On the number of solutions of a transcendental equation arising in the theory of gravitational lensing

The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can actually occur.Comment: 26 pages, 12 figure

Conjugate (solid/fluid) computational fluid dynamics analysis of the space shuttle solid rocket motor nozzle/case and case field joints

Three-dimensional, conjugate (solid/fluid) heat transfer analyses of new designs of the Solid Rocket Motor (SRM) nozzle/case and case field joints are described. The main focus was to predict the consequences of multiple rips (or debonds) in the ambient cure adhesive packed between the nozzle/case joint surfaces and the bond line between the mating field joint surfaces. The models calculate the transient temperature responses of the various materials neighboring postulated flow/leakpaths into, past, and out from the nozzle/case primary O-ring cavity and case field capture O-ring cavity. These results were used to assess if the design was failsafe (i.e., no potential O-ring erosion) and reusable (i.e., no excessive steel temperatures). The models are adaptions and extensions of the general purpose PHOENICS fluid dynamics code. A non-orthogonal coordinate system was employed and 11,592 control cells for the nozzle/case and 20,088 for the case field joints are used with non-uniform distribution. Physical properties of both fluid and solids are temperature dependent. A number of parametric studies were run for both joints with results showing temperature limits for reuse for the steel case on the nozzle joint being exceeded while the steel case temperatures for the field joint were not. O-ring temperatures for the nozzle joint predicted erosion while for the field joint they did not

Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity

Braneworld gravity is a model that endows physical space with an extra dimension. In the type II Randall-Sundrum braneworld gravity model, the extra dimension modifies the spacetime geometry around black holes, and changes predictions for the formation and survival of primordial black holes. We develop a comprehensive analytical formalism for far-field black hole lensing in this model, using invariant quantities to compute all geometric optics lensing observables. We then make the first analysis of wave optics in braneworld lensing, working in the semi-classical limit. We show that wave optics offers the only realistic way to observe braneworld effects in black hole lensing. We point out that if primordial braneworld black holes exist, have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which we call "attolenses," would produce interference fringes in the energy spectra of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the universe could produce similar interference effects; the probability for "attolensing" may be non-negligible. If interference fringes were observed, the fringe spacing would yield a simple upper limit on M. Detection of a primordial black hole with M <~ 1e-19 Msun would challenge general relativity and favor the braneworld model. Further work on lensing tests of braneworld gravity must proceed into the physical optics regime, which awaits a description of the full spacetime geometry around braneworld black holes.Comment: 13 pages, 3 figures; accepted in PRD; expanded discussion of prospects for observing attolensing with GLAS

What Fraction of Gravitational Lens Galaxies Lie in Groups?

We predict how the observed variations in galaxy populations with environment affect the number and properties of gravitational lenses in different environments. Two trends dominate: lensing strongly favors early-type galaxies, which tend to lie in dense environments, but dense environments tend to have a larger ratio of dwarf to giant galaxies than the field. The two effects nearly cancel, and the distribution of environments for lens and non-lens galaxies are not substantially different (lens galaxies are slightly less likely than non-lens galaxies to lie in groups and clusters). We predict that about 20% of lens galaxies are in bound groups (defined as systems with a line-of-sight velocity dispersion sigma in the range 200 < sigma < 500 km/s), and another roughly 3% are in rich clusters (sigma > 500 km/s). Therefore at least roughly 25% of lenses are likely to have environments that significantly perturb the lensing potential. If such perturbations do not significantly increase the image separation, we predict that lenses in groups have a mean image separation that is about 0.2'' smaller than that for lenses in the field and estimate that 20-40 lenses in groups are required to test this prediction with significance. The tail of the distribution of image separations is already illuminating. Although lensing by galactic potential wells should rarely produce lenses with image separations theta >~ 6'', two such lenses are seen among 49 known lenses, suggesting that environmental perturbations of the lensing potential can be significant. Further comparison of theory and data will offer a direct probe of the dark halos of galaxies and groups and reveal the extent to which they affect lensing estimates of cosmological parameters.Comment: 32 pages, 6 embedded figures; accepted for publication in Ap

Observations of Lensed Relativistic Jets as a Tool of Constraining Lens Galaxy Parameters

The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example to illustrate that there exists a great choice of model parameters adequately reproducing its observed large-scale properties but leading to a significant spread in the Hubble constant. The jet image position angle is suggested as an additional parameter that allows the range of models under consideration to be limited. It is shown that the models for which the jet image position angles differ by at least $40^o$ can be distinguished between themselves during observations on very small angular scales. The possibility of observing the geometric properties of lensed relativistic jets and measuring the superluminal velocities of knot images on time scales of several months with very long baseline space interferometers is discussed.Comment: 11 pages, 3 figures, Will be published in the Astronomy Letters, V.37, PP.483-490, 201

High resolution observations and mass modelling of the CLASS gravitational lens B1152+199

We present a series of high resolution radio and optical observations of the CLASS gravitational lens system B1152+199 obtained with the Multi-Element Radio-Linked Interferometer Network (MERLIN), Very Long Baseline Array (VLBA) and Hubble Space Telescope (HST). Based on the milliarcsecond-scale substructure of the lensed radio components and precise optical astrometry for the lensing galaxy, we construct models for the system and place constraints on the galaxy mass profile. For a single galaxy model with surface mass density Sigma(r) propto r^-beta, we find that 0.95 < beta < 1.21 at 2-sigma confidence. Including a second deflector to represent a possible satellite galaxy of the primary lens leads to slightly steeper mass profiles.Comment: 7 pages, post-referee revision for MNRA

Time delay between images of the lensed quasar UM673

We study brightness variations in the double lensed quasar UM673 (Q0142-100) with the aim of measuring the time delay between its two images. In the paper we combine our previously published observational data of UM673 obtained during the 2003 - 2005 seasons at the Maidanak Observatory with archival and recently observed Maidanak and CTIO UM673 data. We analyze the V, R and I-band light curves of the A and B images of UM673, which cover ten observational seasons from August 2001 to November 2010. We also analyze the time evolution of the difference in magnitudes between images A and B of UM673 over more than ten years. We find that the quasar exhibits both short-term (with amplitude of \sim 0.1 mag in the R band) and high-amplitude (\sim 0.3 mag) long-term variability on timescales of about several months and several years, respectively. These brightness variations are used to constrain the time delay between the images of UM673. From cross-correlation analysis of the A and B quasar light curves and error analysis we measure the mean time delay and its error of 89 \pm11 days. Given the input time delay of 88 days, the most probable value of the delay that can be recovered from light curves with the same statistical properties as the observed R-band light curves of UM673 is 95{+5/-16}{+14/-29} days (68 and 95 % confidence intervals). Analysis of the V - I color variations and V, R and I-band magnitude differences of the quasar images does not show clear evidence of the microlensing variations between 1998 and 2010.Comment: Submitted to A&A, 11 pages, 9 figure

Q1208+1011: Search for the lensing galaxy

We present a high-resolution spectrum of the high redshift, lensed quasar Q1208+1101, obtained with the echellette spectrograph on the Multiple Mirror Telescope. We examine the new and published spectra and provide an updated list of high-confidence metal-line absorption systems at z=1.1349, 2.8626, 2.9118, 2.9136, 2.9149. Combining this with a simple model of the gravitational lens system allows us to constrain the possible lens redshifts. The high-redshift (z > 2.5) and low-redshift (z < 0.4) candidates can be ruled out with high confidence. The current spectra effectively probe about 40% of the redshift range in which the lens is expected. In that range, there is only one known metal-line absorption system, an MgII absorber at z=1.1349. We consider the possibility that this system is the lensing galaxy and discuss the implied parameters of the galaxy.Comment: Latex 24 pages, 6 figures. accepted for publication in Astrophysical Journa

Improved Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, $\phi(\sigma)$, to derive lens statistics constraints on $\Omega_\Lambda$ and $\Omega_m$. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of $\phi(\sigma)$ and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of $\Omega_\Lambda = 0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of $\Omega_\Lambda<0.86$. If $\phi(\sigma)$ instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for $\Omega_\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound $\Omega_\Lambda<0.89$. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe.Comment: 35 pages, 15 figures, to be published in Ap

The Quasar Pair Q 1634+267 A, B and the Binary QSO vs. Dark Lens Hypotheses

Deep HST/NICMOS H (F160W) band observations of the z=1.96 quasar pair Q 1634+267A,B reveal no signs of a lens galaxy to a 1 sigma threshold of approximately 22.5 mag. The minimum luminosity for a normal lens galaxy would be a 6L_* galaxy at z > 0.5, which is 650 times greater than our detection threshold. Our observation constrains the infrared mass-to-light ratio of any putative, early-type, lens galaxy to (M/L)_H > 690h_65 (1200h_65) for Omega_0=0.1 (1.0) and H_0=65h_65 km/s/Mpc. We would expect to detect a galaxy somewhere in the field because of the very strong Mg II absorption lines at z=1.1262 in the Q 1634+267 A spectrum, but the HST H-band, I-band (F785LP) and V-band (F555W) images require that any associated galaxy be very under-luminous less than 0.1 L^*_H (1.0 L^*_I) if it lies within less than 40 h^{-1} (100 h^{-1}) kpc from Q 1634+267 A,B. While the large image separation (3.86 arcsec) and the lack of a lens galaxy strongly favor interpreting Q 1634+267A,B as a binary quasar system, the spectral similarity remains a puzzle. We estimate that at most 0.06% of randomly selected quasar pairs would have spectra as similar to each other as the spectra of Q 1634+267 A and B. Moreover, spectral similarities observed for the 14 quasar pairs are significantly greater than would be expected for an equivalent sample of randomly selected field quasars. Depending on how strictly we define similarity, we estimate that only 0.01--3% of randomly drawn samples of 14 quasar pairs would have as many similar pairs as the observational sample.Comment: 24 pages, including 4 figures, LaTex, ApJ accepted, comments from the editor included, minor editorial change