Random Matrix Theory and the Sixth Painlev\'e Equation

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be $\tau$-functions for Painlev\'e systems, allowing for the former to be characterised as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the $\sigma$ form of \PVI. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at $t=0,1,\infty$ of $\sigma$\PVI displayed by a generalisation of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the $\tau$-function of $\sigma$\PVI in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to \PVI.Comment: Dedicated to the centenary of the publication of the Painlev\'e VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

The Motions of Clusters of Galaxies and the Dipoles of the Peculiar Velocity Field

In preceding papers of this series, TF relations for galaxies in 24 clusters with radial velocities between 1000 and 9200 km/s (SCI sample) were obtained, a Tully-Fisher (TF) template relation was constructed and mean offsets of each cluster with respect to the template obtained. Here, an estimate of the line-of-sight peculiar velocities of the clusters and their associated errors are given. It is found that cluster peculiar velocities in the Cosmic Microwave Background reference frame do not exceed 600 k/ms and that their distribution has a line-of-sight dispersion of 300 k/ms, suggesting a more quiescent cluster peculiar velocity field than previously reported. When measured in a reference frame in which the Local Group is at rest, the set of clusters at cz > 3000 km/s exhibits a dipole moment in agreement with that of the CMB, both in amplitude and apex direction. It is estimated that the bulk flow of a sphere of 6000 km/s radius in the CMB reference frame is between 140 and 320 km/s. These results are in agreement with those obtained from an independent sample of field galaxies (Giovanelli et al. 1998; see astro-ph/9807274)Comment: 9 pages, 2 tables, 7 figures, uses AAS LaTex; to appear in A

Disk Galaxies in the Outer Local Supercluster: Optical CCD Surface Photometry and Distribution of Galaxy Disk Parameters

We report new B-band CCD surface photometry on a sample of 76 disk galaxies brighter than B_T = 14.5 mag in the Uppsala General Catalogue of Galaxies, which are confined within a volume located in the outer part of the Local Supercluster. With our earlier published I-band CCD and high S/N-ratio 21cm HI data (Lu et al. 1993), this paper completes our optical surface photometry campaign on this galaxy sample. As an application of this data set, the B-band photometry is used here to illustrate two selection effects which have been somewhat overlooked in the literature, but which may be important in deriving the distribution function of disk central surface brightness (CSB) of disk galaxies from a diameter or/and flux limited sample: a Malmquist-type bias against disk galaxies with small disk scale lengths (DSL) at a given CSB; and a disk inclination dependent selection effect that may, for example, bias toward inclined disks near the threshold of a diameter limited selection if disks are not completely opaque in optical. Taking into consideration these selection effects, we present a method of constructing a volume sampling function and a way to interpret the derived distribution function of CSB and DSL. Application of this method to our galaxy sample implies that if galaxy disks are optically thin, CSB and DSL may well be correlated in the sense that, up to an inclination-corrected limiting CSB of about 24.5 mag per square arcsec that is adequately probed by our galaxy sample, the DSL distribution of galaxies with a lower CSB may have a longer tail toward large values unless the distribution of disk galaxies as a function of CSB rises rapidly toward faint values.Comment: 27 pages including 9 figures and 2 tables. To appear in the October 20, 1998 issue of the Astrophysical Journa

The Ensemble Photometric Variability of ~25000 Quasars in the Sloan Digital Sky Survey

Using a sample of over 25000 spectroscopically confirmed quasars from the Sloan Digital Sky Survey, we show how quasar variability in the rest frame optical/UV regime depends upon rest frame time lag, luminosity, rest wavelength, redshift, the presence of radio and X-ray emission, and the presence of broad absorption line systems. The time dependence of variability (the structure function) is well-fit by a single power law on timescales from days to years. There is an anti-correlation of variability amplitude with rest wavelength, and quasars are systematically bluer when brighter at all redshifts. There is a strong anti-correlation of variability with quasar luminosity. There is also a significant positive correlation of variability amplitude with redshift, indicating evolution of the quasar population or the variability mechanism. We parameterize all of these relationships. Quasars with RASS X-ray detections are significantly more variable (at optical/UV wavelengths) than those without, and radio loud quasars are marginally more variable than their radio weak counterparts. We find no significant difference in the variability of quasars with and without broad absorption line troughs. Models involving multiple discrete events or gravitational microlensing are unlikely by themselves to account for the data. So-called accretion disk instability models are promising, but more quantitative predictions are needed.Comment: 41 pages, 21 figures, AASTeX, Accepted for publication in Ap

Hubble Space Telescope Observations of Field Ultracool Dwarfs at High Galactic Latitude

We present a sample of 17 newly discovered ultracool dwarf candidates later than ~M8, drawn from 231.90 arcmin2 of {\it Hubble Space Telescope} Wide Field Camera 3 infrared imaging. By comparing the observed number counts for 17.5<J_125<25.5 AB mag to an exponential disk model, we estimate a vertical scale height of z_scl=290 +- 25 (random) +- 30 (systematic) pc for a binarity fraction of f_b=0. While our estimate is roughly consistent with published results, we suggest that the differences can be attributed to sample properties, with the present sample containing far more substellar objects than previous work. We predict the object counts should peak at J_{125}~24 AB mag due to the exponentially-declining number density at the edge of the disc. We conclude by arguing that trend in scale height with spectral type may breakdown for brown dwarfs since they do not settle onto the main sequence.Comment: 9 pages, 6 figures, 3 tables, accepted to ApJ (v2 is consistent with Referee changes

The Palomar Testbed Interferometer Calibrator Catalog

The Palomar Testbed Interferometer (PTI) archive of observations between 1998 and 2005 is examined for objects appropriate for calibration of optical long-baseline interferometer observations - stars that are predictably point-like and single. Approximately 1,400 nights of data on 1,800 objects were examined for this investigation. We compare those observations to an intensively studied object that is a suitable calibrator, HD217014, and statistically compare each candidate calibrator to that object by computing both a Mahalanobis distance and a Principal Component Analysis. Our hypothesis is that the frequency distribution of visibility data associated with calibrator stars differs from non-calibrator stars such as binary stars. Spectroscopic binaries resolved by PTI, objects known to be unsuitable for calibrator use, are similarly tested to establish detection limits of this approach. From this investigation, we find more than 350 observed stars suitable for use as calibrators (with an additional $\approx 140$ being rejected), corresponding to $\gtrsim 95$ sky coverage for PTI. This approach is noteworthy in that it rigorously establishes calibration sources through a traceable, empirical methodology, leveraging the predictions of spectral energy distribution modeling but also verifying it with the rich body of PTI's on-sky observations.Comment: 100 pages, 7 figures, 7 tables; to appear in the May 2008ApJS, v176n

Long-term Optical Variability of Radio-Selected Quasars from the FIRST Survey

We have obtained single-epoch optical photometry for 201 quasars, taken from the FIRST Bright Quasar Survey, which span a wide range in radio loudness. Comparison with the magnitudes of these objects on the POSS-I plates provides by far the largest sample of long-term variability amplitudes for radio-selected quasars yet produced. We find the quasars to be more variable in the blue than in the red band, consistent with work on optically selected samples. The previously noted trend of decreasing variability with increasing optical luminosity applies only to radio-quiet objects. Furthermore, we do not confirm a rise in variability amplitude with redshift, nor do we see any dependence on radio flux or luminosity. The variability over a radio-optical flux ratio range spanning a factor of 60,000 from radio-quiet to extreme radio-loud objects is largely constant, although there is a suggestion of greater variability in the extreme radio-loud objects. We demonstrate the importance of Malmquist bias in variability studies, and develop a procedure to correct for the bias in order to reveal the underlying variability properties of the sample.Comment: 16 pages, 8 figures To be published in 2001 April 1 Astronomical Journa

Starcounts Redivivus. IV. Density Laws Through Photometric Parallaxes

In an effort to more precisely define the spatial distribution of Galactic field stars, we present an analysis of the photometric parallaxes of 70,000 stars covering nearly 15 square degrees in seven Kapteyn Selected Areas. We address the affects of Malmquist Bias, subgiant/giant contamination, metallicity and binary stars upon the derived density laws. The affect of binary stars is the most significant. We find that while the disk-like populations of the Milky Way are easily constrained in a simultaneous analysis of all seven fields, no good simultaneous solution for the halo is found. We have applied halo density laws taken from other studies and find that the Besancon flattened power law halo model (c/a=0.6, r^-2.75) produces the best fit to our data. With this halo, the thick disk has a scale height of 750 pc with an 8.5% normalization to the old disk. The old disk scale height is 280-300 pc. Corrected for a binary fraction of 50%, these scale heights are 940 pc and 350-375 pc, respectively. Even with this model, there are systematic discrepancies between the observed and predicted density distributions. Our model produces density overpredictions in the inner Galaxy and density underpredictions in the outer Galaxy. A possible solution is modeling the stellar halo as a two-component system in which the halo has a flattened inner distribution and a roughly spherical, but substructured outer distribution. Further reconciliation could be provided by a flared thick disk, a structure consistent with a merger origin for that population. (Abridged)Comment: 66 pages, accepted to Astrophysical journal, some figures compresse

On the cosmic evolution of the scaling relations between black holes and their host galaxies: Broad Line AGN in the zCOSMOS survey

(Abriged) We report on the measurement of the rest frame K-band luminosity and total stellar mass of the hosts of 89 broad line Active Galactic Nuclei detected in the zCOSMOS survey in the redshift range 1<z<2.2. The unprecedented multiwavelength coverage of the survey field allows us to disentangle the emission of the host galaxy from that of the nuclear black hole in their Spectral Energy Distributions. We derive an estimate of black hole masses through the analysis of the broad Mg II emission lines observed in the medium-resolution spectra taken with VIMOS/VLT as part of the zCOSMOS project. We found that, as compared to the local value, the average black hole to host galaxy mass ratio appears to evolve positively with redshift, with a best fit evolution of the form (1+z)^{0.68 \pm0.12 +0.6 -0.3}, where the large asymmetric systematic errors stem from the uncertainties in the choice of IMF, in the calibration of the virial relation used to estimate BH masses and in the mean QSO SED adopted. A thorough analysis of observational biases induced by intrinsic scatter in the scaling relations reinforces the conclusion that an evolution of the MBH-M* relation must ensue for actively growing black holes at early times: either its overall normalization, or its intrinsic scatter (or both) appear to increase with redshift. This can be interpreted as signature of either a more rapid growth of supermassive black holes at high redshift, a change of structural properties of AGN hosts at earlier times, or a significant mismatch between the typical growth times of nuclear black holes and host galaxies.Comment: 47 pages, 8 figures. Accepted for publication in Ap

Evaluando el progreso de la eficiencia con tecnología en una cadena de hoteles española

This paper analyzes the changes in the total factor productivity index of a Spanish hotel chain in the period from 2007 to 2010 with the purpose of identifying efficiency patterns for the chain in a period of financial crisis. The data envelopment analysis (DEA) Malmquist productivity index was used to estimate productivity change in 38 hotels of the AC chain. Results reveal AC hotels’ efficiency trends and, therefore, their competitiveness in the recession period; they also show the changes experienced in these hotels’ total productivity and its components: technological and efficiency changes. Positive efficiency changes were due to positive technical efficiency rather than technological efficiency. The recession period certainly influenced the performance of AC Hotels, which focused on organizational changes rather than investing in technology.Este artigo analisa as mudanças no fator total de produtividade de uma cadeia de hotéis na Espanha, no período de 2007-2010, com o propósito de identificar os padrões da cadeia em um período de crise financeira. O índice data envelopment analysis (DEA) Malmquist de produtividade foi usado para estimar a mudança da produtividade nos 38 hotéis da AC Cadeia de Hotéis. Os resultados revelaram as tendências de eficiência e competitividade da AC Hotéis em um período de recessão, bem como as mudanças vivenciadas na produtividade total e, consequentemente, em seus componentes de eficiência e tecnológicos. O período de recessão influenciou, sem dúvida, o comportamento da AC Hotéis, que buscou mais mudanças organizacionais do que tecnológicas.Este artículo analiza los cambios del índice de productividad del factor total de una cadena de hoteles españoles en el periodo de 2007 hasta 2010, con el propósito de identificar patrones de eficiencia para la cadena en un periodo de crisis financiera. El índice de productividad data envelopment analysis (DEA) Malmquist fue utilizado para estimar el cambio de productividad en 38 hoteles de la cadena AC. Los resultados revelan las tendencias de la eficiencia de los hoteles AC y, por lo tanto, su competitividad en el periodo de recisión; ellos también demuestran los cambios experimentados en la productividad total de eses hoteles y sus componentes: cambios de eficiencia y tecnológicos. Cambios de eficiencia positivos se debieron más bien a eficiencias técnicas positivas que a eficiencias tecnológicas. El periodo de recesión ciertamente ha influenciado los Hoteles AC, que enfocaron más en los cambios organizacionales que en invirtiendo en tecnología