Investigation of Gravitational Lens Mass Models

We have previously reported the discovery of strong gravitational lensing by faint elliptical galaxies using the WFPC2 on HST and here we investigate their potential usefulness in putting constraints on lens mass models. We compare various ellipsoidal surface mass distributions, including those with and without a core radius, as well as models in which the mass distributions are assumed to have the same axis ratio and orientation as the galaxy light. We also study models which use a spherical mass distribution having various profiles, both empirical and following those predicted by CDM simulations. These models also include a gravitational shear term. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed HST WFPC2 images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the lensed image components. The motivation for this study was to distinguish between these mass models with this technique. However, we find that, despite using the full image data rather than just locations and integrated magnitudes, the lenses are fit equally well with several of the mass models. Each of the mass models generates a similar configuration but with a different magnification and cross-sectional area within the caustic, and both of these latter quantities govern the discovery probability of lensing in the survey. These differences contribute to considerable cosmic scatter in any estimate of the cosmological constant using gravitational lenses.Comment: 10 pages with 6 embedded figures, tentatively scheduled to be published in the July 2001 issue of The Astronomical Journal. For additional information see http://mds.phys.cmu.edu/lense

Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem

The Workflow Satisfiability Problem (WSP) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a plan -- an assignment of tasks to authorized users -- such that all constraints are satisfied. The WSP is, in fact, the conservative Constraint Satisfaction Problem (i.e., for each variable, here called task, we have a unary authorization constraint) and is, thus, NP-complete. It was observed by Wang and Li (2010) that the number k of tasks is often quite small and so can be used as a parameter, and several subsequent works have studied the parameterized complexity of WSP regarding parameter k. We take a more detailed look at the kernelization complexity of WSP(\Gamma) when \Gamma\ denotes a finite or infinite set of allowed constraints. Our main result is a dichotomy for the case that all constraints in \Gamma\ are regular: (1) We are able to reduce the number n of users to n' <= k. This entails a kernelization to size poly(k) for finite \Gamma, and, under mild technical conditions, to size poly(k+m) for infinite \Gamma, where m denotes the number of constraints. (2) Already WSP(R) for some R \in \Gamma\ allows no polynomial kernelization in k+m unless the polynomial hierarchy collapses.Comment: An extended abstract appears in the proceedings of IPEC 201

The VIRMOS deep imaging survey: III. ESO/WFI deep U-band imaging of the 0226-04 deep field

In this paper we describe the U-band imaging of the F02 deep field, one of the fields in the VIRMOS Deep Imaging Survey. The observations were done at the ESO/MPG 2.2m telescope at La Silla (Chile) using the 8k x 8k Wide-Field Imager (WFI). The field is centered at alpha(J2000)=02h 26m 00s and delta(J2000)=-04deg 30' 00", the total covered area is 0.9 deg**2 and the limiting magnitude (50% completeness) is U(AB) ~ 25.4 mag. Reduction steps, including astrometry, photometry and catalogue extraction, are first discussed. The achieved astrometric accuracy (RMS) is ~ 0.2" with reference to the I-band catalog and ~ 0.07" internally (estimated from overlapping sources in different exposures). The photometric accuracy including uncertainties from photometric calibration, is < 0.1 mag. Various tests are then performed as a quality assessment of the data. They include: (i) the color distribution of stars and galaxies in the field, done together with the BVRI data available from the VIMOS survey; (ii) the comparison with previous published results of U-band magnitude-number counts of galaxies.Comment: 10 pages, 13 figures, accepted for publication on Astronomy and Astrophysic

Four quasars above redshift 6 discovered by the Canada-France High-z Quasar Survey

The Canada-France High-z Quasar Survey (CFHQS) is an optical survey designed to locate quasars during the epoch of reionization. In this paper we present the discovery of the first four CFHQS quasars at redshift greater than 6, including the most distant known quasar, CFHQS J2329-0301 at z=6.43. We describe the observational method used to identify the quasars and present optical, infrared, and millimeter photometry and optical and near-infrared spectroscopy. We investigate the dust properties of these quasars finding an unusual dust extinction curve for one quasar and a high far-infrared luminosity due to dust emission for another. The mean millimeter continuum flux for CFHQS quasars is substantially lower than that for SDSS quasars at the same redshift, likely due to a correlation with quasar UV luminosity. For two quasars with sufficiently high signal-to-noise optical spectra, we use the spectra to investigate the ionization state of hydrogen at z>5. For CFHQS J1509-1749 at z=6.12, we find significant evolution (beyond a simple extrapolation of lower redshift data) in the Gunn-Peterson optical depth at z>5.4. The line-of-sight to this quasar has one of the highest known optical depths at z~5.8. An analysis of the sizes of the highly-ionized near-zones in the spectra of two quasars at z=6.12 and z=6.43 suggest the IGM surrounding these quasars was substantially ionized before these quasars turned on. Together, these observations point towards an extended reionization process, but we caution that cosmic variance is still a major limitation in z>6 quasar observations.Comment: 15 pages, 9 figures, AJ, in press, minor changes to previous versio

Cosmological constraints from lensing statistics and supernovae on the cosmic equation of state

We investigate observational constraints from lensing statistics and high-z type Ia supernovae on flat cosmological models with nonrelativistic matter and an exotic fluid with equation of state, $p_x=(m/3 -1)\rho_x$. We show that agreement with both tests at the 68% confidence level is possible if the parameter $m$ is low ($m \lesssim 0.85$) and $0.24 \lesssim \Omega_{m0} \lesssim 0.38$ with lower values of $\Omega_{m0}$ corresponding to higher $m$. We find that a conventional cosmological constant model with $\Omega_{m0}\simeq 0.33$ is the best fit model of the combined likelihood.Comment: 7 pages, 4 postscript figures, revtex, submitted to Phys. Rev.

531 new spectroscopic redshifts from the CDFS and a test on the cosmological relevance of the GOODS-South field

(Abbrev.) This paper prepares a series of papers analysing the Intermediate MAss Galaxy Evolution Sequence (IMAGES) up to z=1. Intermediate mass galaxies (MJ <=-20.3) are selected from the Chandra Deep Field South (CDFS) for which we identify a serious lack of spectroscopically determined redshifts..... We have spectroscopically identified 691 objects including 580 gal., 7 QSOs, and 104 stars. This study provides 531 new redshifts in the CDFS. It confirms the presence of several large scale structures in the CDFS. To test the impact of these structures in the GOODS-South field, we ... compare the evolution of rest-frame U, B, V and K galaxy luminosity densities to that derived from the CFRS. The CDFS field shows a significant excess of luminosity densities in the z=0.5-0.75 range, which increases with the wavelength, reaching up to 0.5 dex at 2.1 um. Stellar mass and specific star formation evolutions might be significantly affected by the presence of the peculiar large scale structures at z= 0.668 and at z= 0.735, that contain a significant excess of evolved, massive galaxies when compared to other fields. This leads to a clear warning to results based on the CDFS/GOODS South fields, especially those related to the evolution of red luminosity densities, i.e. stellar mass density and specific star formation rate. Photometric redshift techniques, when applied to that field, are producing quantities which are apparently less affected by cosmic variance (0.25 dex at 2.1 um), however at the cost of the difficulty in disentangling between evolutionary and cosmic variance effects.Comment: Accepted for publication in A&A, 19 pages, 13 figure

Shear and Ellipticity in Gravitational Lenses

Galaxies modeled as singular isothermal ellipsoids with an axis ratio distribution similar to the observed axis ratio distribution of E and S0 galaxies are statistically consistent with both the observed numbers of two-image and four-image lenses and the inferred ellipticities of individual lenses. However, no four-image lens is well fit by the model (typical $\chi^2/N_{dof} \sim 20$), the axis ratio of the model can be significantly different from that of the observed lens galaxy, and the major axes of the model and the galaxy may be slightly misaligned. We found that models with a second, independent, external shear axis could fit the data well (typical $\chi^2/N_{dof} \sim 1$), while adding the same number of extra parameters to the radial mass distribution does not produce such a dramatic improvement in the fit. An independent shear axis can be produced by misalignments between the luminous galaxy and its dark matter halo, or by external shear perturbations due to galaxies and clusters correlated with the primary lens or along the line of sight. We estimate that the external shear perturbations have no significant effect on the expected numbers of two-image and four-image lenses, but that they can be important perturbations in individual lens models. However, the amplitudes of the external shears required to produce the good fits are larger than our estimates for typical external shear perturbations (10-15% shear instead of 1-3% shear) suggesting that the origin of the extra angular structure must be intrinsic to the primary lens galaxy in most cases.Comment: 38 pages, 9 figures, submitted to Ap

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schr\"odinger type via a z=2 QCP.Comment: references added. minor changes. version published in JHE