Analytic Expressions for Mean Magnification by a Quadrupole Gravitational Lens

Finch, Tehani K.; Carlivati, Lisa P.; Winn, Joshua N.; Schechter, Paul L.

doi:10.1086/342163

Cited by 24 publications

(51 citation statements)

References 22 publications

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“…The high fraction of four-image lenses (50% of JVAS/ CLASS lenses have four or more images) compared to the expectations for simple ellipsoidal lenses in reasonable tidal fields (20%-30%) has been a long-standing puzzle in understanding the statistics of gravitational lenses (King & Browne 1996;Kochanek 1996b;Keeton et al 1997;Finch et al 2002;Rusin & Tegmark 2001). We find that the problem is largely explained by the changes in the caustic structures produced by including the effects of nearby satellite galaxies when we normalize the abundance of these satellites to match the abundance of satellites in the JVAS/CLASS lens sample.…”

Section: Discussionmentioning

confidence: 99%

The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses

Cohn¹,

Kochanek

2004

ApJ

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Surveys for gravitational lens systems have typically found a significantly larger fraction of lenses with four (or more) images than are predicted by standard ellipsoidal lens models (50% versus 25%-30%). We show that including the effects of smaller satellite galaxies, with an abundance normalized by the observations, significantly increases the expected number of systems with more than two images and largely explains the discrepancy. The effect is dominated by satellites with $20% the luminosity of the primary lens, in rough agreement with the typical luminosities of the observed satellites. We find that the lens systems with satellites cannot be dropped from estimates of the cosmological model based on gravitational lens statistics without significantly biasing the results.

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Section: Discussionmentioning

confidence: 99%

The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses

Cohn¹,

Kochanek

2004

ApJ

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“…( Finch et al 2002). For < 1 3 the radial caustic completely encloses the tangential caustic, so all sources outside the radial caustic and all images outside the 1-2 transition locus are singly imaged.…”

Section: Appendix Maximum Singly Imaged Magnification For Isothermal mentioning

confidence: 97%

Gravitational Lensing Magnification without Multiple Imaging

Keeton

Kuhlen

Haiman

2005

ApJ

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Gravitational lensing can amplify the apparent brightness of distant sources. Images that are highly magnified are often part of multiply imaged systems, but we consider the possibility of having large magnifications without additional detectable images. In rare but nonnegligible situations, lensing can produce a single highly magnified image; this phenomenon is mainly associated with massive cluster-scale halos (k10 13.5 M ). Alternatively, lensing can produce multiply imaged systems in which the extra images are either unresolved or too faint to be detectable. This phenomenon is dominated by galaxies and lower mass halos (P10 12 M ) and is very sensitive to the inner density profile of the halos. Although we study the general problem, we customize our calculations to four quasars at redshift z % 6 in the Sloan Digital Sky Survey (SDSS), for which Richards et al. (2004) have ruled out the presence of extra images down to an image splitting of Á ¼ 0B3 and a flux ratio of f ¼ 0:01. We predict that 9%-29% of all z % 6 quasars that are magnified by a factor of > 10 would lack detectable extra images, with 5%-10% being true singly imaged systems. The maximum of 29% is reached only in the unlikely event that all low-mass (P10 10 M ) halos have highly concentrated (isothermal) profiles. In more realistic models in which dwarf halos have flatter (Navarro-Frenk-White) inner profiles, the maximum probability is $10%. We conclude that the probability that all four SDSS quasars are magnified by a factor of 10 is P10 À4 . The only escape from this conclusion is if there are many (>10) multiply imaged z % 6 quasars in the SDSS database that have not yet been identified, which seems unlikely. In other words, lensing cannot explain the brightnesses of the z % 6 quasars, and models that invoke lensing to avoid having billion-solar-mass black holes in the young universe are not viable.

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“…d Kovner (1987);Finch et al (2002); Keeton, Gaudi & Petters (2003). e Chang & Refsdal (1979, 1984Schneider, Ehlers & Falco (1992); An & Evans (2006).…”

Section: General Review For the Five Quad Lensesmentioning

confidence: 99%

Cusp summations and cusp relations of simple quad lenses

Zhang

Lin

2015

Monthly Notices of the Royal Astronomical Society

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We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total images of a given source is a constant, we calculate the cusp summations for the five lens models. We find that the cusp summations are always larger than 0 for source on the major cusps, while can be larger or smaller than 0 for source on the minor cusps. We also find that if these lenses tend to the circular lens, the major and minor cusp summations will have infinite values, and with positive and negative signs respectively. The cusp summations do not change significantly if the sources are slightly deviated from the cusps. In addition, through the magnification invariants, we also derive the analytical signed cusp relations on the axes for three lens models. We find that both on the major and the minor axes the larger the lenses deviated from the circular lens, the larger the signed cusp relations. The major cusp relations are usually larger than the absolute minor cusp relations, but for some lens models with very large deviation from circular lens, the minor cusp relations can be larger than the major cusp relations.

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Analytic Expressions for Mean Magnification by a Quadrupole Gravitational Lens

Cited by 24 publications

References 22 publications

The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses

The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses

Gravitational Lensing Magnification without Multiple Imaging

Cusp summations and cusp relations of simple quad lenses

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