Magnification Cross-section Research Articles

Magnification Cross Sections for the Elliptic Umbilic Caustic Surface

In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ − 2 for fold caustics and μ − 2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as μ − 2.5 in the two-image region and μ − 2 in the four-image region, where μ is the total unsigned magnification. In both cases our results are supported both numerically and analytically.

Strong lensing cross-sections for isothermal models. I. Finite source effects in the circular case

The strong galaxy-galaxy lensing produces highly magnified and distorted images of background galaxies in the form of arcs and Einstein rings. Statistically, these effects are quantified, for example, in the number counts of highly luminous sub-millimeter galaxies and of gravitational arcs. Two key quantities to model these statistics are the magnification and the arc cross sections. These are usually computed using either the circular infinitesimal source approximation or ray-tracing simulations for sources of finite size. In this work, we use an analytic solution for gravitational arcs to obtain these cross sections as a function of image magnification and length-to-width ratio in closed form, for finite sources. These analytical solutions provide simple interpretations to the numerical results, can be employed to test the computational codes, and can be used for fast a computation of the abundance of distant sources and arcs. In this paper, the lens is modeled by a Singular Isothermal Sphere, which is an excellent approximation to radial density profile of Early-Type galaxies, and the sources are also axisymmetric. We derive expressions for the geometrical properties of the images, such as the area and several definitions of length and width. We obtain the magnification cross section in exact form and derive a simple analytic approximation covering the arc and Einstein ring regimes. The arc cross section is obtained down to the formation of an Einstein ring and given in terms of elementary functions. Perturbative expansions of these results are worked out, showing explicitly the correction terms for finite sources.

Gravitational lensing effects on submillimetre galaxy counts

We study the effects on the number counts of submillimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross-section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalization σ8). We show that the ellipticity does not strongly affect the magnification cross-section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two-halo-population model is explored where galaxies are modelled as a singular isothermal sphere profile and clusters as a Navarro, Frenk and White profile. We find that the transition mass between the two has modest effects on the lensing probability. The cosmological parameter σ8 alters the abundance of haloes and therefore affects our results. Compared with other methods, our model is simpler and more realistic. The conclusions of previous works confirm that gravitational lensing is a natural explanation for the number count excess at the bright end.

Lensing magnification: implications for counts of submillimetre galaxies and SZ clusters

We study lensing magnification of source galaxies by intervening galaxy groups and clusters using a halo model. Halos are modeled with truncated NFW profiles with ellipticity added to their lensing potential and propagated to observable lensing statistics. We present the formalism to calculate observable effects due to a distribution of halos of different masses at different redshifts along the l ine of sight. We calculate the effects of magnification on the number counts of high-redshift galaxies. Using BLAST survey data for submillimeter galaxies (SMGs), we find that magnification affects the steep, high flux par t of the counts by about 60%. The effect becomes much stronger if the intrinsic distribution is signi ficantly steeper than observed. We also consider the effect of this high-redshift galaxy population on contaminating the Sunyaev-Zel'dovich (SZ) signal of massive clusters using the halo model approach. We find that for the majority of clusters expected to be detected with ongoing SZ surveys, there is significant contamination from the Poisson noise due to background SMGs. This contr ibution can be comparable to the SZ increment for typical clusters and can also contaminate the SZ decrement of low mass clusters. Thus SZ observations, especially for the increment part of the SZ spectrum, need to include careful modeling of this irreducible contamination for mass estimation. Lensing further enhances the contamination, especially close to the cores of massive clusters and for very disturbed clusters with large magnification cross-section.

Reduction of etched AlGaAs sidewall roughness by oxygen-enhanced wet thermal oxidation

The authors demonstrate that the oxidation smoothing of sidewall roughness of dry-etched Al0.3Ga0.7As ridge structures is enabled through a modified wet thermal oxidation process which involves the addition of dilute amounts of O2 to the water vapor ambient. High magnification cross-section and top-view scanning electron microscope imagings both before and after oxide removal clearly show a substantial reduction of photolithography- and dry-etching-induced sidewall roughness (from σ∼100nm down to σ∼1–2nm), occurring only with the participation of added O2. The smoothing process provides means to realize high-index-contrast GaAs-based optical waveguides with both low bend and scattering losses.

Discs in early-type lensing galaxies: effects on magnification ratios and measurements ofH0

Observations of early-type galaxies, both in the local Universe and in clusters at medium redshifts, suggest that these galaxies often contain discs or disc-like structures. Using the results of Kelson et al. for the incidence of disc-components among the galaxies in the redshift z = 0.33 cluster CL 1358+62, we investigate the effect of disc structures on the lensing properties of early-type galaxies. Statistical properties, like magnification cross-sections and the expected number of quad (four-image) lens systems, are not affected greatly by the inclusion of discs that contain less than similar to10 per cent of the total stellar mass. However, the properties of individual lens systems are affected. We estimate that 10-30 per cent of all quad-lens systems, with early-type deflector galaxies, would be affected measurably by the presence of disc components. Intriguingly, the image magnification ratios are altered significantly. The amplitude of the predicted change is sufficient to explain the observed magnification ratios in systems like B1422+231 without requiring compact substructure. Furthermore, time-delays between images also change; fitting a bulge-only model to early-type lenses that in fact contain a disc would yield a value of the Hubble constant H-0 that is systematically too low by similar to25 per cent.

Gravitational lensing of extended high redshift sources by dark matter haloes

ABSTRA C T High-redshift galaxies and quasi-stellar objects (QSOs) are most likely to be strongly lensed by intervening haloes between the source and the observer. In addition, a large fraction of lensed sources is expected to be seen in the submillimetre region, as a result of the enhanced magnification bias on the steep intrinsic number counts. We extend in three directions Blain’s earlier study of this effect. First, we use a modification of the Press ‐ Schechter mass function and detailed lens models to compute the magnification probability distribution. We compare the magnification crosssections of populations of singular isothermal spheres and Navarro, Frenk & White (NFW) haloes and find that they are very similar, in contrast to the image-splitting statistics which were recently investigated in other studies. The distinction between the two types of density profile is therefore irrelevant for our purposes. Secondly, we discuss quantitatively the maximum magnification, mmax, that can be achieved for extended sources (galaxies) with realistic luminosity profiles, taking into account the possible ellipticity of the lensing potential. We find that mmax plausibly falls into the range 10‐30 for sources of 1‐10 h 21 kpc effective radius at redshifts within 1‐4. Thirdly, we apply our model for the lensing magnification to a class of sources following the luminosity evolution typical for a unified scheme of QSO formation. As a result of the peculiar steepness of their intrinsic number counts, we find that the lensed source counts at a fiducial wave length of 850mm can exceed the unlensed counts by several orders of magnitude at flux densities *100 mJy, even with a conservative choice of the maximum magnification.

Strong gravitational lensing by multiple galaxies

We discuss strong gravitational lensing by multiple objects along any line of sight. The probability for strong gravitational lensing by more than one lens is small, but a number of strong lens systems in which more than one separate lens contribute significantly to the lensing potential will be detected in the large sample of lens systems compiled with new instruments. Using multi-lens ray-tracing, we estimate the likelihood for gravitational lensing by two lenses at different redshifts and investigate typical image geometries and magnification cross-sections. We find that, for a cosmology with Omega (M) = 0.3 and Omega (Lambda) = 0.7, about one in 20 lens systems consists of two lenses with merging caustics. Multiple lens systems differ from single lenses as the presence of a second lens in close proximity along the line of sight leads to a strongly asymmetric potential, which increases the multiple imaging cross-section and significantly changes the image configuration. The external shear induced by a second nearby galaxy, group or cluster can significantly affect image positions even for more widely separated lens pairs. Both of these effects must be accounted for in lens modelling. We also show how the presence of aligned discs in the pair of lensing galaxies can lead to very large high-magnification cross-sections. Lensing by more than one galaxy along the line of sight can lead to interesting image configurations. Such systems will be important in future, both for constraining lens models of individual systems and for statistical lensing.

Transmission Electron Microscopy Study of Y2O3 Nanotips Grown on LaAlO3

Y2O3 is a super refractory oxide with high thermal stability and finds various applications in optics and microelectronic devices. Recently, Eu-activated Y2O3 films attracted much research interest due to its promising applications in flat panel field emission displays. Epitaxial Y2O3:Eu thin films have been grown on LaA1O3(LAO). in this paper we report a transmission electron microscopy (TEM) study of Y2O3 nano tip-structure grown on LAO by pulsed laser deposition using stoichiometric YBa2Cu3O7-σ.a target under a low oxygen pressure. The experimental work was conducted within a JEOL2010F TEM equipped with an ED AX system.Fig.l is a low magnification cross-section TEM image of the nano-tip structure grown on (001) LAO. The lattice parameters of the tips were calculated to be that of Y2O3 by using LAO as a standard for indexing the diffraction patterns. Nano electron beam diffraction patterns from the tips along [100] and [110] axis are shown in Fig.2a and Fig.2b, respectively, in agreement with the simulated ones using bulk Y2O3 structure.

Statistics of Gravitational Microlensing Magnification. I. Two‐dimensional Lens Distribution

The propagation of light from distant sources through a distribution of clumpy matter, acting as lenses, produces multiple images that contribute to the total brightness of the observed macroimages. In this paper, we refine the theory of gravitational microlensing for a planar distribution of point masses. In an accompanying paper, we extend the analysis to a three-dimensional lens distribution. In the two-dimensional case, we derive the probability distribution of macroimage magnification, P(A), at A - 1 τ2 for a low optical depth lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual point-mass plus lenses. A lens perturbed by weak shear S produces an astroid-shaped caustic. We show that the magnification cross section σ(A|S) of the plus weak-shear lens obeys a simple scaling property, and we provide a useful analytic approximation for the cross section. By convolving this cross section with the probability distribution of the shear due to the neighboring point masses, we obtain a caustic-induced feature in P(A) that also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A ≈ 2/τ. In the low-magnification (A - 1 1) limit, the macroimage consists of a single bright primary image and a large number of faint secondary images formed close to each of the point masses. The magnifications of the primary and the secondary images can be strongly correlated. Taking into account the correlations, we derive P(A) for low magnification and find that P(A) has a peak of amplitude ≈ 0.16/τ2 at A - 1 ≈ 0.84τ2. The low-magnification distribution matches smoothly the distribution for A - 1 τ2 in the overlapping regimes A - 1 τ2 and A 1/τ. Finally, after a discussion of the correct normalization for P(A), we combine the results and obtain a practical semianalytic expression for the macroimage magnification distribution P(A). This semianalytic distribution is in qualitative agreement with the results of previous numerical simulations, but the latter show stronger caustic-induced features at moderate A (1.5 A 10) for τ as small as 0.1. We resolve this discrepancy by reexamining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approximately 1 - exp (-8τ). For τ = 0.1, the fraction is surprisingly high: ≈ 55%. A simple criterion for the low optical depth analysis to be valid is τ , though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.05.

Cellular basis for volume related wall thickness changes in the rat left ventricle

Nine arrested rat hearts fixed by glutaraldehyde perfusion of the coronary arteries were studied in vertical cross-sections of the left ventricle by phase contrast microscopy. The number of fibers per unit area in the wall and the number of fibers between the epicardium and endocardium were measured and correlated with ventricular volume and wall thickness. Average center to center fiber separation was derived from these measurements. Increasing ventricular volume is associated with a decrease in wall thickness and fiber diameter which follows theoretical predictions. The relationship between these measurements, however, presents a dimensional paradox in that the decreases in wall thickness are 3 to 4 times greater than the decrease observed in separation of fiber centers. Thus, an increase in fixation volume from 0.03 to 0.60 ml results in a 68% decrease in wall thickness, while center to center fiber separation decreases only 20%. Changes in wall thickness are therefore mainly accounted for by internal rearrangement of the disposition of fibers composing the ventricular wall. A mechanism for such rearrangements is illustrated by low magnification cross-sections of the ventricular wall which demonstrate open spaces or sliding planes between groups of muscle fibers. A volume related alteration in the orientation of these sliding planes is noted.