Why Is the Fraction of Four‐Image Radio Lens Systems So High?

Rusin, D.; Tegmark, Max

doi:10.1086/320955

Cited by 74 publications

(133 citation statements)

References 68 publications

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“…The inclusion of nonsphericity in the lenses is beyond the scope of this paper. Although previous studies found that the introduction of ellipticities d0.2 into nearly singular profiles has little effect on the lensing cross section and image magnification, the strong magnification bias will favor a high fraction of four-image lenses (Rusin & Tegmark 2001), as well as an increase in the number of multiple image systems. One consequence of this effect will be to double the expected microlensing rate (see x 6).…”

Section: Lens Populationmentioning

confidence: 82%

Gravitational Lensing of the Sloan Digital Sky Survey High‐Redshift Quasars

Wyithe

Loeb

2002

ApJ

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We predict the effects of gravitational lensing on the color-selected flux-limited samples of z s $ 4:3 and z s e5:8 quasars, recently published by the Sloan Digital Sky Survey (SDSS). Our main findings are the following: (1) The lensing probability should be 1-2 orders of magnitude higher than for conventional surveys. The expected fraction of multiply imaged quasars is highly sensitive to redshift and the uncertain slope of the bright end of the luminosity function, h . For h ¼ 2:58 (3.43) we find that at z s $ 4:3 and i Ã < 20:0 the fraction is $4% (13%), while at z s $ 6 and z Ã < 20:2 the fraction is $7% (30%). (2) The distribution of magnifications is heavily skewed; sources having the redshift and luminosity of the SDSS z s e5:8 quasars acquire median magnifications of medðl obs Þ $ 1:1 1:3 and mean magnifications of hl obs i $ 5 50. Estimates of the quasar luminosity density at high redshift must therefore filter out gravitationally lensed sources. (3) The flux in the Gunn-Peterson trough of the highest redshift (z s ¼ 6:28) quasar is known to be f < 3 Â 10 À19 ergs s À1 cm À2 Å À1 . Should this quasar be multiply imaged, we estimate a 40% chance that light from the lens galaxy would have contaminated the same part of the quasar spectrum with a higher flux. Hence, spectroscopic studies of the epoch of reionization need to account for the possibility that a lens galaxy, which boosts the quasar flux, also contaminates the Gunn-Peterson trough. (4) Microlensing by stars should result in $ 1 3 of multiply imaged quasars in the z s e5:8 catalog varying by more than 0.5 mag over the next decade. The median emission-line equivalent width of multiply imaged quasars would be lowered by $20% with respect to the intrinsic value because of differential magnification of the continuum and emission-line regions.

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Section: Lens Populationmentioning

confidence: 82%

Gravitational Lensing of the Sloan Digital Sky Survey High‐Redshift Quasars

Wyithe

Loeb

2002

ApJ

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“…5 The data give the shape of the light distribution, while what we need is the shape of the mass distribution. The mass and light shapes may not be correlated on a case-by-case basis, but for our purposes it is sufficient to assume that their distributions are similar (see Rusin & Tegmark 2001). 6 It is possible to obtain an analytic NFW model by putting the elliptical symmetry in the potential rather than the density (e.g., Golse & Kneib 2002;Meneghetti et al 2003).…”

Section: Definitionsmentioning

confidence: 99%

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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“…However, symmetric models only produce two-image lenses and cannot be used to interpret the statistics of each morphology separately. More recently, numerical studies have been performed with more realistic elliptical lens models (e.g., King & Browne 1996;Wallington & Narayan 1993;Kochanek 1996;Keeton, Kochanek, & Seljak 1997;Rusin & Tegmark 2001). While numerical calculations are certainly valuable, they tend to obscure the roles of competing contributions to what is being calculated.…”

Section: Introductionmentioning

confidence: 99%

Analytic Expressions for Mean Magnification by a Quadrupole Gravitational Lens

Finch

Carlivati²,

Winn

et al. 2002

ApJ

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We derive an analytic expression for the mean magnification due to strong gravitational lensing, using a simple lens model: a singular isothermal sphere embedded in an external shear field. We compute separate expressions for two-image and four-image lensing. For four-image lensing, the mean magnification takes a particularly simple form:, where is the external shear. We compare our analytic results with a numerical evaluation of the full magnification distribution. The results can be used to understand the magnification bias that favors the discovery of four-image systems over two-image systems in fluxlimited lens surveys.

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Why Is the Fraction of Four‐Image Radio Lens Systems So High?

Cited by 74 publications

References 68 publications

Gravitational Lensing of the Sloan Digital Sky Survey High‐Redshift Quasars

Gravitational Lensing of the Sloan Digital Sky Survey High‐Redshift Quasars

Gravitational Lensing Magnification without Multiple Imaging

Analytic Expressions for Mean Magnification by a Quadrupole Gravitational Lens

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