Degeneracies and scaling relations in general power-law models for gravitational lenses

MNRAS 332 (2002) 951

DOI: 10.1046/j.1365-8711.2002.05426.x (http) or 10.1046/j.1365-8711.2002.05426.x (doi)
ADS bibcode 2002MNRAS.332..951W
astro-ph/0202376

O. Wucknitz [1,2]

  1. Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany
  2. Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DK, UK

Abstract

The time delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. For systems with accurately measured positions and time delays, the most important uncertainty is related to the mass model used. Simple parametric models like isothermal ellipsoidal mass distributions seem to provide consistent results with a reasonably small scatter when applied to several lens systems. We discuss a family of models with a separable radial power-law and an arbitrary angular dependence for the potential psi=r^beta F(theta). Isothermal potentials are a special case of these models with beta=1. An additional external shear is used to take into account perturbations from other galaxies. Using a simple linear formalism for quadruple lenses, we can derive H0 as a function of the observables and the shear. If the latter is fixed, the result depends on the assumed power-law exponent according to H0 propto (2-beta)/beta. The effect of external shear is quantified by introducing a `critical shear' gamma_c as a measure for the amount of shear that changes the result significantly. The analysis shows, that in the general case H0 and gamma_c do not depend on the position of the lens galaxy. Spherical lens models with images close to the Einstein radius with fitted external shear differ by a factor of beta/2 from shearless models, leading to H0 propto 2-beta in this case. We discuss these results and compare with numerical models for a number of real lens systems.

Key words: gravitational lensing -- quasars: individual: Q2237+0305 -- quasars: individual: PG1115+080 -- quasars: individual: RX J0911.4+0551 -- quasars: individual: B1608+656 -- distance scale

For more details, have a look at my PhD thesis.


MNRAS 332 (2002) 951 (link to online journal)
DOI (Digital Object Identifier): 10.1046/j.1365-8711.2002.05426.x (http) or 10.1046/j.1365-8711.2002.05426.x (doi)
ADS bibcode 2002MNRAS.332..951W (link to ADS entry)
astro-ph/0202376 (link to e-print archive)


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This is an electronic version of an article published in Monthly Notices of the Royal Astronomical Society: complete citation information for the final version of the paper, as published in the print edition of Monthly Notices of the Royal Astronomical Society, is available on the Blackwell Science Synergy online delivery service, accessible via the journal's Website at: http://www.blacksci.co.uk/MNR


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