Gravitational Lenses and the Hubble Constant : Present and Future

L. J. Goicoechea1, and E. Mediavilla2

1Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander, Cantabria, Spain; goicol@besaya.unican.es
2 Instituto de Astrofisica de Canarias, E-38200 La Laguna (Tenerife), Spain; emg@iac.es, aoscoz@iac.es, mserra@iac.es, jgb@iac.es


For a multiple QSO, the propagation time from the source to the observer varies from one image to another, and this difference ($\Delta\tau$) can be measured when the source is variable. In general, assuming a flat universe without cosmological constant, the parameter $\Delta\tau$ x $H_0$ depends on the redshifts of the lens and the source, as well as the positions and fluxes of the individual images. However, this parameter is not related to the basic observations (redshifts, angular positions and fluxes) in a single way. Firstly, the observations of multiple images of the same source are used to infer a lens model : the source position and the adjustable parameters that appear in the picture of the deflector (King profile, etc.), and secondly, $H_0$ is deduced from $\Delta\tau$, the basic observations and the lens model corresponding to the lens picture.

A golden system (which is suitable for determining $H_0$) must be a multiple QSO with well resolved images and verifying some properties : (1) visible lensing objects, (2) simple lens with simple picture, (3) measurable source variability and (4) absence of strong short timescale microlensing. The best determined $\Delta\tau$ is that for the famous Twin QSO, which verifies (1), (3) and (4). For this system, the lens is complex (a giant elliptical galaxy plus a cluster of galaxies). In spite of the problems with the choice of a "good" picture, by using recent lens models, a ten percent measurement of $H_0$ is attainable. In this short review, we discuss the present quasi-golden systems and the perspectives in a near future.


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