A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

True ‘gravitational lens’ effect for cylindrical deflectors

We show that gravitational light deflection is truly equivalent to the optical effect of a prism and a thin diverging lens when the massive deflector has cylindrical symmetry. We then investigate the possibility of cosmological measurements analogous to those proposed by Refsdal in the spherically-symmetric case.This work was partially supported by FINEP, CNPq, and CAPES.     

Self-consistent gravitational lens reconstruction

We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellization of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellization can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.     

A systematic review of strong gravitational lens modeling software

Despite expanding research activity in gravitational lens modeling, there is no particular software which is considered a standard. Much of the gravitational lens modeling software is written by individual investigators for their own use. Some gravitational lens modeling software is freely available for download but is widely variable with regard to ease of use and quality of documentation. This review of 13 software packages was undertaken to provide a single source of information. Gravitational lens models are classified as parametric models or non-parametric models, and can be further divided into research and educational software. Software used in research includes the GRAVLENS package (with both gravlens and lensmodel), Lenstool, LensPerfect, glafic, PixeLens, SimpLens, Lensview, and GRALE. In this review, GravLensHD, G-Lens, Gravitational Lensing, lens and MOWGLI are categorized as educational programs that are useful for demonstrating various aspects of lensing. Each of the 13 software packages is reviewed with regard to software features (installation, documentation, files provided, etc.) and lensing features (type of model, input data, output data, etc.) as well as a brief review of studies where they have been used. Recent studies have demonstrated the utility of strong gravitational lensing data for mass mapping, and suggest increased use of these techniques in the future. Coupled with the advent of greatly improved imaging, new approaches to modeling of strong gravitational lens systems are needed. This is the first systematic review of strong gravitational lens modeling software, providing investigators with a starting point for future software development to further advance gravitational lens modeling research.     

The continuous limit of the multiple lens effect and the optical scalar equation

We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. We define a new, light-path dependent angular diameter distance     and show that it satisfies the optical scalar equation. The distance provides relations between quantities used in gravitational lensing theory (the convergence, the shear and the twist terms) and those used in scalar optics theory (the rates of expansion, shear and rotation).     

A small mass,large image separation gravitational lens model

It is shown that gravitational lensing could produce images of comparable brightness which are separated by an angular distance larger than the angular size of the Einstein ring of the lens distribution. Hence, specific lens configurations allow given image separations to be derived with significantly less mass than a standard single lens model. A specific example is supplied, a simple case of two properly positioned lenses acting instead of one. Observational consequences are discussed that would result if such a model was used to explain the candidate gravitational lens systems Hazard 1146+111 B, C and PKS 1145–071. Such a lens distribution might, in many cases, be verifiable with VLBI techniques.     

Multiwavelength focusing with the Sun as gravitational lens

The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at infinity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed.The perturbations by the solar corona plasma will significantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 10⁸ amplification factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single field. Some possible targets are considered, such as Sagitarius A observed in X and γ rays.In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericity of the sun and coronal plasma index, we derive limits within which such observations could be possible.     

A new limit on time dependence of the gravitational constant from gravity modified quantum electrodynamics

The time variation of the gravitational constantG is discussed in the light of the gravity modified form of quantum electrodynamics. From the experimental upper limit |a/| < 5 × 10^–15 yr^–1 on the time variation of the electromagnetic fine structure constant one finds |/G| < 5 × 10^–13 yr^–1.     

The resolution of the compact core of quasars and active galaxies with the gravitational lens effect

The central energy source of quasars and active galactic nuclei cannot be resolved by observation. When such a compact source is affected by gravitational micro-lensing (lensing of stars in a distant galaxy), brightness changes of the order of magnitudes may occur. Since it is an eclipse-like effect, it gives the possibility of calculating the one-dimensional source profile from the lightcurve. We present the method and the results of its application on simulated lightcurves. It should be possible to obtain information on the structure of the source on a scale smaller than 10^–3 pc. The micro gravitational lens effect gives, therefore, the only known possibility of observing directly the central energy source of quasars and active galactic nuclei.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Noise properties of gravitational lens mass reconstruction

Gravitational lensing is potentially able to observe mass-selected haloes, and to measure the projected cluster mass function. An optimal mass selection requires a quantitative understanding of the noise behaviour in mass maps. This paper is an analysis of the noise properties in mass maps reconstructed from a maximum-likelihood method.
The first part of this work is the derivation of the noise power spectrum and the mass error bars as a straightforward extension of the Kaiser & Squires algorithm for the case of a correlated noise. Very good agreement is found between these calculations and the noise properties measured in the mass reconstructions limited to non-critical clusters of galaxies. It demonstrates that Kaiser & Squires and maximum-likelihood methods have similar noise properties and that the weak lensing approximation is valid for describing these properties .
In a second stage I show that the statistics of peaks in the noise follows accurately the peak statistics of a two-dimensional Gaussian random field (using the BBKS techniques) if the smoothing aperture contains enough galaxies. This analysis provides a full procedure for deriving the significance of any convergence peak as a function of its amplitude and profile.
I demonstrate that a detailed quantitative analysis of the structures in mass maps can be carried out, and that, to a very good approximation, a mass map is the sum of the lensing signal and known two-dimensional Gaussian random noise. A straightforward application is the measurement of the projected mass function in wide-field lensing surveys, down to small mass overdensities that are individually undetectable.     

The validity of the continuum limit in the gravitational N-body problem

This paper attempts to give quantitative as well as qualitative answers to the question of the analogy between smooth potentials and N-body systems. A number of simulations were performed in both integrable and nonintegrable smooth environments and their frozen N-body analogues, and comparisons were made using a number of different tools. The comparisons took place on both statistical and pointwise levels. The results of this study suggest that microscopic chaos associated with discreteness effects is always present in N-body configurations. This chaos is different from the macroscopic chaos which is associated with the bulk potential and persists even for very large N. Although the Lyapunov exponents of orbits evolving in N-body environments do not decrease as N increases, comparisons associated with the statistical properties, as well as with the power spectra of the orbits, affirm the existence of the continuum limit.     

A new quadruple gravitational lens system: CLASS B0128+437

High-resolution MERLIN observations of a newly discovered four-image gravitational lens system, B0128+437, are presented. The system was found after a careful re-analysis of the entire CLASS data set. The MERLIN observations resolve four components in a characteristic quadruple-image configuration; the maximum image separation is 542 mas and the total flux density is 48 mJy at 5 GHz. A best-fitting lens model with a singular isothermal ellipsoid results in large errors in the image positions. A significantly improved fit is obtained after the addition of a shear component, suggesting that the lensing system is more complex and may consist of multiple deflectors. The integrated radio spectrum of the background source indicates that it is a gigahertz peaked spectrum source. It may therefore be possible to resolve structure within the radio images with deep VLBI observations and thus to constrain the lensing mass distribution better.     

A complete infrared Einstein ring in the gravitational lens system B1938 + 666

We report the discovery, using NICMOS on the Hubble Space Telescope , of an arcsec-diameter Einstein ring in the gravitational lens system B1938+666. The lensing galaxy is also detected, and is most likely an early-type galaxy. Modelling of the ring is presented and compared with the radio structure from MERLIN maps. We show that the Einstein ring is consistent with the gravitational lensing of an extended infrared component, centred between the two radio components.     

Caustic crossing in the gravitational lens Q2237+0305

The monitoring of the gravitational lens Q2237+0305 carried out by the OGLE group during 1997–2000 is analyzed. The significant light amplifications in the C and A quasar components with maxima in mid-and late 1999, respectively, are interpreted as the crossing of microlens caustics by the source. A constraint on the emitting-region size R≤10¹⁵ cm has been obtained from the light-curve shape by assuming a power-law quasar brightness distribution (r ²+R ²)^?p . To estimate the exponent p～1.2 requires refining the standard model for the quasar continuum formation in an optically thick accretion disk with p=1.5.     

Motion of quasar images by gravitational lens galaxies

Rotational motions of twin quasar images due to the motion of a gravitational lens galaxy are studied. A weak gravity field and a point mass lens are assumed. Twin images of a quasar appear and rotate when a lens galaxy passes near a straight line connecting the observer with the quasar. The positions and velocities of the quasar images are calculated using various sets of parameters.Conclusions: (1) Quasar images move a few hundred milli-arc-seconds per year or more, if the lens galaxy passes within a thousandth parsec from the line connecting the observer with the quasar, (2) the distance between the galactic center and the quasar images is about ten kilo-parsec at the most.As an example, the velocities of 0957+561 A, B1 and B2 are calculated. Even the fastest case, they are 1.5, 1.8, and 1.6×10^–5 milli-arc-second per year, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

A new gravitational lens from the MUSCLES survey: ULAS J082016.1+081216

We present observations of a new double-image gravitational lens system, ULAS J082016.1+081216, of image separation 2.3 arcsec and high (∼6) flux ratio. The system is selected from the Sloan Digital Sky Survey (SDSS) spectroscopic quasar list using new high-quality images from the UKIRT (United Kingdom Infrared Telescope) Deep Sky Survey (UKIDSS). The lensed quasar has a source redshift of 2.024, and we identify the lens galaxy as a faint red object of redshift  0.803 ± 0.001  . Three other objects from the UKIDSS survey, selected in the same way, were found not to be lens systems. Together with the earlier lens found using this method, the SDSS–UKIDSS lenses have the potential to significantly increase the number of quasar lenses found in SDSS, to extend the survey to higher flux ratios and lower separations, and to give greater completeness which is important for statistical purposes.     

The lens and source of the optical Einstein ring gravitational lens ER 0047–2808

We perform a detailed analysis of the optical gravitational lens ER 0047–2808 imaged with the Wide Field Planetary Camera 2 on the Hubble Space Telescope . Using software specifically designed for the analysis of resolved gravitational lens systems, we focus on how the image alone can constrain the mass distribution in the lens galaxy. We find that the data are of sufficient quality to strongly constrain the lens model with no a priori assumptions about the source. Using a variety of mass models, we find statistically acceptable results for elliptical isothermal-like models with an Einstein radius of 1.17 arcsec. An elliptical power-law model  (Σ∝ R ^−β)  for the surface mass density favours a slope slightly steeper than isothermal with  β= 1.08 ± 0.03  . Other models including a constant mass-to-light ratio (M/L), pure Navarro, Frenk & White halo and (surprisingly) an isothermal sphere with external shear are ruled out by the data. We find the galaxy light profile can only be fit with a Sérsic plus point-source model. The resulting total  M/L _B   contained within the images is  4.7  h ₆₅± 0.3  . In addition, we find the luminous matter is aligned with the total mass distribution within a few degrees. This is the first time a resolved optical gravitational lens image has been quantitatively reproduced using a non-parametric source.
The source, reconstructed by the software, is revealed to have two bright regions, with an unresolved component inside the caustic and a resolved component straddling a fold caustic. The angular size of the entire source is ∼0.1 arcsec and its (unlensed) Lyα flux is  3 × 10⁻¹⁷ erg s⁻¹ cm⁻²  .     

Models of the Cosmic Horseshoe gravitational lens J1004+4112

We model the extremely massive and luminous lens galaxy in the Cosmic Horseshoe Einstein ring system J1004+4112, recently discovered in the Sloan Digital Sky Survey. We use the semilinear method of Warren & Dye, which pixelizes the source surface brightness distribution, to invert the Einstein ring for sets of parametrized lens models. Here, the method is refined by exploiting Bayesian inference to optimise adaptive pixelization of the source plane and to choose between three differently parametrized models: a singular isothermal ellipsoid, a power-law model and a Navarro, Frenk & White (NFW) profile. The most probable lens model is the power law with a volume mass density  ρ∝ r ^{−1.96±0.02}  and an axis ratio of ∼0.8. The mass within the Einstein ring (i.e. within a cylinder with projected distance of ∼30 kpc from the centre of the lens galaxy) is  (5.02 ± 0.09) × 10¹² M _⊙  , and the mass-to-light ratio is ∼30. Even though the lens lies in a group of galaxies, the preferred value of the external shear is almost zero. This makes the Cosmic Horseshoe unique amongst large separation lenses, as almost all the deflection comes from a single, very massive galaxy with little boost from the environment.