Analytic time delays and H0 estimates for gravitational lenses

Hans J. Witt; Shude Mao; Charles R. Keeton

doi:https://doi.org/10.1086/317201

Analytic time delays and H₀ estimates for gravitational lenses

Hans J. Witt, Shude Mao, Charles R. Keeton

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay in proportion to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H₀; the complicated Q0957 + 561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H₀, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.

Original language	American English
Pages (from-to)	98-103
Number of pages	6
Journal	Astrophysical Journal
Volume	544
Issue number	1 PART 1
DOIs	https://doi.org/10.1086/317201
State	Published - Nov 20 2000
Externally published	Yes

ASJC Scopus subject areas

Astronomy and Astrophysics
Space and Planetary Science

Keywords

Distance scale
Gravitational lensing

Access to Document

https://doi.org/10.1086/317201

Cite this

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title = "Analytic time delays and H0 estimates for gravitational lenses",

abstract = "We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay in proportion to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H0; the complicated Q0957 + 561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.",

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AU - Mao, Shude

AU - Keeton, Charles R.

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N2 - We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay in proportion to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H0; the complicated Q0957 + 561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.

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