The Hubble Constant from Gravitational Lensing

Refsdal (1964) showed that to first order the Hubble Constant can be measured from a multiple-image GL system, if the time delay between an image pair and the mass distribution of the deflector is known. This has prompted the monitoring of and search for new GL systems, after the discovery of the first GL system Q0957+561 (Walsh, Carswell & Weymann 1979). Only recently has the time delay in Q0957+561 been measured unambiguously (e.g. Kundic et al. 1997). Since then time delays from seven other GL systems have been reported, of which five (including Q0957+561) have 1- time-delay errors that are claimed to be less than about 10% (e.g. Schechter et al. 2000). Hence, if the uncertainty on the value of H₀ was only due to the measurement error on the time delay, the technique of gravitational lensing would already have surpassed that of the local distance-ladder techniques in accuracy, which in case of the HST Key-Project is about 10% on their final value of H₀=728 kms^-1Mpc^-1 (e.g. Feedman et al. 2001). Unfortunately, however, it is not the measurement of the time delays, but the determination of the deflector potential¹ which is at present the `bottle-neck' in the attempt to accurately determine the value of H₀ from GL systems.

To solve the latter problem, it is clear that one would like to have a significantly larger sample of GL systems with measured time delays than is currently available. This will (i) reduce the statistical error on the average value of H₀ inferred from different GL systems, which is dominated by the errors on the measured time delays, (ii) allow one to select only those GL systems for the determination of an average value of H₀ that are relatively isolated (i.e. no strong perturbing mass distributions in the surrounding field) and (iii) enable one to find systematic differences between GL systems for example due to differences in the slope of the radial mass profile or the mass-sheet degeneracy. Unfortunately, systematic uncertainties in the deflector potential (e.g. the slope of the radial mass profile) could potentially `skew' values of H₀, determined from different GL systems, in the same direction. Hence, even though the resulting statistical scatter can be relatively small (e.g. Koopmans & Fassnacht 1999), a large systematic uncertainty (i.e. a scale-factor in H₀) can remain undetected. This problem can only be solved with detailed modeling of each individual GL system, making use of all available information such as extended image structure (e.g. rings, arcs, jets), knowledge about the lens potential (e.g. the stellar velocity dispersion in the lens galaxy, rotation curves) or general ideas about the structure of galaxies (e.g. N-body simulations). Not all GL systems have this additional information readily available, however, which again stresses the need to increase the number of GL systems with measured time delays.

For this reason, the Cosmic Lens All-Sky Survey (CLASS) collaboration (e.g. Browne & Myers 2000) has started to monitor a number of GL systems over the past few years. In Sect.2, I will review results from three systems with measured time delays. In Sect.3, I shortly discuss the values of H₀ estimated from these GL systems, under some very simple assumptions. In Sect.4, I discuss future prospects, including two new programs with the Very Large Array (VLA) and Multi Element Radio-Linked Interferometer Network (MERLIN) to monitor a combined total of 14 CLASS GL systems.

© Copyright Astronomical Society of Australia 1997