from a sample selected according to our criteria in future research. Methods: We used support vector machines (SVM) to study the distribution of stars and galaxies in the AKARIs multicolor space. We defined the training samples of these objects by calculating their infrared stellarity parameter (sgc). We created the most efficient classifier and then tested it on the whole sample. We confirmed the developed separation with auxiliary optical data obtained by the Subaru telescope and by creating Euclidean normalized number count plots. Results: We obtain a 90% accuracy in pinpointing galaxies and 98% accuracy for stars in infrared multicolor space with the infrared SVM classifier. The source counts and comparison with the optical data (with a consistency of 65% for selecting stars and 96% for galaxies) confirm that our star/galaxy separation methods are reliable. Conclusions: The infrared classifier derived with the SVM method based on infrared sgc- selected training samples proves to be very efficient and accurate in selecting stars and galaxies in deep surveys at infrared wavelengths carried out without any previous target object selection.Comment: 8 pages, 8 figure