Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory

The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group representation theory to Lie algebras as well as crepant resolutions of Gorenstein singularities. On the physics side, we have the graph-theoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the ADE type in two complex dimensions. An intricate web of inter-relations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry and references adde

A bipolar outflow from the massive protostellar core W51e2-E

We present high resolution images of the bipolar outflow from W51e2, which are produced from the Submillimeter Array archival data observed for CO(3-2) and HCN(4-3) lines with angular resolutions of 0.8" x 0.6" and 0.3" x 0.2", respectively. The images show that the powerful outflow originates from the protostellar core W51e2-E rather than from the ultracompact HII region W51e2-W. The kinematic timescale of the outflow from W51e2-E is about 1000 yr, younger than the age (~5000 yr) of the ultracompact HII region W51e2-W. A large mass loss rate of ~1 x 10^{-3} M_sun yr^{-1} and a high mechanical power of 120 L_sun are inferred, suggesting that an O star or a cluster of B stars are forming in W51e2-E. The observed outflow activity along with the inferred large accretion rate indicates that at present W51e2-E is in a rapid phase of star formation.Comment: 5 pages, 2 figures, 1 table, accepted for publication in ApJL. v2: some typos correcte

Intrinsic/Extrinsic Density-Ellipticity Correlations and Galaxy-Galaxy Lensing

We compute both extrinsic (lensing) and intrinsic contributions to the (galaxy-)density-ellipticity correlation function, the latter done using current analytic theories of tidal alignment. The gravitational lensing contribution has two components: one is analogous to galaxy-galaxy lensing and the other arises from magnification bias -- that gravitational lensing induces a modulation of the galaxy density as well as ellipticity. On the other hand, the intrinsic alignment contribution vanishes, even after taking into account source clustering corrections, which suggests the density-ellipticity correlation might be an interesting diagnostic in differentiating between intrinsic and extrinsic alignments. {\it However}, an important assumption, commonly adopted by current analytic alignment theories, is the Gaussianity of the tidal field. Inevitable non-Gaussian fluctuations from gravitational instability induces a non-zero intrinsic density-ellipticity correlation, which we estimate. We also argue that non-Gaussian contributions to the intrinsic {\it ellipticity-ellipticity} correlation are often non-negligible. This leads to a linear rather than, as is commonly assumed, quadratic scaling with the power spectrum on sufficiently large scales. Finally, we estimate the contribution of intrinsic alignment to low redshift galaxy-galaxy lensing measurements (e.g. SDSS), due to the partial overlap between foreground and background galaxies: the intrinsic contamination is about 10 - 30 % at 10'. Uncertainties in this estimate are discussed.Comment: 14 pages, 5 figures, submitted to Ap

Nature of W51e2: Massive Cores at Different Phases of Star Formation

We present high-resolution continuum images of the W51e2 complex processed from archival data of the Submillimeter Array (SMA) at 0.85 and 1.3 mm and the Very Large Array (VLA) at 7 and 13 mm. We also made line images and profiles of W51e2 for three hydrogen radio recombination lines (H26\alpha, H53\alpha, and H66\alpha) and absorption of two molecular lines of HCN(4-3) and CO(2-1). At least four distinct continuum components have been detected in the 3" region of W51e2 from the SMA continuum images at 0.85 and 1.3 mm with resolutions of 0.3"x0.2" and 1.4"x0.7", respectively. The west component, W51e2-W, coincides with the UC HII region reported from previous radio observations. The H26\alpha line observation reveals an unresolved hyper-compact ionized core (<0.06" or <310 AU) with a high electron temperature of 1.2x10^4 K, with corresponding emission measure EM>7x10^{10} pc cm^{-6} and electron density N_e>7x10^6 cm^{-3}. The inferred Lyman continuum flux implies that the HII region W51e2-W requires a newly formed massive star, an O8 star or a cluster of B-type stars, to maintain the ionization. The east component, W51e2-E, has a total mass of ~140 M_{\sun} according to our SED analysis and a large infall rate of > 1.3x10^{-3} M_{\sun}yr^{-1} inferred from the absorption of HCN. W51e2-E appears to be the accretion center in W51e2 and to host one or more growing massive proto-stars. Located 2" northwest from W51e2-E, W51e2-NW is not detected in the continuum emission at \lambda>=7 mm. Along with the maser activities previously observed, our analysis suggests that W51e2-NW is at an earlier phase of star formation. W51e2-N is located 2" north of W51e2-E and has only been detected at 1.3 mm with a lower angular resolution (~1"), suggesting that it is a primordial, massive gas clump in the W51e2 complex.Comment: 10 pages, 5 figures, 3 table, accepted for publication in Ap