@article{WucknitzSperhake2004,
  author    = {Wucknitz, Olaf and Sperhake, U.},
  title     = {Deflection of light and particles by moving gravitational lenses},
  issn      = {0556-2821},
  year      = {2004},
  abstract  = {Various authors have investigated the problem of light deflection by radially moving gravitational lenses, but the results presented so far do not appear to agree on the expected deflection angles. Some publications claim a scaling of deflection angles with 1-v to first order in the radial lens velocity v, while others obtained a scaling with 1-2 v. In this paper we generalize the calculations for arbitrary lens velocities and show that the first result is the correct one. We discuss the seeming inconsistency of relativistic light deflection with the classical picture of moving test particles by generalizing the lens effect to test particles of arbitrary velocity, including light as a limiting case. We show that the effect of radial motion of the lens is very different for slowly moving test particles and light and that a critical test particle velocity exists for which the motion of the lens has no effect on the deflection angle to first order. An interesting and not immediately intuitive result is obtained in the limit of a highly relativistic motion of the lens towards the observer, where the deflection angle of light reduces to zero. This phenomenon is elucidated in terms of moving refractive media. Furthermore, we discuss the dragging of inertial frames in the field of a moving lens and the corresponding Lense-Thirring precession. in order to shed more light on the geometrical effects in the surroundings of a moving mass. In a second part we discuss the effect of transversal motion on the observed redshift of lensed sources. We demonstrate how a simple kinematic calculation explains the effects for arbitrary velocities of the lens and test particles. Additionally we include the transversal motion of the source and observer to show that all three velocities can be combined into an effective relative transversal velocity similar to the approach used in microlensing studies},
  language  = {en}
}
@article{WucknitzBiggsBrowne2004,
  author    = {Wucknitz, Olaf and Biggs, Andy D. and Browne, Ian W. A.},
  title     = {Models for the lens and source of B0218+357 : a LensClean approach to determine H-0},
  issn      = {0035-8711},
  year      = {2004},
  abstract  = {B0218 + 357 is one of the most promising systems to determine the Hubble constant from time-delays in gravitational lenses. Consisting of two bright images, which are well resolved in very long baseline interferometry (VLBI) observations, plus one of the most richly structured Einstein rings, it potentially provides better constraints for the mass model than most other systems. The main problem left until now was the very poorly determined position of the lensing galaxy. After presenting detailed results from classical lens modelling, we apply our improved version of the LENSCLEAN algorithm which for the first time utilizes the beautiful Einstein ring for lens modelling purposes. The primary result using isothermal lens models is a now very well defined lens position of (255 +/- 6, 119 +/- 4) mas relative to the A image, which allows the first reliable measurement of the Hubble constant from the time-delay of this system. The result of H-0 = (78 +/- 6) km s(-1) Mpc(-1) (2sigma) is very high compared with other lenses. It is, however, compatible with local estimates from the Hubble Space Telescope (HST) key project and with WMAP results, but less prone to systematic errors. We furthermore discuss possible changes of these results for different radial mass profiles and find that the final values cannot be very different from the isothermal expectations. The power-law exponent of the potential is constrained by VLBI data of the compact images and the inner jet to be beta = 1.04 +/- 0.02, which confirms that the mass distribution is approximately isothermal (corresponding to beta = 1), but slightly shallower. The effect on H-0 is reduced from the expected 4 per cent decrease by an estimated shift of the best galaxy position of circa 4 mas to at most 2 per cent. Maps of the unlensed source plane produced from the best LENSCLEAN brightness model show a typical jet structure and allow us to identify the parts which are distorted by the lens to produce the radio ring. We also present a composite map which for the first time shows the rich structure of B0218 + 357 on scales ranging from mas to arcsec, both in the image plane and in the reconstructed source plane. Finally, we use a comparison of observations at different frequencies to investigate the question of possible weakening of one of the images by propagation effects and/or source shifts with frequency. The data clearly favour the model of significant 'extinction' without noticeable source position shifts. The technical details of our variant of the LENSCLEAN method are presented in the accompanying Paper I.},
  language  = {en}
}
@article{Wucknitz2004,
  author    = {Wucknitz, Olaf},
  title     = {LensClean revisited},
  issn      = {0035-8711},
  year      = {2004},
  abstract  = {We discuss the LENSCLEAN algorithm which for a given gravitational lens model fits a source brightness distribution to interferometric radio data in a similar way as standard CLEAN does in the unlensed case. The lens model parameters can then be varied in order to minimize the residuals and determine the best model for the lens mass distribution. Our variant of this method is improved in order to be useful and stable even for high dynamic range systems with nearly degenerated lens model parameters. Our test case B0218 + 357 is dominated by two bright images but the information needed to constrain the unknown parameters is provided only by the relatively smooth and weak Einstein ring. The new variant of LENSCLEAN is able to fit lens models even in this difficult case. In order to allow the use of general mass models with LENSCLEAN, we develop the new method LENTIL which inverts the lens equation much more reliably than any other method. This high reliability is essential for the use as part of LENSCLEAN. Finally a new method is developed to produce source plane maps of the unlensed source from the best LENSCLEAN brightness models. This method is based on the new concept of 'dirty beams' in the source plane. The application to the lens B0218 + 357 leads to the first useful constraints for the lens position and thus to a result for the Hubble constant. These results are presented in the accompanying Paper II, together with a discussion of classical lens modelling for this system},
  language  = {en}
}