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.     

Degeneracy of semi-analytic solution for axially symmetric lens equations

We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when   r /ξ₀≪ 1  and ξ₀ is the scalelength of the density profile. At the strong lensing regime, which is mostly constrained by the inner part of the mass density profile, we assume ρ∝ r ^α.
A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c ₁ and the total mass M . We apply our semi-analytical model to show how the solutions of the axially symmetric lens equations are degenerated in respect to the parameters α and c ₁.
In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed.
Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter  α=[−2.0, −1.0]  .     

Bayesian galaxy shape measurement for weak lensing surveys – I. Methodology and a fast-fitting algorithm

The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP).     

The Gravitational Effects of a Celestial Body with Magnetic Charge and Moment

The gravitational effects (precession of charge-less particles and deflec-tion of light)in the gravitational field of a celestial body with magnetic charge and moment(CM)are investigated.We found that the magnetic charge always weak-ens the pure Schwarzschild effects,while the magnetic dipole moment deforms the effects in a more complicated way.     

Statistics of weak lensing at small angular scales: analytical predictions for lower order moments

Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasi-linear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcmin, for which the relevant physical length-scales are in the non-linear regime of gravitational clustering. We use the hierarchical ansatz to compute the multipoint statistics of the weak lensing convergence for these small smoothing angles. We predict the multipoint cumulants and cumulant correlators up to fourth order and compare our results with high-resolution ray-tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Ω and Λ.     

B2114+022: a distant radio source gravitationally lensed by a starburst galaxy

We have discovered a radio source (B2114+022) with a unique structure during the course of the JVAS gravitational lens survey. VLA, MERLIN, VLBA and MERLIN+EVN radio maps reveal four compact components, in a configuration unlike that of any known lens system, or, for that matter, any of the ∼15 000 radio sources in the JVAS and CLASS surveys. Three of the components are within 0.3 arcsec of each other while the fourth is separated from the group by 2.4 arcsec. The widest separation pair of components have similar radio structures and spectra. The other pair also have similar properties. This latter pair have spectra which peak at ∼5 GHz. Their surface brightnesses are much lower than expected for synchrotron self-absorbed components.
Ground-based and Hubble Space Telescope optical observations show two galaxies ( z =0.3157 and 0.5883) separated by 1.25 arcsec. The lower redshift galaxy has a post-starburst spectrum and lies close to, but not coincident with, the compact group of three radio components. No optical or infrared emission is detected from any of the radio components down to I =25 and H =23 . We argue that the most likely explanation of the B2114+022 system is that the post-starburst galaxy, assisted by the second galaxy, lenses a distant radio source producing the two wide-separation images. The other two radio components are then associated with the post-starburst galaxy. The combination of the angular sizes of these components, their radio spectra and their location with respect to their host galaxy still remains puzzling.     

A Study Of Global Monopole In Einstein–Cartan Theory

The gravitational field of a global monopole in the context of Einstein–Cartan theory is investigated. A comparison is made with the corresponding results predicted by general relativity. PACS Nos: 98.80cq; 04.20 jb; 04.50     

MESOSCALE NONLINEAR GRAVITATIONAL WAVES AND THEIR INTERACTION IN VERTICAL SHEAR FLOW*

Interaction equations of two nonlinear gravitational waves in baroclinic atmosphere are presented via multi-scale perturbation method,which can be classified into coupling nonlinear Schrodinger equations.In particular,the interaction course of two nonlinear gravitational waves of basic flow in vertical linear and quadratic shear is illustrated.Numerical calculation displays that wave amplitude enlarges and wave width narrows when two solitary gravitational waves meet and chase;that basic flow with single shear is more beneficial than that with quadratic shear to the interaction of two nonlinear wave packets;and that the interaction of two wave packets makes wave shape change more greatly and energy more dispersive,which contributes to the occurrence of changeable weather.Therefore,one of the probable mechanisms for the appearance of strong convection weather is the interaction between mesoscale nonlinear gravitational waves.