The classification of two-loop integrand basis in pure four-dimension

In this paper, we have made the attempt to classify the integrand basis of all two-loop diagrams in pure four-dimension space-time. Our classification includes the topology of two-loop diagrams which determines the structure of denominators, and the set of numerators under different kinematic configurations of external momenta by using Gr\"{o}bner basis method. In our study, the variety defined by setting all propagators to on-shell has played an important role. We discuss the structure of variety and how it splits to various irreducible branches when external momenta at each corner of diagrams satisfy some special kinematic conditions. This information is crucial to the numerical or analytical fitting of coefficients for integrand basis in reduction process.Comment: 52 pages, 9 figures. v2 reference added, v3 published versio

The VMC survey III : Mass-loss rates and luminosities of LMC AGB stars

Context. Asymptotic giant branch (AGB) stars are major contributors to both the chemical enrichment of the interstellar medium and the integrated light of galaxies. Despite its importance, the AGB is one of the least understood phases of stellar evolution. The main difficulties associated with detailed modelling of the AGB are related to the mass-loss process and the 3rd dredge-up efficiency Aims. We provide direct measures of mass-loss rates and luminosities for a complete sample of AGB stars in the Large Magellanic Cloud, disentangling the C- and O-rich stellar populations. Methods. Dust radiative transfer models are presented for all 374 AGB stars candidates in one of the fields observed by the new VISTA survey of the Magellanic Clouds (VMC). Mass-loss rates, luminosities and a classification of C-and O-rich stars are derived by fitting the models to the spectral energy distribution (SED) obtained by combining VMC data with existing optical, near-, and mid-infrared photometry. Results. The classification technique is reliable at a level of - at worst -75% and significantly better for the reddest dusty stars. We classified none of the stars with a relevant mass-loss rate as O-rich, and we can exclude the presence of more than one dusty O-rich star at a similar to 94% level. The bolometric luminosity function we obtained is fully consistent with most of the literature data on the LMC and with the prediction of theoretical models, with a peak of the C-star distribution at M-bol similar or equal to -4.8 mag and no stars brighter than the classical AGB tip, at M-bol = -7.1 mag. Conclusions. This exploratory study shows that our method provides reliable mass-loss rates, luminosities and chemical classifications for all AGB stars. These results offer already important constraints to AGB evolutionary models. Most of our conclusions, especially for the rarer dust-enshrouded extreme AGB stars, are however strongly limited by the relatively small area covered by our study. Forthcoming VMC observations will easily remove this limitation.Peer reviewe

Modelling the alumina abundance of oxygen-rich evolved stars in the Large Magellanic Cloud

In order to determine the composition of the dust in the circumstellar envelopes of oxygen-rich asymptotic giant branch (AGB) stars we have computed a grid of modust radiative-transfer models for a range of dust compositions, mass-loss rates, dust shell inner radii and stellar parameters. We compare the resulting colours with the observed oxygen-rich AGB stars from the SAGE-Spec Large Magellanic Cloud (LMC) sample, finding good overall agreement for stars with a mid-infrared excess. We use these models to fit a sample of 37 O-rich AGB stars in the LMC with optically thin circumstellar envelopes, for which 5$-$35-$\mu$m Spitzer infrared spectrograph (IRS) spectra and broadband photometry from the optical to the mid-infrared are available. From the modelling, we find mass-loss rates in the range $\sim 8\times10^{-8}$ to $5\times10^{-6}$ M$_{\odot}\ \mathrm{yr}^{-1}$, and we show that a grain mixture consisting primarily of amorphous silicates, with contributions from amorphous alumina and metallic iron provides a good fit to the observed spectra. Furthermore, we show from dust models that the AKARI [11]$-$[15] versus [3.2]$-$[7] colour-colour diagram, is able to determine the fractional abundance of alumina in O-rich AGB stars.Comment: 22 pages, 17 figures, accepted MNRA

An Algebraic Pairing Model with Sp(4) Symmetry and its Deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+ ground states, they also have a large effect on the energies of excited states, including especially excited 0^+ states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp_{(q)}(4) to different realizations of u_{(q)}(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0^{+} states of even-even and odd-odd nuclei in the 1d_{3/2}, 1f_{7/2}, and 1f_{5/2}2p_{1/2}2p_{3/2}1g_{9/2} shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp_{q}(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0^{+} energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.Comment: 19 pages, 5 figures minor changes; improvements to achieve a better and clearer presentation of our messages and idea

The population of SNe/SNRs in the starburst galaxy Arp 220. A self-consistent analysis of 20 years of VLBI monitoring

The nearby ultra-luminous infrared galaxy (ULIRG) Arp 220 is an excellent laboratory for studies of extreme astrophysical environments. For 20 years, Very Long Baseline Interferometry (VLBI) has been used to monitor a population of compact sources thought to be supernovae (SNe), supernova remnants (SNRs) and possibly active galactic nuclei (AGNs). Using new and archival VLBI data spanning 20 years, we obtain 23 high-resolution radio images of Arp 220 at wavelengths from 18 cm to 2 cm. From model-fitting to the images we obtain estimates of flux densities and sizes of all detected sources. We detect radio continuum emission from 97 compact sources and present flux densities and sizes for all analysed observation epochs. We find evidence for a LD-relation within Arp 220, with larger sources being less luminous. We find a compact source LF $n(L)\propto L^\beta$ with $\beta=-2.19\pm0.15$, similar to SNRs in normal galaxies. Based on simulations we argue that there are many relatively large and weak sources below our detection threshold. The observations can be explained by a mixed population of SNe and SNRs, where the former expand in a dense circumstellar medium (CSM) and the latter interact with the surrounding interstellar medium (ISM). Nine sources are likely luminous, type IIn SNe. This number of luminous SNe correspond to few percent of the total number of SNe in Arp 220 which is consistent with a total SN-rate of 4 yr$^{-1}$ as inferred from the total radio emission given a normal stellar initial mass function (IMF). Based on the fitted luminosity function, we argue that emission from all compact sources, also below our detection threshold, make up at most 20\% of the total radio emission at GHz frequencies.Comment: Accepted for publication in Astronomy and Astrophysic

Imaging the asymmetric dust shell around CI Cam with long baseline optical interferometry

We present the first high angular resolution observation of the B[e] star/X-ray transient object CI Cam, performed with the two-telescope Infrared Optical Telescope Array (IOTA), its upgraded three-telescope version (IOTA3T) and the Palomar Testbed Interferometer (PTI). Visibilities and closure phases were obtained using the IONIC-3 integrated optics beam combiner. CI Cam was observed in the near-infrared H and K spectral bands, wavelengths well suited to measure the size and study the geometry of the hot dust surrounding CI Cam. The analysis of the visibility data over an 8 year period from soon after the 1998 outburst to 2006 shows that the dust visibility has not changed over the years. The visibility data shows that CI Cam is elongated which confirms the disc-shape of the circumstellar environment and totally rules out the hypothesis of a spherical dust shell. Closure phase measurements show direct evidence of asymmetries in the circumstellar environment of CI Cam and we conclude that the dust surrounding CI Cam lies in an inhomogeneous disc seen at an angle. The near-infrared dust emission appears as an elliptical skewed Gaussian ring with a major axis a = 7.58 +/- 0.24 mas, an axis ratio r = 0.39 +/- 0.03 and a position angle theta = 35 +/- 2 deg.Comment: 9 pages, 5 figures, accepted MNRA

Identifying Young Stellar Objects in the Outer Galaxy: l = 224 deg Region in Canis Major

We study a very young star-forming region in the outer Galaxy that is the most concentrated source of outflows in the Spitzer Space Telescope GLIMPSE360 survey. This region, dubbed CMa-l224, is located in the Canis Major OB1 association. CMa-l224 is relatively faint in the mid-infrared, but it shines brightly at the far-infrared wavelengths as revealed by the Herschel Space Observatory data from the Hi-GAL survey. Using the 3.6 and 4.5 $\mu$m data from the Spitzer/GLIMPSE360 survey, combined with the JHK$_s$ 2MASS and the 70-500 $\mu$m Herschel/Hi-GAL data, we develop a young stellar object (YSO) selection criteria based on color-color cuts and fitting of the YSO candidates' spectral energy distributions with YSO 2D radiative transfer models. We identify 293 YSO candidates and estimate physical parameters for 210 sources well-fit with YSO models. We select an additional 47 sources with GLIMPSE360-only photometry as `possible YSO candidates'. The vast majority of these sources are associated with high H$_2$ column density regions and are good targets for follow-up studies. The distribution of YSO candidates at different evolutionary stages with respect to Herschel filaments supports the idea that stars are formed in the filaments and become more dispersed with time. Both the supernova-induced and spontaneous star formation scenarios are plausible in the environmental context of CMa-l224. However, our results indicate that a spontaneous gravitational collapse of filaments is a more likely scenario. The methods developed for CMa-l224 can be used for larger regions in the Galactic plane where the same set of photometry is available.Comment: Accepted for publication in the Astrophysical Journal Supplement Series; 54 pages including appendice

The Mass-Loss Return From Evolved Stars to The Large Magellanic Cloud VI: Luminosities and Mass-Loss Rates on Population Scales

We present results from the first application of the Grid of Red Supergiant and Asymptotic Giant Branch ModelS (GRAMS) model grid to the entire evolved stellar population of the Large Magellanic Cloud (LMC). GRAMS is a pre-computed grid of 80,843 radiative transfer (RT) models of evolved stars and circumstellar dust shells composed of either silicate or carbonaceous dust. We fit GRAMS models to ~30,000 Asymptotic Giant Branch (AGB) and Red Supergiant (RSG) stars in the LMC, using 12 bands of photometry from the optical to the mid-infrared. Our published dataset consists of thousands of evolved stars with individually determined evolutionary parameters such as luminosity and mass-loss rate. The GRAMS grid has a greater than 80% accuracy rate discriminating between Oxygen- and Carbon-rich chemistry. The global dust injection rate to the interstellar medium (ISM) of the LMC from RSGs and AGB stars is on the order of 1.5x10^(-5) solar masses/yr, equivalent to a total mass injection rate (including the gas) into the ISM of ~5x10^(-3) solar masses/yr. Carbon stars inject two and a half times as much dust into the ISM as do O-rich AGB stars, but the same amount of mass. We determine a bolometric correction factor for C-rich AGB stars in the K band as a function of J - K color, BC(K) = -0.40(J-K)^2 + 1.83(J-K) + 1.29. We determine several IR color proxies for the dust mass-loss rate (MLR) from C-rich AGB stars, such as log (MLR) = (-18.90)/((K-[8.0])+3.37)-5.93. We find that a larger fraction of AGB stars exhibiting the `long-secondary period' phenomenon are O-rich than stars dominated by radial pulsations, and AGB stars without detectable mass-loss do not appear on either the first-overtone or fundamental-mode pulsation sequences.Comment: 19 pages, 19 figure