Search

Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms (e.g. sigma-clipping). We develop and implement a generic Bayesian approach to linear regression, based on Student's t-distributions, that is robust to outliers and mis-specification of the noise model. Our method is validated using simulated datasets with various degrees of model mis-specification; the derived constraints are shown to be systematically less biased than those from a similar model using normal distributions. We demonstrate that, for a dataset without outliers, a worst-case inference using t-distributions would give unbiased results with $\lesssim\!10$ per cent increase in the reported parameter uncertainties. We also compare with existing analyses of real-world datasets, finding qualitatively different results where normal distributions have been used and agreement where more robust methods have been applied. A Python implementation of this model, t-cup, is made available for others to use., Comment: 14 pages, 19 figures

Upcoming surveys such as Euclid, the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and the Nancy Grace Roman Telescope (Roman) will detect hundreds of high-redshift (z > 7) quasars, but distinguishing them from the billions of other sources in these catalogues represents a significant data analysis challenge. We address this problem by extending existing selection methods by using both i) Bayesian model comparison on measured fluxes and ii) a likelihood-based goodness-of-fit test on images, which are then combined using an Fbeta statistic. The result is an automated, reproduceable and objective high-redshift quasar selection pipeline. We test this on both simulations and real data from the cross-matched Sloan Digital Sky Survey (SDSS) and UKIRT Infrared Deep Sky Survey (UKIDSS) catalogues. On this cross-matched dataset we achieve an AUC score of up to 0.795 and an F3 score of up to 0.79, sufficient to be applied to the Euclid, LSST and Roman data when available., Comment: 21 pages, 24 figures; to be submitted to the Open Journal of Astrophysics

We present an efficient Bayesian method for estimating individual photometric redshifts and galaxy properties under a pre-trained population model (pop-cosmos) that was calibrated using purely photometric data. This model specifies a prior distribution over 16 stellar population synthesis (SPS) parameters using a score-based diffusion model, and includes a data model with detailed treatment of nebular emission. We use a GPU-accelerated affine invariant ensemble sampler to achieve fast posterior sampling under this model for 292,300 individual galaxies in the COSMOS2020 catalog, leveraging a neural network emulator (Speculator) to speed up the SPS calculations. We apply both the pop-cosmos population model and a baseline prior inspired by Prospector-$\alpha$, and compare these results to published COSMOS2020 redshift estimates from the widely-used EAZY and LePhare codes. For the $\sim 12,000$ galaxies with spectroscopic redshifts, we find that pop-cosmos yields redshift estimates that have minimal bias ($\sim10^{-4}$), high accuracy ($\sigma_\text{MAD}=7\times10^{-3}$), and a low outlier rate ($1.6\%$). We show that the pop-cosmos population model generalizes well to galaxies fainter than its $r<25$ mag training set. The sample we have analyzed is $\gtrsim3\times$ larger than has previously been possible via posterior sampling with a full SPS model, with average throughput of 15 GPU-sec per galaxy under the pop-cosmos prior, and 0.6 GPU-sec per galaxy under the Prospector prior. This paves the way for principled modeling of the huge catalogs expected from upcoming Stage IV galaxy surveys., Comment: 24 pages, 15 figures. Accepted for publication in ApJ. Catalog of redshifts and galaxy properties available on Zenodo at https://zenodo.org/doi/10.5281/zenodo.13627488

We present a simple method for assessing the predictive performance of high-dimensional models directly in data space when only samples are available. Our approach is to compare the quantiles of observables predicted by a model to those of the observables themselves. In cases where the dimensionality of the observables is large (e.g. multiband galaxy photometry), we advocate that the comparison is made after projection onto a set of principal axes to reduce the dimensionality. We demonstrate our method on a series of two-dimensional examples. We then apply it to results from a state-of-the-art generative model for galaxy photometry (pop-cosmos; arXiv:2402.00935) that generates predictions of colors and magnitudes by forward simulating from a 16-dimensional distribution of physical parameters represented by a score-based diffusion model. We validate the predictive performance of this model directly in a space of nine broadband colors. Although motivated by this specific example, we expect that the techniques we present will be broadly useful for evaluating the performance of flexible, non-parametric population models of this kind, and other settings where two sets of samples are to be compared., Comment: 21 pages, 11 figures. Accepted for publication in ApJS. Companion paper to arXiv:2402.00935

Gravitational-wave (GW) observations of neutron star-black hole (NSBH) mergers are sensitive to the nuclear equation of state (EOS). We present a new methodology for EOS inference with non-parametric Gaussian process (GP) priors, enabling direct constraints on the pressure at specific densities and the length-scale of correlations on the EOS. Using realistic simulations of NSBH mergers, incorporating both GW and electromagnetic (EM) selection to ensure sample purity, we find that a GW detector network operating at O5-sensitivities will constrain the radius of a $\unit[1.4]{M_{\odot}}$ NS and the maximum NS mass with $1.6\%$ and $13\%$ precision, respectively. With the same sample, the projected constraint on the length-scale of correlations in the EOS is $\geq~\unit[3.2]{MeV~fm^{-3}}$. These results demonstrate strong potential for insights into the nuclear EOS from NSBH systems, provided they are robustly identified., Comment: 10 pages, 4 Figures. Accepted in PRD

Gravitational wave (GW) and electromagnetic (EM) observations of neutron-star-black-hole (NSBH) mergers can provide precise local measurements of the Hubble constant ($H_0$), ideal for resolving the current $H_0$ tension. We perform end-to-end analyses of realistic populations of simulated NSBHs, incorporating both GW and EM selection for the first time. We show that NSBHs could achieve unbiased 1.5-2.4% precision $H_0$ estimates by 2030. The achievable precision is strongly affected by the details of spin precession and tidal disruption, highlighting the need for improved modeling of NSBH mergers., Comment: Version published in Physical Review Letters. 10 pages, 3 figures. Code available at https://github.com/sfeeney/nsbh

When modelling strong gravitational lenses, i.e., where there are multiple images of the same source, the most widely used parameterisation for the mass profile in the lens galaxy is the singular power-law model $\rho(r)\propto r^{-\gamma}$. This model may be insufficiently flexible for very accurate work, for example measuring the Hubble constant based on time delays between multiple images. Here we derive the lensing properties - deflection angle, shear, and magnification - of a more adaptable model where the projected mass surface density is parameterised as a continuous two-dimensional broken power-law (2DBPL). This elliptical 2DBPL model is characterised by power-law slopes $t_1$, $t_2$ either side of the break radius $\theta_\mathrm{B}$. The key to the 2DBPL model is the derivation of the lensing properties of the truncated power law (TPL) model, where the surface density is a power law out to the truncation radius $\theta_\mathrm{T}$ and zero beyond. This TPL model is also useful by itself. We create mock observations of lensing by a TPL profile where the images form outside the truncation radius, so there is no mass in the annulus covered by the images. We then show that the slope of the profile interior to the images may be accurately recovered for lenses of moderate ellipticity. This demonstrates that the widely-held notion that lensing measures the slope of the mass profile in the annulus of the images, and is insensitive to the mass distribution at radii interior to the images, is incorrect., Comment: 8 pages, 3 figures, accepted to MNRAS

We present constraints on an astrophysical population of neutrino sources imposed by recent data from the IceCube neutrino observatory. By using the IceCube point source search method to model the detection of sources, our detection criterion is more sensitive than using the observation of high-energy neutrino multiplets for source identification. We frame the problem as a Bayesian hierarchical model to connect the high-level population parameters to the IceCube data, allowing us to consistently account for all relevant sources of uncertainty in our model assumptions. Our results show that sources with a local density of $n_0 \gtrsim 10^{-7}$ $\rm{Mpc}^{-3}$ and luminosity $L \lesssim 10^{43}$ erg/s are the most likely candidates, but that populations of rare sources with $n_0 \simeq 10^{-9}$ $\rm{Mpc}^{-3}$ and $L \simeq 10^{45}$ erg/s can still be consistent with the IceCube observations. We demonstrate that these conclusions are strongly dependent on the source evolution considered, for which we consider a wide range of models. In doing so, we present realistic, model-independent constraints on the population parameters that reflect our current state of knowledge from astrophysical neutrino observations. We also use our framework to investigate constraints in the case of possible source detections and future instrument upgrades. Our approach is flexible and can be used to model specific source cases and extended to include multi-messenger information., Comment: Update to address erratum published at DOI: 10.1103/PhysRevD.105.129904. Code available online at https://github.com/cescalara/nu_pop

We present a systematic analysis of the constraints $\sigma_\gamma$ on the mass profile slope $\gamma$ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio $S=100$ in the images. We analyse the results using a combination of theory and a simplified model which identifies the contribution to the constraints of the individual fluxes and positions in each of the lensed images. The main results are: 1. For any lens ellipticity, the constraints $\sigma_\gamma$ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for $\sigma_\gamma$ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems, $\sigma_\gamma$ is limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on $\gamma$ in these systems derive from the complementary positional information of the images alone, without using flux. The complementarity improves as the offset of the source from the axis increases, such that the best constraints $\sigma_\gamma<0.01$, for $S=100$, occur when the source approaches the caustic., Comment: 12 pages, 9 figures. Accepted for publication in MNRAS

In this series of papers we develop a formalism for constraining mass profiles in strong gravitational lenses with extended images, using fluxes in addition to positional information. We start in this paper with a circular power-law profile and show that the slope $\gamma$ is uniquely determined by only two observables: the flux ratio $f_1/f_2$ and the image position ratio $\theta_1/\theta_2$ of the two images. We derive an analytic expression relating these two observables to the slope, a result which does not depend on the Einstein angle or the structure or brightness of the source. We then find an expression for the uncertainty on the slope $\sigma_\gamma$ that depends only on the position ratio $\theta_1/\theta_2$ and the total S/N in the images. For example, in a system with position ratio $\theta_1/\theta_2=0.5$, S/N $=100$ and $\gamma=2$ we find that $\gamma$ is constrained to a precision of $\pm0.03$. We then test these results against a series of mock observations. We invert the images and fit an 11 parameter model, including ellipticity and position angle for both lens and source and measure the uncertainty on $\gamma$. We find agreement with the theoretical estimate for all mock observations. In future papers we will examine the radial range of the galaxy over which the constraint on the slope applies, and extend the analysis to elliptical lenses., Comment: 12 pages, 5 figures. Accepted for publication in MNRAS

Gravitational wave (GW) observations of binary neutron star (BNS) mergers can be used to measure luminosity distances and hence, when coupled with estimates for the mergers' host redshifts, infer the Hubble constant, $H_0$. These observations are, however, affected by GW measurement noise, uncertainties in host redshifts and peculiar velocities, and are potentially biased by selection effects and the mis-specification of the cosmological model or the BNS population. The estimation of $H_0$ from samples of BNS mergers with optical counterparts is tested here by using a phenomenological model for the GW strains that captures both the data-driven event selection and the distance-inclination degeneracy, while being simple enough to facilitate large numbers of simulations. A rigorous Bayesian approach to analyzing the data from such simulated BNS merger samples is shown to yield results that are unbiased, have the appropriate uncertainties, and are robust to model mis-specification. Applying such methods to a sample of $N \simeq 50$ BNS merger events, as LIGO+Virgo could produce in the next $\sim 5$ years, should yield robust and accurate Hubble constant estimates that are precise to a level of $\sim 2$ km s$^{-1}$ Mpc$^{-1}$, sufficient to reliably resolve the current tension between local and cosmological measurements of $H_0$., Comment: 21 pages (including eight-page appendices); 9 figures. Matches version accepted by PRD

We present a Bayesian hierarchical model which enables a joint fit of the ultra-high-energy cosmic ray (UHECR) energy spectrum and arrival directions within the context of a physical model for the UHECR phenomenology. In this way, possible associations with astrophysical source populations can be assessed in a physically and statistically principled manner. The importance of including the UHECR energy data and detection effects is demonstrated through simulation studies, showing that the effective GZK horizon is significantly extended for typical reconstruction uncertainties. We also verify the ability of the model to fit and recover physical parameters from CRPropa 3 simulations. Finally, the model is used to assess the fraction of the the publicly available dataset of 231 UHECRs detected by the Pierre Auger Observatory (PAO) which are associated with the Fermi-LAT 2FHL catalogue, a set of starburst galaxies and Swift-BAT hard X-ray sources. We find association fractions of 9.5 (+2.4,-5.9), 22.7 (+6.6, -12.4) and 22.8 (+6.6, -8.0) per cent for the 2FHL, starburst galaxies and Swift-BAT catalogues respectively., Comment: Update to match published version

The Gaia mission will provide precise astrometry for an unprecedented number of white dwarfs (WDs), encoding information on stellar evolution, Type Ia supernovae progenitor scenarios, and the star formation and dynamical history of the Milky Way. With such a large data set, it is possible to infer properties of the WD population using only astrometric and photometric information. We demonstrate a framework to accomplish this using a mock data set with SDSS ugriz photometry and Gaia astrometric information. Our technique utilises a Bayesian hierarchical model for inferring properties of a WD population while also taking into account all observational errors of individual objects, as well as selection and incompleteness effects. We demonstrate that photometry alone can constrain the WD population's distributions of temperature, surface gravity and phenomenological type, and that astrometric information significantly improves determination of the WD surface gravity distribution. We also discuss the possibility of identifying unresolved binary WDs using only photometric and astrometric information., Comment: 11 pages, 9 figures

The Hubble constant ($H_0$) estimated from the local Cepheid-supernova (SN) distance ladder is in 3-$\sigma$ tension with the value extrapolated from cosmic microwave background (CMB) data assuming the standard cosmological model. Whether this tension represents new physics or systematic effects is the subject of intense debate. Here, we investigate how new, independent $H_0$ estimates can arbitrate this tension, assessing whether the measurements are consistent with being derived from the same model using the posterior predictive distribution (PPD). We show that, with existing data, the inverse distance ladder formed from BOSS baryon acoustic oscillation measurements and the Pantheon SN sample yields an $H_0$ posterior near-identical to the Planck CMB measurement. The observed local distance ladder value is a very unlikely draw from the resulting PPD. Turning to the future, we find that a sample of $\sim50$ binary neutron star "standard sirens" (detectable within the next decade) will be able to adjudicate between the local and CMB estimates., Comment: Eight pages, four figures. v3: matches version accepted by Physical Review Letters. Code available at https://github.com/sfeeney/hh0

Estimates of the Hubble constant, $H_0$, from the distance ladder and the cosmic microwave background (CMB) differ at the $\sim$3-$\sigma$ level, indicating a potential issue with the standard $\Lambda$CDM cosmology. Interpreting this tension correctly requires a model comparison calculation depending on not only the traditional `$n$-$\sigma$' mismatch but also the tails of the likelihoods. Determining the form of the tails of the local $H_0$ likelihood is impossible with the standard Gaussian least-squares approximation, as it requires using non-Gaussian distributions to faithfully represent anchor likelihoods and model outliers in the Cepheid and supernova (SN) populations, and simultaneous fitting of the full distance-ladder dataset to correctly propagate uncertainties. We have developed a Bayesian hierarchical model that describes the full distance ladder, from nearby geometric anchors through Cepheids to Hubble-Flow SNe. This model does not rely on any distributions being Gaussian, allowing outliers to be modeled and obviating the need for arbitrary data cuts. Sampling from the $\sim$3000-parameter joint posterior using Hamiltonian Monte Carlo, we find $H_0$ = (72.72 $\pm$ 1.67) ${\rm km\,s^{-1}\,Mpc^{-1}}$ when applied to the outlier-cleaned Riess et al. (2016) data, and ($73.15 \pm 1.78$) ${\rm km\,s^{-1}\,Mpc^{-1}}$ with SN outliers reintroduced. Our high-fidelity sampling of the low-$H_0$ tail of the distance-ladder likelihood allows us to apply Bayesian model comparison to assess the evidence for deviation from $\Lambda$CDM. We set up this comparison to yield a lower limit on the odds of the underlying model being $\Lambda$CDM given the distance-ladder and Planck XIII (2016) CMB data. The odds against $\Lambda$CDM are at worst 10:1 or 7:1, depending on whether the SNe outliers are cut or modeled, or 60:1 if an approximation to the Planck Int. XLVI (2016) likelihood is used., Comment: 24 pages, 14 figures, matches version submitted to MNRAS. The model code used in this analysis is available for download at https://github.com/sfeeney/hh0

We present a search for metal absorption line systems at the highest redshifts to date using a deep (30h) VLT/X-Shooter spectrum of the z = 7.084 quasi-stellar object (QSO) ULAS J1120+0641. We detect seven intervening systems at z > 5.5, with the highest-redshift system being a C IV absorber at z = 6.51. We find tentative evidence that the mass density of C IV remains flat or declines with redshift at z < 6, while the number density of C II systems remains relatively flat over 5 < z < 7. These trends are broadly consistent with models of chemical enrichment by star formation-driven winds that include a softening of the ultraviolet background towards higher redshifts. We find a larger number of weak ( W_rest < 0.3A ) Mg II systems over 5.9 < z < 7.0 than predicted by a power-law fit to the number density of stronger systems. This is consistent with trends in the number density of weak Mg II systems at z = 2.5, and suggests that the mechanisms that create these absorbers are already in place at z = 7. Finally, we investigate the associated narrow Si IV, C IV, and N V absorbers located near the QSO redshift, and find that at least one component shows evidence of partial covering of the continuum source., Comment: 18 pages, 23 figures, accepted for publication in MNRAS

The accurate spatial location of gamma-ray bursts (GRBs) is crucial for both producing a detector response matrix (DRM) and follow-up observations by other instruments. The Fermi Gamma-ray Burst Monitor (GBM) has the largest field of view (FOV) for detecting GRBs as it views the entire unocculted sky, but as a non-imaging instrument it relies on the relative count rates observed in each of its 14 detectors to localize transients. Improving its ability to accurately locate GRBs and other transients is vital to the paradigm of multi-messenger astronomy, including the electromagnetic follow-up of gravitational wave signals. Here we present the BAyesian Location Reconstruction Of GRBs ({\tt BALROG}) method for localizing and characterising GBM transients. Our approach eliminates the systematics of previous approaches by simultaneously fitting for the location and spectrum of a source. It also correctly incorporates the uncertainties in the location of a transient into the spectral parameters and produces reliable positional uncertainties for both well-localized sources and those for which the GBM data cannot effectively constrain the position. While computationally expensive, {\tt BALROG} can be implemented to enable quick follow-up of all GBM transient signals. Also, we identify possible response problems that require attention as well as caution when using standard, public GBM DRMs. Finally, we examine the effects of including the variance in location on the spectral parameters of GRB 080916C. We find that spectral parameters change and no extra components are required when these effects are included in contrast to when we use a fixed location. This finding has the potential to alter both the GRB spectral catalogs as well as the reported spectral composition of some well-known GRBs., Comment: 22 pages, 23 figures, submitted to MNRAS

Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometric errors and parameter degeneracies, the redshift and type distributions can be recovered robustly thanks to the hierarchical nature of the model, which is not possible with common photometric redshift estimation techniques. As a result, redshift uncertainties can be fully propagated in cosmological analyses for the first time, fulfilling an essential requirement for the current and future generations of surveys., Comment: 10 pages, matches version accepted in MNRAS, including new appendix describing the effect of Bayesian shrinkage in a simplified setting

The origins of ultra-high energy cosmic rays (UHECRs) remain an open question. Several attempts have been made to cross-correlate the arrival directions of the UHECRs with catalogs of potential sources, but no definite conclusion has been reached. We report a Bayesian analysis of the 69 events from the Pierre Auger Observatory (PAO), that aims to determine the fraction of the UHECRs that originate from known AGNs in the Veron-Cety & Veron (VCV) catalog, as well as AGNs detected with the Swift Burst Alert Telescope (Swift-BAT), galaxies from the 2MASS Redshift Survey (2MRS), and an additional volume-limited sample of 17 nearby AGNs. The study makes use of a multi-level Bayesian model of UHECR injection, propagation and detection. We find that for reasonable ranges of prior parameters, the Bayes factors disfavour a purely isotropic model. For fiducial values of the model parameters, we report 68% credible intervals for the fraction of source originating UHECRs of 0.09+0.05-0.04, 0.25+0.09-0.08, 0.24+0.12-0.10, and 0.08+0.04-0.03 for the VCV, Swift-BAT and 2MRS catalogs, and the sample of 17 AGNs, respectively.

Quasars are the most luminous non-transient sources in the epoch of cosmological reionization (i.e., which ended a billion years after the Big Bang, corresponding to a redshift of z ~ 5), and are powerful probes of the inter-galactic medium at that time. This review covers current efforts to identify high-redshift quasars and how they have been used to constrain the reionization history. This includes a full description of the various processes by which neutral hydrogen atoms can absorb/scatter ultraviolet photons, and which lead to the Gunn-Peterson effect, dark gap and dark pixel analyses, quasar near zones and damping wing absorption. Finally, the future prospects for using quasars as probes of reionization are described., Comment: Book chapter in 'Understanding the Epoch of Cosmic Reionization: Challenges and Progress', Springer International Publishing, ed. Andrei Mesinger, ISBN 978-3-319-21956-1

The standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable then it is possible to use some of the data to obtain the necessary parameter distributions, the rest of the data being retained for model comparison. While such methods are not fully prescriptive, they provide a route to applying Bayesian model comparison in cosmological situations where it could not otherwise be used., Comment: 4 pages, 2 figures; to appear in Statistical Challenges in 21st Century Cosmology, Proceedings IAU Symposium No. 306, A. H. Heavens & J.-L. Starck, eds

Aims. We present a method, named photo-type, to identify and accurately classify L and T dwarfs onto the standard spectral classification system using photometry alone. This enables the creation of large and deep homogeneous samples of these objects efficiently, without the need for spectroscopy. Methods. We created a catalogue of point sources with photometry in 8 bands, ranging from 0.75 to 4.6 microns, selected from an area of 3344 deg^2, by combining SDSS, UKIDSS LAS, and WISE data. Sources with 13.0 < J < 17.5, and Y - J > 0.8, were then classified by comparison against template colours of quasars, stars, and brown dwarfs. The L and T templates, spectral types L0 to T8, were created by identifying previously known sources with spectroscopic classifications, and fitting polynomial relations between colour and spectral type. Results. Of the 192 known L and T dwarfs with reliable photometry in the surveyed area and magnitude range, 189 are recovered by our selection and classification method. We have quantified the accuracy of the classification method both externally, with spectroscopy, and internally, by creating synthetic catalogues and accounting for the uncertainties. We find that, brighter than J = 17.5, photo-type classifications are accurate to one spectral sub-type, and are therefore competitive with spectroscopic classifications. The resultant catalogue of 1157 L and T dwarfs will be presented in a companion paper., Comment: 15 pages, 12 figures, Accepted for publication in A & A

We investigate the relationship between spectral solar irradiance (SSI) and ozone in the tropical upper stratosphere. We find that solar cycle (SC) changes in ozone can be well approximated by considering the ozone response to SSI changes in a small number individual wavelength bands between 176 and 310 nm, operating independently of each other. Additionally, we find that the ozone varies approximately linearly with changes in the SSI. Using these facts, we present a Bayesian formalism for inferring SC SSI changes and uncertainties from measured SC ozone profiles. Bayesian inference is a powerful, mathematically self-consistent method of considering both the uncertainties of the data and additional external information to provide the best estimate of parameters being estimated. Using this method, we show that, given measurement uncertainties in both ozone and SSI datasets, it is not currently possible to distinguish between observed or modelled SSI datasets using available estimates of ozone change profiles, although this might be possible by the inclusion of other external constraints. Our methodology has the potential, using wider datasets, to provide better understanding of both variations in SSI and the atmospheric response., Comment: 21 pages, 4 figures, Journal of Space Weather and Space Climate (accepted), pdf version is in draft mode of Space Weather and Space Climate

We use Bayesian model comparison to determine whether extensions to Standard-Model neutrino physics -- primarily additional effective numbers of neutrinos and/or massive neutrinos -- are merited by the latest cosmological data. Given the significant advances in cosmic microwave background (CMB) observations represented by the Planck data, we examine whether Planck temperature and CMB lensing data, in combination with lower redshift data, have strengthened (or weakened) the previous findings. We conclude that the state-of-the-art cosmological data do not show evidence for deviations from the standard cosmological model (which has three massless neutrino families). This does not mean that the model is necessarily correct -- in fact we know it is incomplete as neutrinos are not massless -- but it does imply that deviations from the standard model (e.g., non-zero neutrino mass) are too small compared to the current experimental uncertainties to be inferred from cosmological data alone., Comment: 16 pages, 2 figures, small changes to match journal accepted version

The angular power spectrum is a powerful statistic for analysing cosmological signals imprinted in the clustering of matter. However, current galaxy and quasar surveys cover limited portions of the sky, and are contaminated by systematics that can mimic cosmological signatures and jeopardise the interpretation of the measured power spectra. We provide a framework for obtaining unbiased estimates of the angular power spectra of large-scale structure surveys at the largest scales using quadratic estimators. The method is tested by analysing the 600 CMASS mock catalogues constructed by Manera et al. (2013) for the Baryon Oscillation Spectroscopic Survey (BOSS). We then consider the Richards et al. (2009) catalogue of photometric quasars from the Sixth Data Release (DR6) of the Sloan Digital Sky Survey (SDSS), which is known to include significant stellar contamination and systematic uncertainties. Focusing on the sample of ultraviolet-excess (UVX) sources, we show that the excess clustering power present on the largest-scales can be largely mitigated by making use of improved sky masks and projecting out the modes corresponding to the principal systematics. In particular, we find that the sample of objects with photometric redshift $1.3 < z_p < 2.2$ exhibits no evidence of contamination when using our most conservative mask and mode projection. This indicates that any residual systematics are well within the statistical uncertainties. We conclude that, using our approach, this sample can be used for cosmological studies., Comment: 18 pages, 18 figures. Version accepted by MNRAS

A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to the standard cosmological model, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively., Comment: 34 pages, 18 figures. v3: corrected very minor typos to match published version

Fluctuations in the cosmic microwave background (CMB) contain information which has been pivotal in establishing the current cosmological model. These data can also be used to test well-motivated additions to this model, such as cosmic textures. Textures are a type of topological defect that can be produced during a cosmological phase transition in the early universe, and which leave characteristic hot and cold spots in the CMB. We apply Bayesian methods to carry out a rigorous test of the texture hypothesis, using full-sky data from the Wilkinson Microwave Anisotropy Probe. We conclude that current data do not warrant augmenting the standard cosmological model with textures. We rule out at 95% confidence models that predict more than 6 detectable cosmic textures on the full sky., Comment: 5 pages, 2 figures. v2: replaced with version accepted by PRL (minor amendments to reduce length and address referee comments)

The intergalactic medium was not completely reionized until approximately a billion years after the Big Bang, as revealed by observations of quasars with redshifts of less than 6.5. It has been difficult to probe to higher redshifts, however, because quasars have historically been identified in optical surveys, which are insensitive to sources at redshifts exceeding 6.5. Here we report observations of a quasar (ULAS J112001.48+064124.3) at a redshift of 7.085, which is 0.77 billion years after the Big Bang. ULAS J1120+0461 had a luminosity of 6.3x10^13 L_Sun and hosted a black hole with a mass of 2x10^9 M_Sun (where L_Sun and M_Sun are the luminosity and mass of the Sun). The measured radius of the ionized near zone around ULAS J1120+0641 is 1.9 megaparsecs, a factor of three smaller than typical for quasars at redshifts between 6.0 and 6.4. The near zone transmission profile is consistent with a Ly alpha damping wing, suggesting that the neutral fraction of the intergalactic medium in front of ULAS J1120+0641 exceeded 0.1., Comment: 5 pages, 4 figures; source data available at http://astro.ic.ac.uk/~mortlock/ulas_j1120+0641/

The quasar ULAS J1120+0641 at redshift z=7.085 has a highly ionised near zone which is smaller than those around quasars of similar luminosity at z~6. The spectrum also exhibits evidence for a damping wing extending redward of the systemic Lya redshift. We use radiative transfer simulations in a cosmological context to investigate the implications for the ionisation state of the inhomogeneous IGM surrounding this quasar. Our simulations show that the transmission profile is consistent with an IGM in the vicinity of the quasar with a volume averaged HI fraction of f_HI>0.1 and that ULAS J1120+0641 has been bright for 10^6--10^7 yr. The observed spectrum is also consistent with smaller IGM neutral fractions, f_HI ~ 10^-3--10-4, if a damped Lya system in an otherwise highly ionised IGM lies within 5 proper Mpc of the quasar. This is, however, predicted to occur in only ~5 per cent of our simulated sight-lines for a bright phase of 10^6--10^7 yr. Unless ULAS J1120+0641 grows during a previous optically obscured phase, the low age inferred for the quasar adds to the theoretical challenge of forming a 2x10^9 M_sol black hole at this high redshift., Comment: 5 pages, 4 figures, accepted to MNRAS letters

High redshift quasars (HZQs) with redshifts of z >~ 6 are so rare that any photometrically-selected sample of sources with HZQ-like colours is likely to be dominated by Galactic stars and brown dwarfs scattered from the stellar locus. It is impractical to reobserve all such candidates, so an alternative approach was developed in which Bayesian model comparison techniques are used to calculate the probability that a candidate is a HZQ, P_q, by combining models of the quasar and star populations with the photometric measurements of the object. This method was motivated specifically by the large number of HZQ candidates identified by cross-matching the UKIRT Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS) to the Sloan Digital Sky Survey (SDSS): in the ~1900 deg^2 covered by the LAS in the UKIDSS Seventh Data Release (DR7) there are ~10^3 real astronomical point-sources with the measured colours of the target quasars, of which only ~10 are expected to be HZQs. Applying Bayesian model comparison to the sample reveals that most sources with HZQ-like colours have P_q <~ 0.1 and can be confidently rejected without the need for any further observations. In the case of the UKIDSS DR7 LAS, there were just 88 candidates with P_q >= 0.1; these object were prioritized for reobservation by ranking according to P_q (and their likely redshift, which was also inferred from the photometric data). Most candidates were rejected after one or two (moderate depth) photometric measurements by recalculating P_q using the new data. That left seven confirmed HZQs, three of which were previously identified in the SDSS and four of which were new UKIDSS discoveries. The high efficiency of this Bayesian selection method suggests that it could usefully be extended to other HZQ surveys (e.g. searches by Pan-STARRS or VISTA) as well as to other searches for rare objects., Comment: submitted to MNRAS; 20 pages, 13 figures

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis., Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with version accepted by PRD. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchanged

The eternal inflation scenario predicts that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting LCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky to be less than 1.6 at 68% CL. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis., Comment: Companion to arXiv:1012.3667. 5 pages, 2 figures. v3: replaced with version accepted by PRL. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchanged

Star-galaxy classification is one of the most fundamental data-processing tasks in survey astronomy, and a critical starting point for the scientific exploitation of survey data. For bright sources this classification can be done with almost complete reliability, but for the numerous sources close to a survey's detection limit each image encodes only limited morphological information. In this regime, from which many of the new scientific discoveries are likely to come, it is vital to utilise all the available information about a source, both from multiple measurements and also prior knowledge about the star and galaxy populations. It is also more useful and realistic to provide classification probabilities than decisive classifications. All these desiderata can be met by adopting a Bayesian approach to star-galaxy classification, and we develop a very general formalism for doing so. An immediate implication of applying Bayes's theorem to this problem is that it is formally impossible to combine morphological measurements in different bands without using colour information as well; however we develop several approximations that disregard colour information as much as possible. The resultant scheme is applied to data from the UKIRT Infrared Deep Sky Survey (UKIDSS), and tested by comparing the results to deep Sloan Digital Sky Survey (SDSS) Stripe 82 measurements of the same sources. The Bayesian classification probabilities obtained from the UKIDSS data agree well with the deep SDSS classifications both overall (a mismatch rate of 0.022, compared to 0.044 for the UKIDSS pipeline classifier) and close to the UKIDSS detection limit (a mismatch rate of 0.068 compared to 0.075 for the UKIDSS pipeline classifier). The Bayesian formalism developed here can be applied to improve the reliability of any star-galaxy classification schemes based on the measured values of morphology statistics alone., Comment: Accepted 22 November 2010, 19 pages, 17 figures

It is possible that ultra-high energy cosmic rays (UHECRs) are generated by active galactic nuclei (AGNs), but there is currently no conclusive evidence for this hypothesis. Several reports of correlations between the arrival directions of UHECRs and the positions of nearby AGNs have been made, the strongest detection coming from a sample of 27 UHECRs detected by the Pierre Auger Observatory (PAO). However, the PAO results were based on a statistical methodology that not only ignored some relevant information (most obviously the UHECR arrival energies but also some of the information in the arrival directions) but also involved some problematic fine-tuning of the correlation parameters. Here we present a fully Bayesian analysis of the PAO data (collected before 2007 September), which makes use of more of the available information, and find that a fraction F_AGN = 0.15^(+0.10)_(-0.07) of the UHECRs originate from known AGNs in the Veron-Cetty & Veron (VCV) catalogue. The hypothesis that all the UHECRs come from VCV AGNs is ruled out, although there remains a small possibility that the PAO-AGN correlation is coincidental (F_AGN = 0.15 is 200 times as probable as F_AGN = 0.00)., Comment: MNRAS, accepted; 8 pages, 7 figures

Recent attempts to constrain cosmological variation in the fine structure constant, alpha, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for (Delta alpha)/(alpha), the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable., Comment: IAU 2009 JD9 conference proceedings. 6 pages, 2 figures. MmSAI, vol. 80 in press Paolo Molaro & Elisabeth Vangioni eds

It is possible to reliably identify white dwarfs (WDs) without recourse to spectra, instead using photometric and astrometric measurements to distinguish them from Main Sequence stars and quasars. WDs' colours can also be used to infer their intrinsic properties (effective temperature, surface gravity, etc.), but the results obtained must be interpreted with care. The difficulties stem from the existence of a solid angle degeneracy, as revealed by a full exploration of the likelihood, although this can be masked if a simple best-fit approach is used. Conversely, this degeneracy can be broken if a Bayesian approach is adopted, as it is then possible to utilise the prior information on the surface gravities of WDs implied by spectroscopic fitting. The benefits of such an approach are particularly strong when applied to outliers, such as the candidate halo and ultra-cool WDs identified by Vidrih et al. (2007). A reanalysis of these samples confirms their results for the latter sample but suggests that that most of the halo candidates are thick disk WDs in the tails of the photometric noise distribution., Comment: MNRAS in press; 19 pages, 16 figures; major revisions to text but conclusions unchanged

The UKIRT Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS) has the necessary combination of filters (Y, J, H and K), depth (Y <~ 20.2) and area coverage (~4000 deg^2) to detect several redshift z >~ 6.4 quasars. The Third Data Release (DR3) included ~1000 deg^2 of LAS observations which have so far yielded two previously known z ~= 6 quasars and two new discoveries: ULAS J0203+0012, at z = 5.72; and ULAS J1319+0950, at z = 6.13., Comment: to appear in Proceedings of the XXth Moriond Meeting: Cosmology, J. Tran Thanh Van et al., eds.; 4 pages, 2 figures

This paper has been withdrawn. It was an early draft submitted prematurely in error. A complete version is to be submitted shortly., Comment: Withdrawn. Early draft submitted prematurely in error. Complete version to be submitted shortly

The 100,000 spectra from the 2 degree Field Galaxy Redshift Survey (2dFGRS) in the 100k Public Data Release represent the largest single compilation of galaxy spectra available. By virtue of its sheer size and the properties of the photometric catalogue that defines the sample, the 2dFGRS is expected to contain a number of potentially interesting objects other than galaxies. A search of the spectra in the 100k Data Release results in a census of 55 candidate high-redshift (z > 0.3) quasars. One additional 2dFGRS spectrum of a low-redshift galaxy shows an apparent anomalous broad emission feature perhaps indicating the presence of a gravitationally lensed quasar. These objects have been identified primarily using two automated routines that we have developed specifically for this task, one of which uses a matched filter and the other a wavelet transform. A number of the quasar images possess complicated morphologies, suggesting the presence of either diffuse foreground objects along the line-of-sight or very nearby point sources. The quasar catalogue will form a target list for future absorption and lensing studies, as well as providing an assessment of the loss of quasars with non-stellar images from the companion 2dF QSO Redshift Survey., Comment: Latex 13 pages, 8 figures. Accepted for publication in MNRAS

Despite the fact that the physics of the cosmic microwave background anisotropies is most naturally expressed in Fourier space, pixelised maps are almost always used in the analysis and simulation of microwave data. A complementary approach is investigated here, in which maps are used only in the visualisation of the data, and the temperature anisotropies and polarization are only ever expressed in terms of their spherical multipoles. This approach has a number of advantages: there is no information loss (assuming a band-limited observation); deconvolution of asymmetric beam profiles and the temporal response of the instrument are naturally included; correlated noise can easily be taken into account, removing the need for additional destriping; polarization is also analysed in the same framework; and reliable estimates of the spherical multipoles of the sky and their errors are obtained directly for subsequent component separation and power spectrum estimation. The formalism required to analyse experiments which survey the full sky by scanning on circles is derived here, with particular emphasis on the Planck mission. A number of analytical results are obtained in the limit of simple scanning strategies. Although there are non-trivial computational obstacles to be overcome before the techniques described here can be implemented at high resolution, if these can be overcome the method should allow for a more robust return from the next generation of full-sky microwave background experiments., Comment: 18 pages, 2 figures. To appear in MNRAS

We present a harmonic model for the data analysis of an all-sky cosmic microwave background survey, such as Planck, where the survey is obtained through ring-scans of the sky. In this model, resampling and pixelisation of the data are avoided. The spherical transforms of the sky at each frequency, in total intensity and polarization, as well as the bright-point-source catalogue, are derived directly from the data reduced onto the rings. Formal errors and the most significant correlation coefficients for the spherical transforms of the frequency maps are preserved. A clean and transparent path from the original samplings in the time domain to the final scientific products is thus obtained. The data analysis is largely based on Fourier analysis of rings; the positional stability of the instrument's spin axis during these scans is a requirement for the data model and is investigated here for the Planck satellite. Brighter point sources are recognised and extracted as part of the ring reductions and, on the basis of accumulated data, used to build a catalogue. The analysis of the rings is performed iteratively, involving a range of geometric and detector response calibrations. The reconstructed spherical transforms of the sky form the input to the subsequent analysis stages. Although the methods in this paper were developed with the data processing for Planck in mind, many aspects should have wider application, such as in the construction of real-space pixelised maps. (Abridged), Comment: 20 pages, 9 figures. To appear in MNRAS

Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes no definite predictions about gravitational lensing. The most obvious form that MONDian lensing might take is that photons experience twice the deflection of massive particles moving at the speed of light, as in general relativity (GR). In such a theory there is no general thin-lens approximation (although one can be made for spherically-symmetric deflectors), but the three-dimensional acceleration of photons is in the same direction as the relativistic acceleration would be. In regimes where the deflector can reasonably be approximated as a single point-mass (specifically low-optical depth microlensing and weak galaxy-galaxy lensing), this naive formulation is consistent with observations. Forthcoming galaxy-galaxy lensing data and the possibility of cosmological microlensing have the potential to distinguish unambiguously between GR and MOND. Some tests can also be performed with extended deflectors, for example by using surface brightness measurements of lens galaxies to model quasar lenses, although the breakdown of the thin-lens approximation allows an extra degree of freedom. Nonetheless, it seems unlikely that simple ellipsoidal galaxies can explain both constraints. Further, the low-density universe implied by MOND must be completely dominated by the cosmological constant (to fit microwave background observations), and such models are at odds with the low frequency of quasar lenses. These conflicts might be resolved by a fully consistent relativistic extension to MOND; the alternative is that MOND is not an accurate description of the universe., Comment: MNRAS, in press; 11 pages, 10 figures

If it is hypothesised that there is no dark matter then some alternative gravitational theory must take the place of general relativity (GR) on the largest scales. Dynamical measurements can be used to investigate the nature of such a theory, but only where there is visible matter. Gravitational lensing is potentially a more powerful probe as it can be used to measure deflections far from the deflector, and, for sufficiently large separations, allow it to be treated as a point-mass. Microlensing within the local group does not yet provide any interesting constraints, as only images formed close to the deflectors are appreciably magnified, but stacking of multiple light-curves and observations of microlensing on cosmological scales may be able to discriminate between GR and non-dark matter theories. Galaxy-galaxy lensing is likely to be an even more powerful probe of gravity, with the Sloan Digital Sky Survey (SDSS) commissioning data used here to constrain the deflection law of galaxies to be A(R) propto R^(0.1 +/- 0.1) for impact parameters in the range 50 kpc < R < 1 Mpc. Together with observations of flat rotation curves, these results imply that, in any gravitational theory, photons must experience (close to) twice the deflection of massive particles moving at the speed of light (at least on these physical scales). The full SDSS data-set will also be sensitive to asymmetry in the lensing signal and variation of the deflection law with galaxy type. A detection of either of these effects would represent an independent confirmation that galaxies are dark matter-dominated; conversely azimuthal symmetry of the shear signal would rule out the typically ellipsoidal haloes predicted by most simulations of structure formation., Comment: MNRAS, in press; 5 pages, 1 figure

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe., Comment: PASA (OzLens edition), in press; 5 pages, 1 figure

The 2 degree Field (2dF) galaxy redshift survey will involve obtaining approximately 2.5 x 10^5 spectra of objects previously identified as galaxy candidates on morphological grounds. Included in these spectra should be about ten gravitationally-lensed quasars, all with low-redshift galaxies as deflectors (as the more common lenses with high-redshift deflectors will be rejected from the survey as multiple point-sources). The lenses will appear as superpositions of galaxy and quasar spectra, and both cross-correlation techniques and principal components analysis should be able to identify candidates systematically. With the 2dF survey approximately half-completed it is now viable to begin a systematic search for these spectroscopic lenses, and the first steps of this project are described here., Comment: PASA (OzLens edition), in press; 4 pages, 0 figures

It is possible to detect gravitationally-lensed quasars spectroscopically if the spectra obtained during galaxy surveys are searched for the presence of quasar emission lines. The up-coming 6 degree Field (6dF) redshift survey on the United Kingdom Schmidt Telescope (UKST) will involve obtaining 10^5 spectra of near-infrared selected galaxies to a magnitude limit of K = 13. Applying previously developed techniques implies that at least one lens should be discovered in the 6dF survey, but that as many as ten could be found if quasars typically have B_J - K = 8. In this model there could be up to fifty lensed quasars in the sample, but most of them could only be detected by infrared spectroscopy., Comment: PASA (OzLens edition), in press; 4 pages, 0 figures

If the statistics of quasar lensing are to be used to constrain the cosmological model, the various potential systematic uncertainties in the deflector population must be accounted for. One ambiguity in the lensing properties of the dominant deflectors - elliptical galaxies - is their dynamical normalisation. Assuming they can be modelled as isothermal spheres, it is shown that their mass normalisation is sufficiently high that current upper limits on the cosmological constant remain valid, and in fact probably strengthened, even if ellipticals have significant core radii., Comment: New Cosmological Data and the Values of the Fundamental Parameters, A.N. Lasenby & A. Wilkinson, eds.; 2 pages, 1 figure

Gravitationally-lensed quasars should be discovered as a by-product of large galaxy redshift surveys, being discovered spectroscopically when a low-redshift galaxy exhibits high-redshift quasar emission lines. The number of lenses expected is higher than previously estimated, mainly due to the fact that the presence of the quasar images brings faint deflector galaxies above the survey limit. Thus the a posteriori likelihood of the discovery of Q 2237+0305 in the Center for Astrophysics redshift survey is approximately 0.03. In the future, the 2 degree Field survey should yield at least 10 lensed quasars, and the Sloan Digitial Sky Survey up to 100., Comment: Gravitational Lensing: Recent Progress and Future Goals, C.S. Kochanek & T.G. Brainerd, eds., in press; 2 pages, 1 figure

The probability that high-redshift sources are gravitationally-lensed with large image separations (i.e., greater than can be produced by galactic deflectors) is determined by the cosmological population of group- and cluster-sized halos. Thus the observed frequency of wide-separation lensed quasars can be used to constrain not only the halo distribution, but also a number of cosmological parameters. A calculation of the optical depth due to collapsed, isothermal halos is a useful guide to the lens statistics, and illustrates that the number of wide-separation lenses is a sensitive probe of the mean density of the universe and the present day density variance whilst being nearly independent of the cosmological constant., Comment: Cosmological Physics with Gravitational Lensing, J.-P. Kneib, Y. Mellier, M. Moniez & J. Tran Thanh Van, eds., in press; 4 pages; 7 figures