New Modeling of the Lensing Galaxy and Cluster of Q0957+561: Implications for the Global Value of the Hubble Constant

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.Comment: 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue

Changes in the measured image separation of the gravitational lens system, PKS 1830-211

We present eight epochs of 43 GHz, dual-polarisation VLBA observations of the gravitational lens system PKS 1830-211, made over fourteen weeks. A bright, compact ``core'' and a faint extended ``jet'' are clearly seen in maps of both lensed images at all eight epochs. The relative separation of the radio centroid of the cores (as measured on the sky) changes by up to 87 micro arcsec between subsequent epochs. A comparison with the previous 43 GHz VLBA observations (Garrett et al. 1997) made 8 months earlier show even larger deviations in the separation of up to 201 micro arcsec. The measured changes are most likely produced by changes in the brightness distribution of the background source, enhanced by the magnification of the lens. A relative magnification matrix that is applicable on the milliarcsecond scale has been determined by relating two vectors (the ``core-jet'' separations and the offsets of the polarised and total intensity emission) in the two lensed images. The determinant of this matrix, -1.13 +/-0.61, is in good agreement with the measured flux density ratio of the two images. The matrix predicts that the 10 mas long jet, that is clearly seen in previous 15 and 8.4 GHz VLBA observations (Garrett et al. 1997, Guirado et al. 1999), should correspond to a 4 mas long jet trailing to the south-east of the SW image. The clear non-detection of this trailing jet is a strong evidence for sub-structure in the lens and may require more realistic lens models to be invoked, e.g. Nair & Garrett (2000).Comment: 8 pages, 5 figure

Prácticas en la enseñanza de las ciencias. Problemas y posibilidades

We have effected an analysis of the role attached to practical studies in teaching sciences through the study of works published on this subjetc. The work has been structured starting from the historic development, to go on with the ends and advantages and finishing it outstanding some of the aspects of what can be considered the core of practical work. Finally, we highlight the main objectives to establish these practical classes