Reconstruction of Cluster Masses using Particle Based Lensing I: Application to Weak Lensing

We present Particle-Based Lensing (PBL), a new technique for gravitational lensing mass reconstructions of galaxy clusters. Traditionally, most methods have employed either a finite inversion or gridding to turn observational lensed galaxy ellipticities into an estimate of the surface mass density of a galaxy cluster. We approach the problem from a different perspective, motivated by the success of multi-scale analysis in smoothed particle hydrodynamics. In PBL, we treat each of the lensed galaxies as a particle and then reconstruct the potential by smoothing over a local kernel with variable smoothing scale. In this way, we can tune a reconstruction to produce constant signal-noise throughout, and maximally exploit regions of high information density. PBL is designed to include all lensing observables, including multiple image positions and fluxes from strong lensing, as well as weak lensing signals including shear and flexion. In this paper, however, we describe a shear-only reconstruction, and apply the method to several test cases, including simulated lensing clusters, as well as the well-studied ``Bullet Cluster'' (1E0657-56). In the former cases, we show that PBL is better able to identify cusps and substructures than are grid-based reconstructions, and in the latter case, we show that PBL is able to identify substructure in the Bullet Cluster without even exploiting strong lensing measurements. We also make our codes publicly available.Comment: Accepted for publication in ApJ; Codes available at http://www.physics.drexel.edu/~deb/PBL.htm ; 12 pages,9 figures, section 3 shortene

The Galaxy Octopole Moment as a Probe of Weak Lensing Shear Fields

In this paper, we introduce the octopole moment of the light distribution in galaxies as a probe of the weak lensing shear field. While traditional ellipticity estimates of the local shear derived from the quadrupole moment are limited by the width of the intrinsic ellipticity distribution of background galaxies, the dispersion in the intrinsic octopole distribution is expected to be much smaller, implying that the signal from this higher order moment is ultimately limited by measurement noise, and not by intrinsic scatter. We present the computation of the octopole moment and show that current observations are at the regime where the octopole estimates will soon be able to contribute to the overall accuracy of the estimates of local shear fields. Therefore, the prospects for this estimator from future datasets like the Advanced Camera for Survey and the Next Generation Space Telescope are very promising.Comment: 9 pages, 2 PostScript figures; Submitted to Astrophysical Journa

Liver Transplantation to Provide Low-Density-Lipoprotein Receptors and Lower Plasma Cholesterol in a Child with Homozygous Familial Hypercholesterolemia

A six-year-old girl with severe hypercholesterolemia and atherosclerosis had two defective genes at the low-density-lipoprotein (LDL) receptor locus, as determined by biochemical studies of cultured fibroblasts. One gene, inherited from the mother, produced no LDL receptors; the other gene, inherited from the father, produced a receptor precursor that was not transported to the cell surface and was unable to bind LDL. The patient degraded intravenously administered 125I-LDL at an extremely low rate, indicating that her high plasma LDL-cholesterol level was caused by defective receptor-mediated removal of LDL from plasma. After transplantation of a liver and a heart from a normal donor, the patient's plasma LDL-cholesterol level declined by 81 per cent, from 988 to 184 mg per deciliter. The fractional catabolic rate for intravenously administered 125I-LDL, a measure of functional LDL receptors in vivo, increased by 2.5-fold. Thus, the transplanted liver, with its normal complement of LDL receptors, was able to remove LDL cholesterol from plasma at a nearly normal rate. We conclude that a genetically determined deficiency of LDL receptors can be largely reversed by liver transplantation. These data underscore the importance of hepatic LDL receptors in controlling the plasma level of LDL cholesterol in human beings. (N Engl J Med 1984; 311: 1658–64.). © 1984, Massachusetts Medical Society. All rights reserved

Angular Radii of Stars via Microlensing

We outline a method by which the angular radii of giant and main sequence stars in the Galactic bulge can be measured to a few percent accuracy. The method combines ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise astrometric measurements of the lensed star during the event, to measure the angular radius of the source, theta_*. Dense photometric coverage of one caustic crossing yields the crossing timescale dt. Less frequent coverage of the entire event yields the Einstein timescale t_E and the angle phi of source trajectory with respect to the caustic. The photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield theta_E, the angular Einstein ring radius. Then the angular radius of the source is obtained by theta_*=theta_E(dt/t_E) sin(phi). We argue that theta_* should be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1m-class) telescopes, combined with astrometric observations with a precision of ~10 microarcsec to measure theta_E. We find that a factor of ~50 times fewer photons are required to measure theta_E to a given precision for binary-lens events than single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), ~7 min of SIM time is required to measure theta_E to ~5% accuracy for giant sources in the bulge. For main-sequence sources, theta_E can be measured to ~15% accuracy in ~1.4 hours. With 10 hrs of SIM time, it should be possible to measure theta_* to ~5% for \~80 giant stars, or to 15% for ~7 main sequence stars. A byproduct of such a campaign is a significant sample of precise binary-lens mass measurements.Comment: 13 pages, 3 figures. Revised version, minor changes, required SIM integration times revised upward by ~60%. Accepted to ApJ, to appear in the March 20, 2003 issue (v586

Children use one-to-one correspondence to establish equality after learning tocount

Humans make frequent and powerful use of external symbolsto express number exactly, leading some to question whetherexact number concepts are only available through the acqui-sition of symbolic number systems. Although prior work hasaddressed this longstanding debate on the relationship betweenlanguage and thought in innumerate populations and semi-numerate children, it has frequently produced conflicting re-sults, leaving the origin of exact number concepts unclear.Here, we return to this question by replicating methods pre-viously used to assess exact number knowledge in innumer-ate groups, such as the Pirah ̃a, with a large sample of semi-numerate US toddlers. We replicate previous findings fromboth innumerate cultures and developmental studies showingthat numeracy is linked to the concept of exact number. How-ever, we also find evidence that this knowledge is surprisinglyfragile even amongst numerate children, suggesting that nu-meracy alone does not guarantee a full understanding of exact-ness