The Mass distribution of the Cluster 0957+561 from Gravitational Lensing

Multiply gravitationally lensed objects with known time delays can lead to direct determinations of H$_0$ independent of the distance ladder if the mass distribution of the lens is known. Currently, the double QSO 0957+561 is the only lensed object with a precisely known time delay. The largest remaining source of systematic error in the H$_0$ determination results from uncertainty in the mass distribution of the lens which is comprised of a massive galaxy (G1) and the cluster in which it resides. We have obtained V-band CCD images from CFHT in order to measure the mass distribution in the cluster from its gravitional distorting effect on the appearance of background galaxes. We use this data to constuct a two-dimensional mass map of the field. A mass peak is detected at the $4.5\sigma$ level, offset from, but consistent with, the position of G1. Simple tests reveal no significant substructure and the mass distribution is consistent with a spherical cluster. The peak in the number density map of bright galaxies is offset from G1 similarly to the mass peak. We constructed an azimuthally averaged mass profile centered on G1 out to 2 \arcmin ($400 h^{-1}$ kpc). It is consistent with an isothermal mass distribution with a small core (r_c \approx 5 \arcsec = 17 h^{-1} kpc). The inferred mass within 1 Mpc is consistent with the dynamical mass estimate but $2\sigma$ higher than the upper limits from a ROSAT X-ray study. We discuss implications for H$_0$ in a future paper.Comment: LaTeX, aas version 4 macros. Calibration error in original led to overestimate of cluster mass. Seven out of twelve figures included. Complete paper is available at: http://www.astro.lsa.umich.edu:80/users/philf

Improved Parameters and New Lensed Features for Q0957+561 from WFPC2 Imaging

New HST WFPC2 observations of the lensed double QSO 0957+561 will allow improved constraints on the lens mass distribution and hence will improve the derived value of H$_0$. We first present improved optical positions and photometry for the known components of this lens. The optical separation between the A and B quasar images agrees with VLBI data at the 10 mas level, and the optical center of the primary lensing galaxy G1 coincides with the VLBI source G' to within 10 mas. The best previous model for this lens (Grogin and Narayan 1996) is excluded by these data and must be reevaluated. Several new resolved features are found within 10\arcsec of G1, including an apparent fold arc with two bright knots. Several other small galaxies are detected, including two which may be multiple images of each other. We present positions and crude photometry of these objects.Comment: 7 pages including 2 postscript figures, LaTeX, emulateapj style. Also available at http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Cosmic Shears Should Not Be Measured In Conventional Ways

A long standing problem in weak lensing is about how to construct cosmic shear estimators from galaxy images. Conventional methods average over a single quantity per galaxy to estimate each shear component. We show that any such shear estimators must reduce to a highly nonlinear form when the galaxy image is described by three parameters (pure ellipse), even in the absence of the point spread function (PSF). In the presence of the PSF, we argue that this class of shear estimators do not likely exist. Alternatively, we propose a new way of measuring the cosmic shear: instead of averaging over a single value from each galaxy, we average over two numbers, and then take the ratio to estimate the shear component. In particular, the two numbers correspond to the numerator and denominators which generate the quadrupole moments of the galaxy image in Fourier space, as proposed in Zhang (2008). This yields a statistically unbiased estimate of the shear component. Consequently, measurements of the n-point spatial correlations of the shear fields should also be modified: one needs to take the ratio of two correlation functions to get the desired, unbiased shear correlation.Comment: 13 pages, MNRAS in press. The title has been changed from "Ideal Cosmic Shear Estimators Do Not Exist" to the current one. Instead of showing that conventional/ideal shear estimators do not exist in the presence of PSF, we show in the current version that conventional shear estimators do not exist in convenient form

The Size Distribution of Trans-Neptunian Bodies

[Condensed] We search 0.02 deg^2 for trans-Neptunian objects (TNOs) with m<=29.2 (diameter ~15 km) using the ACS on HST. Three new objects are discovered, roughly 25 times fewer than expected from extrapolation of the differential sky density Sigma(m) of brighter objects. The ACS and other recent TNO surveys show departures from a power law size distribution. Division of the TNO sample into ``classical Kuiper belt'' (CKB) and ``Excited'' samples reveals that Sigma(m) differs for the two populations at 96% confidence. A double power law adequately fits all data. Implications include: The total mass of the CKB is ~0.010 M_Earth, only a few times Pluto's mass, and is predominately in the form of ~100 km bodies. The mass of Excited objects is perhaps a few times larger. The Excited class has a shallower bright-end size distribution; the largest objects, including Pluto, comprise tens of percent of the total mass whereas the largest CKBOs are only ~2% of its mass. The predicted mass of the largest Excited body is close to the Pluto mass; the largest CKBO is ~60 times less massive. The deficit of small TNOs occurs for sizes subject to disruption by present-day collisions, suggesting extensive depletion by collisions. Both accretion and erosion appearing to have proceeded to more advanced stages in the Excited class than the CKB. The absence of distant TNOs implies that any distant (60 AU) population must have less than the CKB mass in the form of objects 40 km or larger. The CKB population is sparser than theoretical estimates of the required precursor population for short period comets, but the Excited population could be a viable precursor population.Comment: Revised version accepted to the Astronomical Journal. Numerical results are very slightly revised. Implications for the origins of short-period comets are substantially revised, and tedious material on statistical tests has been collected into a new Appendi

Noise bias in weak lensing shape measurements

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper we investigate noise bias, a systematic error that arises from second order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general Maximum Likelihood Estimators (MLEs) in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modeled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic 6-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR of 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematics requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper.Comment: 8 pages, 3 figures, submitted to MNRA

Pencil-Beam Surveys for Trans-Neptunian Objects: Limits on Distant Populations

Two populations of minor bodies in the outer Solar System remain particularly elusive: Scattered Disk objects and Sedna-like objects. These populations are important dynamical tracers, and understanding the details of their spatial- and size-distributions will enhance our understanding of the formation and on-going evolution of the Solar System. By using newly-derived limits on the maximum heliocentric distances that recent pencil-beam surveys for Trans-Neptunian Objects were sensitive to, we determine new upper limits on the total numbers of distant SDOs and Sedna-like objects. While generally consistent with populations estimated from wide-area surveys, we show that for magnitude-distribution slopes of {\alpha} > 0.7-1.0, these pencil-beam surveys provide stronger upper limits than current estimates in literature.Comment: Submitted to Icaru

Cosmology with Weak Lensing Surveys

Weak gravitational lensing surveys measure the distortion of the image of distant sources due to the deflections of light rays by the fluctuations of the gravitational potential along the line of sight. Since they probe the non-linear matter power spectrum itself at medium redshift such surveys are complimentary to both galaxy surveys (which follow stellar light) and cosmic microwave background observations (which probe the linear regime at high redshift). Ongoing CMB experiments such as WMAP and the future Planck satellite mission will measure the standard cosmological parameters with unprecedented accuracy. The focus of attention will then shift to understanding the nature of dark matter and vacuum energy: several recent studies suggest that lensing is the best method for constraining the dark energy equation of state. During the next 5 year period ongoing and future weak lensing surveys such as the Joint Dark Energy Mission (JDEM, e.g. SNAP) or the Large-aperture Synoptic Survey Telescope (LSST) will play a major role in advancing our understanding of the universe in this direction. In this review article we describe various aspects of weak lensing surveys and how they can help us in understanding our universe.Comment: 15 pages, review article to appear in 2005 Triennial Issue of Phil. Trans.

Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales

Most of the matter in the universe is not luminous and can be observed directly only through its gravitational effect. An emerging technique called weak gravitational lensing uses background galaxies to reveal the foreground dark matter distribution on large scales. Light from very distant galaxies travels to us through many intervening overdensities which gravitationally distort their apparent shapes. The observed ellipticity pattern of these distant galaxies thus encodes information about the large-scale structure of the universe, but attempts to measure this effect have been inconclusive due to systematic errors. We report the first detection of this ``cosmic shear'' using 145,000 background galaxies to reveal the dark matter distribution on angular scales up to half a degree in three separate lines of sight. The observed angular dependence of this effect is consistent with that predicted by two leading cosmological models, providing new and independent support for these models.Comment: 18 pages, 5 figures: To appear in Nature. (This replacement fixes tex errors and typos.

Distance, Growth Factor, and Dark Energy Constraints from Photometric Baryon Acoustic Oscillation and Weak Lensing Measurements

Baryon acoustic oscillations (BAOs) and weak lensing (WL) are complementary probes of cosmology. We explore the distance and growth factor measurements from photometric BAO and WL techniques and investigate the roles of the distance and growth factor in constraining dark energy. We find for WL that the growth factor has a great impact on dark energy constraints but is much less powerful than the distance. Dark energy constraints from WL are concentrated in considerably fewer distance eigenmodes than those from BAO, with the largest contributions from modes that are sensitive to the absolute distance. Both techniques have some well determined distance eigenmodes that are not very sensitive to the dark energy equation of state parameters w_0 and w_a, suggesting that they can accommodate additional parameters for dark energy and for the control of systematic uncertainties. A joint analysis of BAO and WL is far more powerful than either technique alone, and the resulting constraints on the distance and growth factor will be useful for distinguishing dark energy and modified gravity models. The Large Synoptic Survey Telescope (LSST) will yield both WL and angular BAO over a sample of several billion galaxies. Joint LSST BAO and WL can yield 0.5% level precision on ten comoving distances evenly spaced in log(1+z) between redshift 0.3 and 3 with cosmic microwave background priors from Planck. In addition, since the angular diameter distance, which directly affects the observables, is linked to the comoving distance solely by the curvature radius in the Friedmann-Robertson-Walker metric solution, LSST can achieve a pure metric constraint of 0.017 on the mean curvature parameter Omega_k of the universe simultaneously with the constraints on the comoving distances.Comment: 15 pages, 9 figures, details and references added, ApJ accepte