The Hubble Constant from the Gravitational Lens B1608+656

We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (i) the three independent time-delays and flux-ratios from VLA observations, (ii) the radio-image positions from VLBA observations, (iii) the shape of the deconvolved Einstein Ring from optical and infrared HST images, (iv) the extinction-corrected lens-galaxy centroids and structural parameters, and (v) a stellar velocity dispersion, sigma_ap=247+-35 km/s, of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck--II telescope. The lens mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes which are the key parameters to determine the value of H_0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum-chi^2 model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein Ring. A combined gravitational-lens and stellar dynamical analysis leads to a value of the Hubble Constant of H_0=75(+7/-6) km/s/Mpc (68 percent CL; Omega_m=0.3, Omega_Lambda=0.7. The non-linear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H_0. The lens galaxy G1 is ~5 times more massive than the secondary lens galaxy (G2), and has a mass density slope of gamma_G1=2.03(+0.14/-0.14) +- 0.03 (68 percent CL) for rho~r^-gamma', very close to isothermal (gamma'=2). (Abridged)Comment: 17 pages, 6 figures, 5 tables; revised version with correct fig.6 and clarified text based on referee report; conclusions unchange

Lensing galaxies: light or dark?

In a recent paper, Hawkins (1997) argues on the basis of statistical studies of double-image gravitational lenses and lens candidates that a large population of dark lenses exists and that these outnumber galaxies with more normal mass-to-light ratios by a factor of 3:1. If correct, this is a very important result for many areas of astronomy including galaxy formation and cosmology. In this paper we discuss our new radio-selected gravitational lens sample, JVAS/CLASS, in order to test and constrain this proposition. We have obtained ground-based and HST images of all multiple-image lens systems in our sample and in 12 cases out of 12 we find the lensing galaxies in the optical and/or near infrared. Our success in finding lensing galaxies creates problems for the dark lens hypothesis. If it is to survive, ad hoc modifications seem to be necessary: only very massive galaxies (more than about one trillion solar masses) can be dark, and the cutoff in mass must be sharp. Our finding of lens galaxies in all the JVAS/CLASS systems is complementary evidence which supports the conclusion of Kochanek et al. (1997) that many of the wide-separation optically-selected pairs are physically distinct quasars rather than gravitational lens systems.Comment: 4 pages, 2 included figures, accepted for publication in Astronomy and Astrophysics. Paper version available on request. This replacement amends the text to allow more discussion of the overlap with astro-ph/971016

Keck spectroscopy of CLASS gravitational lenses

We present the optical spectra of four newly discovered gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope as part of a program to study galaxy-scale gravitational lenses. From our spectra we found the redshift of the background source in CLASS B0128+437 (z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123 (z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we also discovered that CLASS B0631+519 may have two lensing galaxies (z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single unidentified emission line from the lensing galaxy in CLASS B0128+437 and the lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

A Determination of H_0 with the CLASS Gravitational Lens B1608+656: I. Time Delay Measurements with the VLA

We present the results of a program to monitor the four-image gravitational lens B1608+656 with the VLA. The system was observed over a seven month period from 1996 October to 1997 May. The 64 epochs of observation have an average spacing of 3.6~d. The light curves of the four images of the background source show that the flux density of the background source has varied at the ~5% level. We measure time delays in the system based on common features that are seen in all four light curves. The three independent time delays in the system are found to be Delta t_{BA} = 31 +/- 7~d, Delta t_{BC} = 36 +/- 7~d, and Delta t_{BD} = 76^{+9}_{-10}~d at 95% confidence. This is the first gravitational lens system for which three independent time delays have been measured. A companion paper presents a mass model for the lensing galaxy which correctly reproduces the observed image positions, flux density ratios, and time delay ratios. The last condition is crucial for determining H_0 with a four-image lens. We combine the time delays with the model to obtain a value for the Hubble constant of H_0 = 59^{+8}_{-7} km/s/Mpc at 95% confidence (statistical) for (Omega_M, Omega_{Lambda}) = (1,0). In addition, there is an estimated systematic uncertainty of +/- 15 km/s/Mpc from uncertainties in modeling the radial mass profiles of the lensing galaxies. The value of H_0 presented in this paper is comparable to recent measurements of H_0 from the gravitational lenses 0957+561, PG1115+080, B0218+357, and PKS1830-211.Comment: Accepted for publication in ApJ. 20 pages, 13 figure

Finding Strong Gravitational Lenses in the Kilo Degree Survey with Convolutional Neural Networks

The volume of data that will be produced by new-generation surveys requires automatic classification methods to select and analyze sources. Indeed, this is the case for the search for strong gravitational lenses, where the population of the detectable lensed sources is only a very small fraction of the full source population. We apply for the first time a morphological classification method based on a Convolutional Neural Network (CNN) for recognizing strong gravitational lenses in $255$ square degrees of the Kilo Degree Survey (KiDS), one of the current-generation optical wide surveys. The CNN is currently optimized to recognize lenses with Einstein radii $\gtrsim 1.4$ arcsec, about twice the $r$-band seeing in KiDS. In a sample of $21789$ colour-magnitude selected Luminous Red Galaxies (LRG), of which three are known lenses, the CNN retrieves 761 strong-lens candidates and correctly classifies two out of three of the known lenses. The misclassified lens has an Einstein radius below the range on which the algorithm is trained. We down-select the most reliable 56 candidates by a joint visual inspection. This final sample is presented and discussed. A conservative estimate based on our results shows that with our proposed method it should be possible to find $\sim100$ massive LRG-galaxy lenses at z\lsim 0.4 in KiDS when completed. In the most optimistic scenario this number can grow considerably (to maximally $\sim$2400 lenses), when widening the colour-magnitude selection and training the CNN to recognize smaller image-separation lens systems.Comment: 24 pages, 17 figures. Published in MNRA

Proper motion in lensed radio jets at redshift 3:A possible dual super-massive black hole system in the early Universe

In this paper, we exploit the gravitational lensing effect to detect proper motion in the highly magnified gravitationally lensed source MG B2016+112. We find positional shifts up to 6 mas in the lensed images by comparing two Very Long Baseline Interferometric (VLBI) radio observations at 1.7 GHz that are separated by 14.359 years, and provide an astrometric accuracy of the order of tens of $\mu$as. From lens modelling, we exclude a shift in the lensing galaxy as the cause of the positional change of the lensed images, and we assign it to the background source. The source consists of four sub-components separated by $\sim 175$ pc, with proper motion of the order of tens $\mu$as yr$^{-1}$ for the two components at highest magnification ($\mu\sim350$) and of the order of a few mas yr$^{-1}$ for the two components at lower magnification ($\mu\sim2$). We propose single AGN and dual AGN scenarios to explain the source plane. Although, the latter interpretation is supported by the archival multi-wavelength properties of the object. In this case, MG B2016+112 would represent the highest redshift dual radio-loud AGN system discovered thus far, and would support the merger interpretation for such systems. Also, given the low probability ($\sim10^{-5}$) of detecting a dual AGN system that is also gravitationally lensed, if confirmed, this would suggest that such dual AGN systems must be more abundant in the early Universe than currently thought.Comment: 11 pages, 4 figures; accepted for publication by Astronomy and Astrophysic

Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State

Strong gravitational lens systems with measured time delays between the multiple images provide a method for measuring the "time-delay distance" to the lens, and thus the Hubble constant. We present a Bayesian analysis of the strong gravitational lens system B1608+656, incorporating (i) new, deep Hubble Space Telescope (HST) observations, (ii) a new velocity dispersion measurement of 260+/-15 km/s for the primary lens galaxy, and (iii) an updated study of the lens' environment. When modeling the stellar dynamics of the primary lens galaxy, the lensing effect, and the environment of the lens, we explicitly include the total mass distribution profile logarithmic slope gamma' and the external convergence kappa_ext; we marginalize over these parameters, assigning well-motivated priors for them, and so turn the major systematic errors into statistical ones. The HST images provide one such prior, constraining the lens mass density profile logarithmic slope to be gamma'=2.08+/-0.03; a combination of numerical simulations and photometric observations of the B1608+656 field provides an estimate of the prior for kappa_ext: 0.10 +0.08/-0.05. This latter distribution dominates the final uncertainty on H_0. Compared with previous work on this system, the new data provide an increase in precision of more than a factor of two. In combination with the WMAP 5-year data set, we find that the B1608+656 data set constrains the curvature parameter to be -0.031 < Omega_k < 0.009 (95% CL), a level of precision comparable to that afforded by the current Type Ia SNe sample. Asserting a flat spatial geometry, we find that, in combination with WMAP, H_0 = 69.7 +4.9/-5.0 km/s/Mpc and w=-0.94 +0.17/-0.19 (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as do the current Baryon Acoustic Oscillation data. (abridged)Comment: 24 pages, 8 figures, revisions based on referee's comments, accepted for publication in Ap

Parametric hazard rate models for long-term sickness absence

PURPOSE: In research on the time to onset of sickness absence and the duration of sickness absence episodes, Cox proportional hazard models are in common use. However, parametric models are to be preferred when time in itself is considered as independent variable. This study compares parametric hazard rate models for the onset of long-term sickness absence and return to work. METHOD: Prospective cohort study on sickness absence with four follow-up years of 53,830 employees working in the private sector in the Netherlands. The time to onset of long-term (>6 weeks) sickness absence and return to work were modelled by parametric hazard rate models. RESULTS: The exponential parametric model with a constant hazard rate most accurately described the time to onset of long-term sickness absence. Gompertz-Makeham models with monotonically declining hazard rates best described return to work. CONCLUSIONS: Parametric models offer more possibilities than commonly used models for time-dependent processes as sickness absence and return to work. However, the advantages of parametric models above Cox models apply mainly for return to work and less for onset of long-term sickness absence