Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SN Ia). When corrected with the light-curve shape (LCS), the peak magnitude of SN Ia provides a standard candle with an uncertainty in apparent magnitude of $\Delta m\simeq 0.1-0.2$. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared to that expected from its LCS and redshift. The average detection rate for SN Ia with a significant mismatch of $\ge2\Delta m$ behind a cluster at $z\simeq0.05-0.15$ is about $1-2$ supernovae per cluster per year at $J,I,R\lesssim25-26$. Since SNe are point-like sources for a limited period, they can experience significant microlensing by MACHOs in the intracluster medium. Microlensing events caused by MACHOs of $\sim10^{-4} M_\odot$ are expected to have time scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow to separate them. Microlensing events due to MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ($z\lesssim0.05$) per year is $\sim 0.02 (f/0.01)$, where $f$ is the fraction of the cluster mass in MACHOs of masses $10^{-7} < M_{macho}/M_\odot < 10^{-4}$.Comment: Accepted for publication in the MNRA

How to Plant a Merger Tree

We investigate several approaches for constructing Monte Carlo realizations of the merging history of virialized dark matter halos (``merger trees'') using the extended Press-Schechter formalism. We describe several unsuccessful methods in order to illustrate some of the difficult aspects of this problem. We develop a practical method that leads to the reconstruction of mean quantities such as the conditional and overall mass functions as given by the Press-Schechter model. This method is convenient, computationally efficient, and works for any power spectrum or background cosmology. In addition, we investigate statistics that describe the distribution of the number of progenitors and their masses as a function of redshift.Comment: 13 pages, LaTeX, 10 postscript figures. To appear in MNRAS. Changed to MNRAS format with inlined figures. Minor changes in text and figures to match published version. No significant changes in conten

Large-Scale Mass Distribution Behind the Galactic Plane

We map the smoothed mass-density distribution in the Galactic zone of avoidance (zoa), within 6000\kms of the Local Group, using potent reconstruction from peculiar velocities of galaxies. The interpolation into the zoa is based on the assumed gravitational nature of the velocity field implying a potential flow. The main dynamical features at a distance r=4000 km/s are (a) the peak of the Great Attractor connecting Centaurus and Pavo at l=330, (b) a moderate bridge connecting Perseus-Pisces and Cepheus at l= 140, and (c) an extension of a large void from the southern Galactic hemisphere into the zoa near the direction of Puppis, l=220-270. We find a strong correlation between the mass density and the IRAS and optical galaxy density at $b=+-20, which indicates that the main dynamical features in the zoa should also be seen in galaxy surveys through the Galactic plane. The gravitational acceleration at the Local Group, based on the mass distribution out to 6000 km/s, is strongly affected by the mass distribution in the zoa: its direction changes by 31 when the |b| < 20 zoa is included, bringing it to within 4 +- 19 of the CMB dipole.Comment: (10 pages, 8 figures, compressed and uudecoded PostScript 1.3Mbyte

Simulating Our Cosmological Neighborhood: Mock Catalogs for Velocity Analysis

We describe the construction of an N-body simulation that mimics the true velocity and mass-density fields in a box of side 256\hmpc about the Local Group , and the production of mock catalogs that mimic in detail current catalogs of redshifts and peculiar velocities. Our main purpose is to provide a tool for developing and testing reconstruction methods, but the different components of the method can be used on their own in other applications. The initial conditions are based on the IRAS 1.2Jy redshift survey, assuming that galaxies trace mass and \Omega=1. A density field smoothed is recovered from the redshift survey, using quasi-linear theory and a power-preserving filter. The corresponding potential field is traced back to the linear regime using the Zel'dovich-Bernoulli equation. Small-scale power is added by means of constrained realization to mimic fluctuations on galactic scales. The gravitating system is evolved forward in time with a PM code of 2\hmpc resolution. The result reproduces the real dynamical structures on large scales and the statistical properties of the structure down to galactic scales. "Galaxies" are identified via a linear biasing scheme (b=1.35) and they are divided into "spirals" and "ellipticals" to obey Dressler's morphology-density relation. The galaxies are assigned internal-velocity parameters and absolute magnitudes scattered about an assumed mean Tully-Fisher relation. They are then "observed" as magnitude-limited samples, trying to mimic the selection criteria of the data sets constituting the Mark III catalog of peculiar velocities. Artificial IRAS 1.2Jy redshift surveys are also compiled. The simulations and mock catalogs will be made available electronically as bench marks for testing reconstruction methods.Comment: 27 pages, Accepted for publication in the Astrophysical Journal. Text only, retrieve text and figures by anonymous ftp to ftp://cfata4.harvard.edu/pub/tsafrir/fgcat_pp.uu (2.7Mb

Lensing by Lyman Limit Systems: Determining the Mass to Gas Ratio

We present a new method to determine the total mass-to-neutral gas ratio in Lyman-limits systems. The method exploits the relation between the neutral hydrogen column density and the magnification of background sources due to the weak gravitational lensing that these systems induce. Because weak lensing does not provide a direct measure of mass, one must use this relation in a statistical sense to solve for the average mass-to-gas ratio and its distribution. We use a detailed mock catalog of quasars (sources) and Lyman-limit systems (lenses) to demonstrate the applicability of this approach through our ability to recover the parameter. This mock catalog also allows us to check for systematics in the method and to sketch its limitations. For a universal constant mass-to-gas ratio and a sample of N quasars, we obtain an unbiased estimate of its value with 95% confidence limits (independent of its actual value) of +/- 140 {10^5/N)^0.5.Comment: 20 pages, 11 figures submitted to Ap

Blind decomposition of transmission light microscopic hyperspectral cube using sparse representation

Abstract-In this paper, we address the problem of fully automated decomposition of hyperspectral images for transmission light microscopy. The hyperspectral images are decomposed into spectrally homogeneous compounds. The resulting compounds are described by their spectral characteristics and optical density. We present the multiplicative physical model of image formation in transmission light microscopy, justify reduction of a hyperspectral image decomposition problem to a blind source separation problem, and provide method for hyperspectral restoration of separated compounds. In our approach, dimensionality reduction using principal component analysis (PCA) is followed by a blind source separation (BSS) algorithm. The BSS method is based on sparsifying transformation of observed images and relative Newton optimization procedure. The presented method was verified on hyperspectral images of biological tissues. The method was compared to the existing approach based on nonnegative matrix factorization. Experiments showed that the presented method is faster and better separates the biological compounds from imaging artifacts. The results obtained in this work may be used for improving automatic microscope hardware calibration and computer-aided diagnostics