VLA Observations of the Gravitational Lens System Q2237+0305

We report observations of the four-image gravitational lens system Q2237+0305 with the VLA at 20 cm and 3.6 cm. The quasar was detected at both frequencies (\approx 0.7 mJy) with a flat spectrum. All four lensed images are clearly resolved at 3.6 cm, and the agreement of the radio and optical image positions is excellent. No radio emission is detected from the lensing galaxy, and any fifth lensed quasar image must be fainter than \sim 20% of the A image flux density. Since the optical quasar images are variable and susceptible to extinction, radio flux ratios provide the best measurement of the macrolensing magnification ratios. The radio B/A and C/A image flux ratios are consistent with the observed range of optical variations, but the D/A ratio is consistently higher in the radio than in the optical. The radio ratios are consistent with magnification ratios predicted by lens models, and weaken alternative interpretations for Q2237+0305. More accurate radio ratios can distinguish between the models, as well as improve our understanding of both microlensing and extinction in this system.Comment: 1 postscript file, 13 pages. To appear in AJ (1996.09), Submitted 1996.03.13, Accepted 1996.05.2

Results from the CASTLES Survey of Gravitational Lenses

We show that most gravitational lenses lie on the passively evolving fundamental plane for early-type galaxies. For burst star formation models (1 Gyr of star formation, then quiescence) in low Omega_0 cosmologies, the stellar populations of the lens galaxies must have formed at z_f > 2. Typical lens galaxies contain modest amounts of patchy extinction, with a median differential extinction for the optical (radio) selected lenses of E(B-V) = 0.04 (0.07) mag. The dust can be used to determine both extinction laws and lens redshifts. For example, the z_l=0.96 elliptical lens in MG0414+0534 has an R_V=1.7 +/- 0.1 mean extinction law. Arc and ring images of the quasar and AGN source host galaxies are commonly seen in NICMOS H band observations. The hosts are typically blue, L < L_* galaxies.Comment: 12 pages, 10 figures, from Proceedings of the 9th Annual Astrophysics Conference in Maryland, After the Dark Ages: When Galaxies Were Youn

A branching fuzzy-logic classifier for building optimization

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 109-110).We present an input-output model that learns to emulate a complex building simulation of high dimensionality. Many multi-dimensional systems are dominated by the behavior of a small number of inputs over a limited range of input variation. Some also exhibit a tendency to respond relatively strongly to certain inputs over small ranges, and to other inputs over very large ranges of input variation. A branching linear discriminant can be used to isolate regions of local linearity in the input space, while also capturing the effects of scale. The quality of the classification may be improved by using a fuzzy preference relation to classify input configurations that are not well handled by the linear discriminant.by Matthew A. Lehar.Ph.D

Lensed Quasar Hosts

Gravitational lensing assists in the detection of quasar hosts by amplifying and distorting the host light away from the unresolved quasar core images. We present the results of HST observations of 30 quasar hosts at redshifts 1 < z < 4.5. The hosts are small in size (r_e <~ 6 kpc), and span a range of morphologies consistent with early-types (though smaller in mass) to disky/late-type. The ratio of the black hole mass (MBH, from the virial technique) to the bulge mass (M_bulge, from the stellar luminosity) at 1<z<1.7 is broadly consistent with the local value; while MBH/M_bulge at z>1.7 is a factor of 3--6 higher than the local value. But, depending on the stellar content the ratio may decline at z>4 (if E/S0-like), flatten off to 6--10 times the local value (if Sbc-like), or continue to rise (if Im-like). We infer that galaxy bulge masses must have grown by a factor of 3--6 over the redshift range 3>z>1, and then changed little since z~1. This suggests that the peak epoch of galaxy formation for massive galaxies is above z~1. We also estimate the duty cycle of luminous AGNs at z>1 to be ~1%, or 10^7 yrs, with sizable scatter.Comment: 8 pages, 6 figures, review article with C. Impey at the conference on "QSO Host Galaxies: Evolution and Environment", Aug. 29-Sep. 2, 2005, Lorentz Center, Leiden, The Netherland