The quantum Casimir operators of \Uq and their eigenvalues

We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one extra central element generate the entire center of \Uq. As a by product of the proof, we obtain intriguing new formulae for eigenvalues of these quantum Casimir operators, which are expressed in terms of the characters of a class of finite dimensional irreducible representations of the classical general linear algebra.Comment: 10 page

How Much Mass do Supermassive Black Holes Eat in their Old Age?

We consider the distribution of local supermassive black hole Eddington ratios and accretion rates, accounting for the dependence of radiative efficiency and bolometric corrections on the accretion rate. We find that black hole mass growth, both of the integrated mass density and the masses of most individual objects, must be dominated by an earlier, radiatively efficient, high accretion rate stage, and not by the radiatively inefficient low accretion rate phase in which most local supermassive black holes are currently observed. This conclusion is particularly true of supermassive black holes in elliptical host galaxies, as expected if they have undergone merger activity in the past which would fuel quasar activity and rapid growth. We discuss models of the time evolution of accretion rates and show that they all predict significant mass growth in a prior radiatively efficient state. The only way to avoid this conclusion is through careful fine-tuning of the accretion/quasar timescale to a value that is inconsistent with observations. Our results agree with a wide range of observational inferences drawn from the quasar luminosity function and X-ray background synthesis models, but our approach has the virtue of being independent of the modeling of source populations. Models in which black holes spend the great majority of their time in low accretion rate phases are thus completely consistent both with observations implying mass gain in relatively short, high accretion rate phases and with the local distribution of accretion rates.Comment: 11 pages, 4 figures, matches version accepted to Ap

Radio Galaxy Zoo: Knowledge Transfer Using Rotationally Invariant Self-Organising Maps

With the advent of large scale surveys the manual analysis and classification of individual radio source morphologies is rendered impossible as existing approaches do not scale. The analysis of complex morphological features in the spatial domain is a particularly important task. Here we discuss the challenges of transferring crowdsourced labels obtained from the Radio Galaxy Zoo project and introduce a proper transfer mechanism via quantile random forest regression. By using parallelized rotation and flipping invariant Kohonen-maps, image cubes of Radio Galaxy Zoo selected galaxies formed from the FIRST radio continuum and WISE infrared all sky surveys are first projected down to a two-dimensional embedding in an unsupervised way. This embedding can be seen as a discretised space of shapes with the coordinates reflecting morphological features as expressed by the automatically derived prototypes. We find that these prototypes have reconstructed physically meaningful processes across two channel images at radio and infrared wavelengths in an unsupervised manner. In the second step, images are compared with those prototypes to create a heat-map, which is the morphological fingerprint of each object and the basis for transferring the user generated labels. These heat-maps have reduced the feature space by a factor of 248 and are able to be used as the basis for subsequent ML methods. Using an ensemble of decision trees we achieve upwards of 85.7% and 80.7% accuracy when predicting the number of components and peaks in an image, respectively, using these heat-maps. We also question the currently used discrete classification schema and introduce a continuous scale that better reflects the uncertainty in transition between two classes, caused by sensitivity and resolution limits

The Mid-IR and X-ray Selected QSO Luminosity Function

We present the J-band luminosity function of 1838 mid-infrared and X-ray selected AGNs in the redshift range 0<z<5.85. These luminosity functions are constructed by combining the deep multi-wavelength broad-band observations from the UV to the mid-IR of the NDWFS Bootes field with the X-ray observations of the XBootes survey and the spectroscopic observations of the same field by AGES. Our sample is primarily composed of IRAC-selected AGNs, targeted using modifications of the Stern et al.(2005) criteria, complemented by MIPS 24 microns and X-ray selected AGNs to alleviate the biases of IRAC mid-IR selection against z~4.5 quasars and AGNs faint with respect to their hosts. This sample provides an accurate link between low and high redshift AGN luminosity functions and does not suffer from the usual incompleteness of optical samples at z~3. We find that the space density of the brightest quasars strongly decreases from z=3 to z=0, while the space density of faint quasars is at least flat, and possibly increasing, over the same redshift range. At z>3 we observe a decrease in the space density of quasars of all brightnesses. We model the luminosity function by a double power-law and find that its evolution cannot be described by either pure luminosity or pure density evolution, but must be a combination of both. Our best-fit model has bright and faint power-law indices consistent with the low redshift measurements based on the 2QZ and 2SLAQ surveys and it generally agrees with the number of bright quasars predicted by other LFs at all redshifts. If we construct the QSO luminosity function using only the IRAC-selected AGNs, we find that the biases inherent to this selection method significantly modify the behavior of phi*(z) only for z<1 and have no significant impact upon the characteristic magnitude M*_J(z).Comment: Corrected minor typo in equations (4) and (6). Accepted for publication in The Astrophysical Journal. 56 pages + 6 tables + 16 figure

M-theory and Characteristic Classes

In this note we show that the Chern-Simons and the one-loop terms in the M-theory action can be written in terms of new characters involving the M-theory four-form and the string classes. This sheds a new light on the topological structure behind M-theory and suggests the construction of a theory of `higher' characteristic classes.Comment: 8 pages. Error in gravitational term fixed; minor corrections; reference and acknowledgement adde

The Phoenix Deep Survey: The 1.4 GHz microJansky catalogue

The initial Phoenix Deep Survey (PDS) observations with the Australia Telescope Compact Array have been supplemented by additional 1.4 GHz observations over the past few years. Here we present details of the construction of a new mosaic image covering an area of 4.56 square degrees, an investigation of the reliability of the source measurements, and the 1.4 GHz source counts for the compiled radio catalogue. The mosaic achieves a 1-sigma rms noise of 12 microJy at its most sensitive, and a homogeneous radio-selected catalogue of over 2000 sources reaching flux densities as faint as 60 microJy has been compiled. The source parameter measurements are found to be consistent with the expected uncertainties from the image noise levels and the Gaussian source fitting procedure. A radio-selected sample avoids the complications of obscuration associated with optically-selected samples, and by utilising complementary PDS observations including multicolour optical, near-infrared and spectroscopic data, this radio catalogue will be used in a detailed investigation of the evolution in star-formation spanning the redshift range 0 < z < 1. The homogeneity of the catalogue ensures a consistent picture of galaxy evolution can be developed over the full cosmologically significant redshift range of interest. The 1.4 GHz mosaic image and the source catalogue are available on the web at http://www.atnf.csiro.au/~ahopkins/phoenix/ or from the authors by request.Comment: 16 pages, 11 figures, 4 tables. Accepted for publication by A

Optical Morphologies of Millijansky Radio Galaxies Observed by HST and in the VLA FIRST Survey

We report on a statistical study of the 51 radio galaxies at the millijansky flux level from the Faint Images of the Radio Sky at Twenty centimeters, including their optical morphologies and structure obtained with the Hubble Space Telescope. Our optical imaging is significantly deeper (~2 mag) than previous studies with the superior angular resolution of space-based imaging. We that find 8/51 (16%) of the radio sources have no optically identifiable counterpart to AB~24 mag. For the remaining 43 sources, only 25 are sufficiently resolved in the HST images to reliably assign a visual classification: 15 (60%) are elliptical galaxies, 2 (8%) are late-type spiral galaxies, 1 (4%) is an S0, 3 (12%) are point-like objects (quasars), and 4 (16%) are merger systems. We find a similar distribution of optical types with measurements of the Sersic index. The optical magnitude distribution of these galaxies peaks at I~20.7+-0.5 AB mag, which is ~3 mag brighter than the depth of our typical HST field and is thus not due to the WFPC2 detection limit. This supports the luminosity-dependent density evolutionary model, where the majority of faint radio galaxies typically have L*-optical luminosities and a median redshift of z~0.8 with a relatively abrupt redshift cut-off at z>~2. We discuss our results in the context of the evolution of elliptical galaxies and active galactic nuclei.Comment: 20 pages, 8 figures, 51 galaxy images, and 5 tables. Uses emulateapj.cls and natbib.sty. Accepted to ApJS. High resolution images are available upon reques