David M. Goldberg

Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy-galaxy lensing, examining isothermal sphere and Navarro-Frenk-White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence-flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.

The Microwave Background Bispectrum, Paper I: Basic Formalism

In this paper, we discuss the potential importance of measuring the CMB anisotropy bispectrum. We develop a formalism for computing the bispectrum and for measuring it from microwave background maps. As an example, we compute the bispectrum resulting from the 2nd order Rees-Sciama effect, and find that is undetectable with current and upcoming missions.

Gravitational Shear, Flexion, and Strong Lensing in Abell 1689

We present a gravitational lensing analysis of the galaxy cluster Abell 1689, incorporating measurements of the weak shear, flexion, and strong lensing induced in background galaxies. This is the first time that a shapelet technique has been used to reconstruct the distribution of mass in this cluster and the first time that a flexion signal has been measured using cluster members as lenses. From weak shear measurements alone, we generate a nonparametric mass reconstruction, which shows significant substructure corresponding to groups of galaxies within the cluster. In addition, our galaxy-galaxy flexion signal demonstrates that the cluster galaxies can be well fit by a singular isothermal sphere model with a characteristic velocity dispersion of σv = (295 ± 40) km s^(-1). We identify a major, distinct dark matter clump, offset by 40 h^(-1) kpc from the central cluster members, which was not apparent from shear measurements alone. This secondary clump is present in a parametric mass reconstruction using flexion data alone, and its existence is suggested in a nonparametric reconstruction of the cluster using a combination of strong and weak lensing. As found in previous studies, the mass profile obtained by combining weak and strong lensing data shows a much steeper profile than that obtained from only weak lensing data.

Hormonal Interactions in the Regulation of Blood Glucose

Publisher Summary This chapter discusses hormonal interactions in the regulation of blood glucose. The regulation of the blood glucose concentration is a well-recognized function of the endocrine system. The efficacy of the various control mechanisms is reflected by the very limited excursions in blood glucose observed in normal humans. In normal man, the bursts of glucagon secretion precipitated by feeding pure protein prevent the inhibition in glucose production and the hypoglycemia that would otherwise accompany protein-stimulated insulin secretion. In contrast, sustained hyperglucagonemia fails to cause glucose intolerance or worsening of preexisting diabetes so long as endogenous or exogenous insulin is available. In the case of insulin, the down regulation of the insulin receptor has been observed to occur in hyperinsulinemic states. The glucagon infusion fails to alter specific binding of insulin or growth hormone, indicating the specificity of the effect of hyperglucagonemia on glucagon binding. Glucagon-induced hyperglycemia can, however, be observed either in circumstances of absolute insulin deficiency or when tissue sensitivity to this hormone is increased. The synergistic nature of these hormone–hormone interactions with respect to raising circulating plasma glucose levels may constitute the mechanism for stress hyperglycemia.

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 in which 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 data sets such as the Advanced Camera for Survey and the Next Generation Space Telescope are very promising.

The Mass Function of Void Galaxies in the Sloan Digital Sky Survey Data Release 2

We estimate the mass function of void galaxies in the second public data release of the Sloan Digital Sky Survey from a sample of 1000 galaxies with local density contrasts of ?v < -0.6. The galaxy sample is split into ellipticals and spirals using a color-S?rsic index criterion. We estimate the virial masses of ellipticals using the measured spectral line widths along with the observed size. Projection effects and uncertainties in halo properties make mass estimates of spirals more difficult. We use an inversion of the Tully-Fisher relation to estimate the isothermal rotational velocity and introduce a scaling factor to estimate the halo extent. We then fit the measured mass function against a theoretical Press-Schechter model and find that the distribution of galaxies in voids appears to be nearly unbiased compared to the mass.

Determination of the Baryon Density from Large-Scale Galaxy Redshift Surveys

We estimate the degree to which the baryon density, Ωb, can be determined from the galaxy power spectrum measured from large-scale galaxy redshift surveys, and in particular, the Sloan Digital Sky Survey. A high baryon density will cause wiggles to appear in the power spectrum, which should be observable at the current epoch. We assume linear theory on scales ≥20 h-1 Mpc and do not include the effects of redshift distortions, evolution, or biasing. With an optimum estimate of P(k) to k ~ 2π/(20 h-1 Mpc), the 1 σ uncertainties in Ωb are roughly 0.07 and 0.016 in flat and open (Ω0 = 0.3) cosmological models, respectively. This result suggests that it should be possible to test for consistency with big bang nucleosynthesis estimates of Ωb if we live in an open universe.

Flexion and Skewness in Map Projections of the Earth

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large-scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map-projection metric; flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts, allowing us to compare different world-map projections. We find that the Winkel-Tripel projection (already adopted for world maps by National Geographic) has low distortion on most measures and excellent quality overall.

Using Astrometry to Deblend Microlensing Events

We discuss the prospect of deblending microlensing events by observing astrometric shifts of the lensed stars. Since microlensing searches are generally performed in very crowded fields, it is expected that stars will be confusion limited rather than limited by photon statistics. By performing simulations of events in crowded fields, we find that if we assume a dark lens and that the lensed star obeys a power-law luminosity function, n(L) ∝ L-β, over half the simulated events show a measurable astrometric shift. Our simulations included 20,000 stars in a 256 × 256 Nyquist-sampled CCD frame. For β = 2, we found that 58% of the events were significantly blended (F*/Ftot ≤ 0.9), and of those, 73% had a large astrometric shift (≥0.5 pixels). Likewise, for β = 3, we found that 85% of the events were significantly blended and that 85% of those had large shifts. Moreover, since the shift may be used to determine the true position of a source star with respect to the observed point-spread function, a high-resolution follow-up survey may be used to identify the source star and determine the blending fraction directly.

The galaxy cluster concentration–mass scaling relation

Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration (