Surface brightness measurements for APM galaxies

This paper considers some simple surface brightness (SB) estimates for galaxies in the Automated Plate Measuring Machine (APM) catalogue in order to derive homogeneous SB data for a very large sample of faint galaxies. The isophotal magnitude and area are used to estimate the central surface brightness and total magnitude based on the assumption of an exponential SB profile. The surface brightness measurements are corrected for field effects on each UK Schmidt plate and the zero-point of each plate is adjusted to give a uniform sample of SB and total magnitude estimates over the whole survey. Results are obtained for 2.4 million galaxies with blue photographic magnitudes brighter than b_J = 20.5 covering 4300 deg^2 in the region of the south galactic cap. Almost all galaxies in our sample have central surface brightness in the range 20 to 24 b_J mag per arcsec^2. The SB measurements we obtain are compared to previous SB measurements and we find an acceptable level of error of +/- 0.2 b_J mag per arcsec^2. The distribution of SB profiles is considered for different galaxy morphologies for the bright APM galaxies. We find that early-type galaxies have more centrally concentrated profiles.Comment: 14 pages, 17 figures, accepted for publication in MNRA

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap

Topology of Neutral Hydrogen Within the Small Magellanic Cloud

In this paper, genus statistics have been applied to an HI column density map of the Small Magellanic Cloud in order to study its topology. To learn how topology changes with the scale of the system, we provide the study of topology for column density maps at varying resolution. To evaluate the statistical error of the genus we randomly reassign the phases of the Fourier modes while keeping the amplitudes. We find, that at the smallest scales studied ($40 {pc}\leq\lambda\leq 80 {pc}$) the genus shift is in all regions negative, implying a clump topology. At the larger scales ($110 {pc}\leq\lambda\leq 250 {pc}$) the topology shift is detected to be negative in 4 cases and positive (``swiss cheese'' topology) in 2 cases. In 4 regions there is no statistically significant topology shift at large scales

A New Estimate of the Hubble Time with Improved Modeling of Gravitational Lenses

This paper examines free-form modeling of gravitational lenses using Bayesian ensembles of pixelated mass maps. The priors and algorithms from previous work are clarified and significant technical improvements are made. Lens reconstruction and Hubble Time recovery are tested using mock data from simple analytic models and recent galaxy-formation simulations. Finally, using published data, the Hubble Time is inferred through the simultaneous reconstruction of eleven time-delay lenses. The result is H_0^{-1}=13.7^{+1.8}_{-1.0} Gyr.Comment: 24 pages, 9 figures. Accepted to Ap

Cosmological Parameter Determination in Free-Form Strong Gravitational Lens Modeling

We develop a novel statistical strong lensing approach to probe the cosmological parameters by exploiting multiple redshift image systems behind galaxies or galaxy clusters. The method relies on free-form mass inversion of strong lenses and does not need any additional information other than gravitational lensing. Since in free-form lensing the solution space is a high-dimensional convex polytope, we consider Bayesian model comparison analysis to infer the cosmological parameters. The volume of the solution space is taken as a tracer of the probability of the underlying cosmological assumption. In contrast to parametric mass inversions, our method accounts for the mass-sheet degeneracy, which implies a degeneracy between the steepness of the profile and the cosmological parameters. Parametric models typically break this degeneracy, introducing hidden priors to the analysis that contaminate the inference of the parameters. We test our method with synthetic lenses, showing that it is able to infer the assumed cosmological parameters. Applied to the CLASH clusters, the method might be competitive with other probes.Comment: 11 pages, 5 figures. Accepted for publication in MNRA

Two-Dimensional Topology of the 2dF Galaxy Redshift Survey

We study the topology of the publicly available data released by the 2dFGRS. The 2dFGRS data contains over 100,000 galaxy redshifts with a magnitude limit of b_J=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75 degree strips) but only within a narrow range of declination (10 degree and 15 degree strips). This allows measurements of the two-dimensional genus to be made. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions are found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble Volume LCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 sigma level. The average genus curve of the 2dFGRS agrees well with that extracted from the LCDM mock catalogs. We compare the amplitude of the 2dFGRS genus curve to the amplitude of a Gaussian random field with the same power spectrum as the 2dFGRS and find, contradictory to results for the 3D genus of other samples, that the amplitude of the GRF genus curve is slightly lower than that of the 2dFGRS. This could be due to a a feature in the current data set or the 2D genus may not be as sensitive as the 3D genus to non-linear clustering due to the averaging over the thickness of the slice in 2D. (Abridged)Comment: Submitted to ApJ A version with Figure 1 in higher resolution can be obtained from http://www.physics.drexel.edu/~hoyle

Nonlinear stochastic biasing from the formation epoch distribution of dark halos

We propose a physical model for nonlinear stochastic biasing of one-point statistics resulting from the formation epoch distribution of dark halos. In contrast to previous works on the basis of extensive numerical simulations, our model provides for the first time an analytic expression for the joint probability function. Specifically we derive the joint probability function of halo and mass density contrasts from the extended Press-Schechter theory. Since this function is derived in the framework of the standard gravitational instability theory assuming the random-Gaussianity of the primordial density field alone, we expect that the basic features of the nonlinear and stochastic biasing predicted from our model are fairly generic. As representative examples, we compute the various biasing parameters in cold dark matter models as a function of a redshift and a smoothing length. Our major findings are (1) the biasing of the variance evolves strongly as redshift while its scale-dependence is generally weak and a simple linear biasing model provides a reasonable approximation roughly at R\simgt 2(1+z)\himpc, and (2) the stochasticity exhibits moderate scale-dependence especially on R\simlt 20\himpc, but is almost independent of $z$. Comparison with the previous numerical simulations shows good agreement with the above behavior, indicating that the nonlinear and stochastic nature of the halo biasing is essentially understood by taking account of the distribution of the halo mass and the formation epoch.Comment: 34 pages, 11 figures, ApJ (2000) in pres

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur

A Counts-in-Cells Analysis of Lyman-break Galaxies at z~3

We have measured the counts-in-cells fluctuations of 268 Lyman-break galaxies with spectroscopic redshifts in six 9 arcmin by 9 arcmin fields at z~3. The variance of galaxy counts in cubes of comoving side length 7.7, 11.9, 11.4 h^{-1} Mpc is \sigma_{gal}^2 ~ 1.3\pm0.4 for \Omega_M=1, 0.2 open, 0.3 flat, implying a bias on these scales of \sigma_{gal} / \sigma_{mass} = 6.0\pm1.1, 1.9\pm0.4, 4.0\pm0.7. The bias and abundance of Lyman-break galaxies are surprisingly consistent with a simple model of structure formation which assumes only that galaxies form within dark matter halos, that Lyman-break galaxies' rest-UV luminosities are tightly correlated with their dark masses, and that matter fluctuations are Gaussian and have a linear power-spectrum shape at z~3 similar to that determined locally (\Gamma~0.2). This conclusion is largely independent of cosmology or spectral normalization \sigma_8. A measurement of the masses of Lyman-break galaxies would in principle distinguish between different cosmological scenarios.Comment: Accepted for publication in ApJ, 16 pages including 4 figure