Lens Models for Compact and Extended Sources

PhD thesis, finished April 2002

ADS bibcode 2002PhDT.........6W

O. Wucknitz [1,2]

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

Abstract

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-1 Mpc-1 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".

Key words: gravitational lenses; radio astronomy; interferometry; astronomy; astrophysics

The analytical lens model degeneracy part was published in "Degeneracies and scaling relations in general power-law models for gravitational lenses". The technical LensCLEAN part (with LenTil) is published in LensClean revisited, the application to B0218+357 together with classical modelling in Models for the lens and source of B0218+357 --- A LensClean approach to determine H0

Find the talk of my PhD defence here.

Errata and updates:

  1. Equation (3.44) on page 24 mistyped: The factor has to be Dds/Ds instead of Ds/Dds.
    This does not affect any of the results.
  2. Equation (2.28) on page 9 mistyped: The sigma on the right hand side should be squared.
    This does not affect any of the results.
  3. Tables 3.1, 6.3-6.6 and 7.7: The Quint3 model is superfluous because it is equivalent to EdS. (m=3 corresponds to normal dust-like matter)
    This does not affect any of the results.
  4. Data update: The new source redshift for B0218+357 of zs=0.944 from Cohen et al. (2002, astro-ph/0209457) instead of the old 0.96 leads to values of H0 higher by 4.4 per cent. This affects Chapter 7 and 9.21.3.
  5. I made an inexcusable mistake in the scaling of the errors for the final uniformly weighted Stokes I VLA result. The errors only for this combination in Fig. 9.35 and Tab. 9.2 are significantly underestimated. This does not affect Stokes LL and RR and Stokes I with natural weighting. Since I conservatively used the combined region of uniformly and naturally weighted results for H0 (section 9.21.3), the final value does not change. Please refer to Paper II on the subject for the final numbers.
    As a result of this, the naturally weighted result is now more accurate than the uniformly weighted version. With the correct scaling, the Stokes I result does now also conform with Stokes LL and RR and with the Monte Carlo simulations for I, which were scaled correctly.
    (17 Dec 2002)
  6. The best value of x0 in Tab. 9.2 is mistyped. It should be 0.258189 instead of 0.259335 arcsec.
    (19 Dec 2002)
  7. In Eq. (9.6) on page 143 factors of muk are missing in the last two terms. They are again correctly printed in Eq. (9.9).
    (16 June 2004)
The downloadable files below reflect the official versions and are not corrected.


ADS bibcode 2002PhDT.........6W (link to ADS entry)


download published version (colour)
gzipped postscript file (5.9 MB, last change 24 Jul 2002)
unzipped postscript file (33.7 MB)
PDF file (13.1 MB, last change 24 Jul 2002)
252 pages, many colour figures.
The PDF version contains internal and external hyperlinks.
(note large files!)
The same version can be found at the Central library of the Hamburg University

download published version (b/w)
gzipped postscript file (5.1 MB, last change 24 Jul 2002)
unzipped postscript file (19.3 MB)
PDF file (12.9 MB, last change 24 Jul 2002)
252 pages, many figures, suitable for printing on b/w printers.
The PDF version contains internal and external hyperlinks.
(note large files!)

download initial version submitted to the referees
gzipped postscript file (5.9 MB, last change 14 Apr 2002)
unzipped postscript file (33.6 MB)
252 pages, many colour figures. Included only for historical reasons.
The other versions include minor updates in the bibliography etc.
(note large files!)


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