Modular Invariant of Quantum Tori II: The Golden Mean

In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined. In this paper, we consider the case of the quantum torus associated to the golden mean. We show that the modular invariant is approximately 9538.249655644 by producing an explicit formula for it involving weighted versions of the Rogers-Ramanujan functions

EAGLE multi-object AO concept study for the E-ELT

EAGLE is the multi-object, spatially-resolved, near-IR spectrograph instrument concept for the E-ELT, relying on a distributed Adaptive Optics, so-called Multi Object Adaptive Optics. This paper presents the results of a phase A study. Using 84x84 actuator deformable mirrors, the performed analysis demonstrates that 6 laser guide stars and up to 5 natural guide stars of magnitude R<17, picked-up in a 7.3' diameter patrol field of view, allow us to obtain an overall performance in terms of Ensquared Energy of 35% in a 75x75 mas^2 spaxel at H band, whatever the target direction in the centred 5' science field for median seeing conditions. The computed sky coverage at galactic latitudes |b|~60 is close to 90%.Comment: 6 pages, to appear in the proceedings of the AO4ELT conference, held in Paris, 22-26 June 200

Chandra X-ray observations of the hyper-luminous infrared galaxy IRAS F15307+3252

Hyper-luminous infrared galaxies (HyLIRGs) lie at the extreme luminosity end of the IR galaxy population with LIR > 1013 L.. They are thought to be closer counterparts of the more distant sub-millimeter galaxies, and should therefore be optimal targets to study the most massive systems in formation.We present deep Chandra observations of IRAS F15307+3252 (100 ks), a classical HyLIRG located at z=0.93 and hosting a radio-loudAGN(L1.4 GHz ∼3.5×1025WHz−1). The Chandra images reveal the presence of extended (r=160 kpc), asymmetric X-ray emission in the soft 0.3-2.0 keV band that has no radio counterpart.We therefore argue that the emission is of thermal origin originating from a hot intragroup or intracluster medium virializing in the potential. We find that the temperature (∼2 keV) and bolometric X-ray luminosity (∼3 × 1043 erg s−1) of the gas follow the expected LX-ray-T correlation for groups and clusters, and that the gas has a remarkably short cooling time of 1.2 Gyr. In addition, VLA radio observations reveal that the galaxy hosts an unresolved compact steep-spectrum (CSS)source, most likely indicating the presence of a young radio source similar to 3C186. We also confirm that the nucleus is dominated by a redshifted 6.4 keV Fe Kα line, strongly suggesting that the AGN is Compton-thick. Finally, Hubble images reveal an overdensity of galaxies and sub-structure in the galaxy that correlates with soft X-ray emission. This could be a snapshot view of on-going groupings expected in a growing cluster environment. IRAS F15307+3252 might therefore be a rare example of a group in the process of transforming into a cluster