Lens Models for Compact and Extended Sources

Details Lens Models for Compact and Extended Sources Lens Models for Compact and Extended Sources

Apr 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phdt.........6w&link_type=abstract

PhD thesis, University of Hamburg

Mathematics

Logic

4

Gravitational Lensing, Model Degeneracies, Cosmology, Hubble Constant, Radio Interferometry, Lensclean

Scientific paper

This work discusses the determination of cosmological parameters, especially the Hubble constant, from observations of gravitational lenses. The lens method has the advantage that it depends on the understanding of only very little astrophysics. This allows very robust results and makes estimates of the remaining uncertainties relatively simple. The most important contribution to possible errors is given by the mass models for the lensing galaxies. It is thus necessary to obtain good estimates of these uncertainties and to reduce them as much as possible. We present analytical calculations for a general family of power-law lens models with arbitrary angular shape plus external perturbations. The latter are parametrized as external shear. To include all constraints for optimal unresolved multiple image lens systems, we examine quadruple systems using the image positions and the three independent time-delays as constraints. It is well known that the radial mass distribution has important effects on the determination of the Hubble constant. Our calculations result in a generic and exact scaling relation for the dependence of the Hubble constant H0 on the power-law exponent of the potential's radial part beta. This scaling is the same for all lens systems in this family of models. Systematic errors in the assumed beta will therefore lead to a systematic error in H0. The effect of external shear is quantified by the new concept of a ``critical shear''. For an external shear exactly equal to this value, all time-delays vanish.
To improve the situation, the parameters of shear and radial mass distribution have to be measured accurately. Multiply imaged unresolved sources, which are commonly used for this purpose, can provide only a limited number of constraints. It is therefore important to study lens systems with extended sources, which can constrain the lens models much better. We use the lens system JVAS B0218+357 as an example and test case. This system has a measured time-delay and can thus be used to determine H0. We show that ``classical'' model fits, using only the two compact images in this system, are not sufficient to determine the position of the lensing galaxy and cannot be used to determine the Hubble constant. To exploit the extended structure of the Einstein ring which is part of this system, the LensCLEAN algorithm can be used. The main part of this thesis is devoted to this method. We discuss a number of significant improvements of LensCLEAN which were necessary to turn it into a useful tool for systems like B0218+357. The parameters of an isothermal elliptical mass model can now be constrained with sufficient accuracy to obtain a competitive result for the Hubble constant of H0 = (71 +- 5) km/s/Mpc for an Einstein-de Sitter universe. The error bar is a 2sigma confidence limit including uncertainties of time-delay and lens model. Only slightly different results are expected for non-isothermal models in the case of B0218+357.
We also present new VLBI observations of B0218+357 which for the first time show parts of the jet in the doubly imaged region. We argue that these data can be used to constrain the radial mass distribution with unprecedented accuracy. Together with the results from scheduled HST observations, B0218+357 will soon be the system with the best constrained lens model and the most robust result for the Hubble constant. It can then fulfill its expectations as a ``golden lens''.

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