Strong Gravitational Lens Systems Research Articles

Support vector machine classification of strong gravitational lenses

The imminent advent of very large-scale optical sky surveys, such as Euclid and LSST, makes it important to find efficient ways of discovering rare objects such as strong gravitational lens systems, where a background object is multiply gravitationally imaged by a foreground mass. As well as finding the lens systems, it is important to reject false positives due to intrinsic structure in galaxies, and much work is in progress with machine learning algorithms such as neural networks in order to achieve both these aims. We present and discuss a Support Vector Machine (SVM) algorithm which makes use of a Gabor filterbank in order to provide learning criteria for separation of lenses and non-lenses, and demonstrate using blind challenges that under certain circumstances it is a particularly efficient algorithm for rejecting false positives. We compare the SVM engine with a large-scale human examination of 100000 simulated lenses in a challenge dataset, and also apply the SVM method to survey images from the Kilo-Degree Survey.

PHL 6625: A Minor Merger-associated QSO Behind NGC 247

Abstract PHL 6625 is a luminous quasi-stellar object (QSO) at z = 0.3954 located behind the nearby galaxy NGC 247 (z = 0.0005). Hubble Space Telescope observations revealed an arc structure associated with it. We report on spectroscopic observations with the Very Large Telescope and multiwavelength observations from the radio to the X-ray band for the system, suggesting that PHL 6625 and the arc are a close pair of merging galaxies, instead of a strong gravitational lens system. The QSO host galaxy is estimated to be (4–28) × 1010 M ☉ and the mass of the companion galaxy is estimated to be M * = (6.8 ± 2.4) × 109 M ☉, suggesting that this is a minor merger system. The QSO displays typical broad emission lines, from which a black hole mass of about (2–5) × 108 M ☉ and an Eddington ratio of about 0.01–0.05 can be inferred. The system represents an interesting and rare case where a QSO is associated with an ongoing minor merger, analogous to Arp 142.

SDSS J1640+1932: a spectacular galaxy–quasar strong lens system

We present Canada-France-Hawaii Telescope (CFHT) MegaCam observations of a galaxy-quasar strong gravitational lens system, SDSS J1640+1932. This system, located at z=0.195 (foreground elliptical galaxy) and z=0.778 (background quasar), was first visually identified by us in the Sloan Digital Sky Survey (SDSS) database. Our CFHT imaging with an angular resolution of 0.7$^{\prime \prime}$ clearly resolves 4 lensed images and a nearly complete Einstein ring. Modeling the system with a singular isothermal ellipsoid (SIE) total mass distribution, we find an Einstein radius of ${2.49^{\prime \prime}}_{-0.049}^{+0.063}$ enclosing a inferred mass of $7.25_{-0.29}^{+0.37}\times10^{11} M_{\odot}$. The quasar and its host galaxy have been magnified by a factor of 23, and the time delay relative to the leading image is determined to be 23.4-25.2 days. These parameters vary minimally when our model is fitted to the {\it{g}}-, {\it{r}}- or {\it{i}}-band images.

H0LiCOW – I. H0 Lenses in COSMOGRAIL's Wellspring: program overview

Strong gravitational lens systems with time delays between the multiple images allow measurements of time-delay distances, which are primarily sensitive to the Hubble constant that is key to probing dark energy, neutrino physics, and the spatial curvature of the Universe, as well as discovering new physics. We present H0LiCOW ($H_0$ Lenses in COSMOGRAIL's Wellspring), a program that aims to measure $H_0$ with $<3.5\%$ uncertainty from five lens systems (B1608+656, RXJ1131-1231, HE0435-1223, WFI2033-4723 and HE1104-1805). We have been acquiring (1) time delays through COSMOGRAIL and Very Large Array monitoring, (2) high-resolution Hubble Space Telescope imaging for the lens mass modeling, (3) wide-field imaging and spectroscopy to characterize the lens environment, and (4) moderate-resolution spectroscopy to obtain the stellar velocity dispersion of the lenses for mass modeling. In cosmological models with one-parameter extension to flat $\Lambda$CDM, we expect to measure $H_0$ to $<3.5\%$ in most models, spatial curvature $\Omega_{\rm k}$ to 0.004, $w$ to 0.14, and the effective number of neutrino species to 0.2 (1$\sigma$ uncertainties) when combined with current CMB experiments. These are, respectively, a factor of $\sim15$, $\sim2$, and $\sim1.5$ tighter than CMB alone. Our data set will further enable us to study the stellar initial mass function of the lens galaxies, and the co-evolution of supermassive black holes and their host galaxies. This program will provide a foundation for extracting cosmological distances from the hundreds of time-delay lenses that are expected to be discovered in current and future surveys.

Quantifying Environmental and Line-of-sight Effects in Models of Strong Gravitational Lens Systems

Abstract Matter near a gravitational lens galaxy or projected along the line of sight (LOS) can affect strong lensing observables by more than contemporary measurement errors. We simulate lens fields with realistic three-dimensional mass configurations (self-consistently including voids), and then fit mock lensing observables with increasingly complex lens models to quantify biases and uncertainties associated with different ways of treating the lens environment (ENV) and LOS. We identify the combination of mass, projected offset, and redshift that determines the importance of a perturbing galaxy for lensing. Foreground structures have a stronger effect on the lens potential than background structures, due to nonlinear effects in the foreground and downweighting in the background. There is dramatic variation in the net strength of ENV/LOS effects across different lens fields; modeling fields individually yields stronger priors for H 0 than ray tracing through N-body simulations. Models that ignore mass outside the lens yield poor fits and biased results. Adding external shear can account for tidal stretching from galaxies at redshifts , but it requires corrections for external convergence and cannot reproduce nonlinear effects from foreground galaxies. Using the tidal approximation is reasonable for most perturbers as long as nonlinear redshift effects are included. Even then, the scatter in H 0 is limited by the lens profile degeneracy. Asymmetric image configurations produced by highly elliptical lens galaxies are less sensitive to the lens profile degeneracy, so they offer appealing targets for precision lensing analyses in future surveys like LSST and Euclid.

Red nuggets grow inside-out: evidence from gravitational lensing

We present a new sample of strong gravitational lens systems where both the foreground lenses and background sources are early-type galaxies. Using imaging from HST/ACS and Keck/NIRC2, we model the surface brightness distributions and show that the sources form a distinct population of massive, compact galaxies at redshifts $0.4 \lesssim z \lesssim 0.7$, lying systematically below the size-mass relation of the global elliptical galaxy population at those redshifts. These may therefore represent relics of high-redshift red nuggets or their partly-evolved descendants. We exploit the magnifying effect of lensing to investigate the structural properties, stellar masses and stellar populations of these objects with a view to understanding their evolution. We model these objects parametrically and find that they generally require two S\'ersic components to properly describe their light profiles, with one more spheroidal component alongside a more envelope-like component, which is slightly more extended though still compact. This is consistent with the hypothesis of the inside-out growth of these objects via minor mergers. We also find that the sources can be characterised by red-to-blue colour gradients as a function of radius which are stronger at low redshift -- indicative of ongoing accretion -- but that their environments generally appear consistent with that of the general elliptical galaxy population, contrary to recent suggestions that these objects are predominantly associated with clusters.

SHARP – III. First use of adaptive-optics imaging to constrain cosmology with gravitational lens time delays

Accurate and precise measurements of the Hubble constant are critical for testing our current standard cosmological model and revealing possibly new physics. With Hubble Space Telescope (HST) imaging, each strong gravitational lens system with measured time delays can allow one to determine the Hubble constant with an uncertainty of $\sim 7\%$. Since HST will not last forever, we explore adaptive-optics (AO) imaging as an alternative that can provide higher angular resolution than HST imaging but has a less stable point spread function (PSF) due to atmospheric distortion. To make AO imaging useful for time-delay-lens cosmography, we develop a method to extract the unknown PSF directly from the imaging of strongly lensed quasars. In a blind test with two mock data sets created with different PSFs, we are able to recover the important cosmological parameters (time-delay distance, external shear, lens mass profile slope, and total Einstein radius). Our analysis of the Keck AO image of the strong lens system RXJ1131-1231 shows that the important parameters for cosmography agree with those based on HST imaging and modeling within 1-$\sigma$ uncertainties. Most importantly, the constraint on the model time-delay distance by using AO imaging with $0.045"$resolution is tighter by $\sim 50\%$ than the constraint of time-delay distance by using HST imaging with $0.09"$when a power-law mass distribution for the lens system is adopted. Our PSF reconstruction technique is generic and applicable to data sets that have multiple nearby point sources, enabling scientific studies that require high-precision models of the PSF.

A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074

We present new VLA 22-GHz and e-MERLIN 5-GHz observations of CLASS B1030+074, a two-image strong gravitational lens system whose background source is a compact flat-spectrum radio quasar. In such systems we expect a third image of the background source to form close to the centre of the lensing galaxy. The existence and brightness of such images is important for investigation of the central mass distributions of lensing galaxies, but only one secure detection has been made so far in a galaxy-scale lens system. The noise levels achieved in our new B1030+074 images reach 3 microJy/beam and represent an improvement in central image constraints of nearly an order of magnitude over previous work, with correspondingly better resulting limits on the shape of the central mass profile of the lensing galaxy. Simple models with an isothermal outer power law slope now require either the influence of a central supermassive black hole, or an inner power law slope very close to isothermal, in order to suppress the central image below our detection limit. Using the central mass profiles inferred from light distributions in Virgo galaxies, moved to z=0.5, and matching to the observed Einstein radius, we now find that 45% of such mass profiles should give observable central images, 10% should give central images with a flux density still below our limit, and the remaining systems have extreme demagnification produced by the central SMBH. Further observations of similar objects will therefore allow proper statistical constraints to be placed on the central properties of elliptical galaxies at high redshift.

Revealing the complex nature of the strong gravitationally lensed system H-ATLAS J090311.6+003906 using ALMA

We have modelled Atacama Large Millimeter/sub-millimeter Array (ALMA) long baseline imaging of the strong gravitational lens system H-ATLAS J090311.6+003906 (SDP.81). We have reconstructed the distribution of band 6 and 7 continuum emission in the z=3.042 source and we have determined its kinematic properties by reconstructing CO(5-4) and CO(8-7) line emission in bands 4 and 6. The continuum imaging reveals a highly non-uniform distribution of dust with clumps on scales of 200 pc. In contrast, the CO line emission shows a relatively smooth, disk-like velocity field which is well fit by a rotating disk model with an inclination angle of 40+/-5 degrees and an asymptotic rotation velocity of 320 km/s. The inferred dynamical mass within 1.5kpc is (3.5+/-0.5)x10^{10} M_sol which is comparable to the total molecular gas masses of (2.7+/-0.5)x10^{10} M_sol and (3.5+/-0.6)x10^{10} M_sol from the dust continuum emission and CO emission respectively. Our new reconstruction of the lensed HST near-infrared emission shows two objects which appear to be interacting, with the rotating disk of gas and dust revealed by ALMA distinctly offset from the near-infrared emission. The clumpy nature of the dust and a low value of the Toomre parameter of Q=0.3 suggest that the disk is in a state of collapse. We estimate a star formation rate in the disk of 470+/-80 M_sol/yr with an efficiency 65 times greater than typical low-redshift galaxies. Our findings add to the growing body of evidence that the most infra-red luminous, dust obscured galaxies in the high redshift Universe represent a population of merger induced starbursts.

A new hybrid framework to efficiently model lines of sight to gravitational lenses

In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e., including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher-order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors.

Herschel ★ -ATLAS: modelling the first strong gravitational lenses

We have determined the mass-density radial profiles of the first five strong gravitational lens systems discovered by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). We present an enhancement of the semi-linear lens inversion method of Warren & Dye which allows simultaneous reconstruction of several different wavebands and apply this to dual-band imaging of the lenses acquired with the Hubble Space Telescope. The five systems analysed here have lens redshifts which span a range, 0.22<z<0.94. Our findings are consistent with other studies by concluding that: 1) the logarithmic slope of the total mass density profile steepens with decreasing redshift; 2) the slope is positively correlated with the average total projected mass density of the lens contained within half the effective radius and negatively correlated with the effective radius; 3) the fraction of dark matter contained within half the effective radius increases with increasing effective radius and increases with redshift.

The stellar and dark matter distributions in elliptical galaxies from the ensemble of strong gravitational lenses

We derive the average mass profile of elliptical galaxies from the ensemble of 161 strong gravitational lens systems selected from several surveys, assuming that the mass profile scales with the stellar mass and effective radius of each lensing galaxy. The total mass profile is well fitted by a power-law \rho(r) \propto r^\gamma with best-fit slope \gamma = -2.11+/-0.05. The decomposition of the total mass profile into stellar and dark matter distributions is difficult due to a fundamental degeneracy between the stellar initial mass function (IMF) and the dark matter fraction f_DM. We demonstrate that this IMF-f_DM degeneracy can be broken by adding direct stellar mass fraction measurements by quasar microlensing observations. Our best-fit model prefers the Salpeter IMF over the Chabrier IMF, and a smaller central dark matter fraction than that predicted by adiabatic contraction models.

THE SL2S GALAXY-SCALE LENS SAMPLE. IV. THE DEPENDENCE OF THE TOTAL MASS DENSITY PROFILE OF EARLY-TYPE GALAXIES ON REDSHIFT, STELLAR MASS, AND SIZE

We present optical and near infrared spectroscopy obtained at Keck, VLT, and Gemini for a sample of 36 secure strong gravitational lens systems and 17 candidates identified as part of the SL2S survey. The deflectors are massive early-type galaxies in the redshift range z_d=0.2-0.8, while the lensed sources are at z_s=1-3.5. We combine this data with photometric and lensing measurements presented in the companion paper III and with lenses from the SLACS and LSD surveys to investigate the cosmic evolution of the internal structure of massive early-type galaxies over half the age of the universe. We study the dependence of the slope of the total mass density profile \gamma' (\rho(r)\propto r^{-\gamma'}) on stellar mass, size, and redshift. We find that two parameters are sufficent to determine \gamma' with less than 6% residual scatter. At fixed redshift, \gamma' depends solely on the surface stellar mass density \partial \gamma'/ \partial \Sigma_*=0.38\pm 0.07, i.e. galaxies with denser stars also have steeper slopes. At fixed M_* and R_{eff}, \gamma' depends on redshift, in the sense that galaxies at a lower redshift have steeper slopes (\partial \gamma' / \partial z = -0.31\pm 0.10). However, the mean redshift evolution of \gamma' for an individual galaxy is consistent with zero d\gamma'/dz=-0.10\pm0.12. This result is obtained by combining our measured dependencies of \gamma' on z,M_*,R_{eff} with the evolution of the R_{eff}-M_* taken from the literature, and is broadly consistent with current models of the formation and evolution of massive early-type galaxies. Detailed quantitative comparisons of our results with theory will provide qualitatively new information on the detailed physical processes at work.

Constraining the dark energy equation of state with double-source plane strong lenses

We investigate the possibility of constraining the dark energy equation of state by measuring the ratio of Einstein radii in a strong gravitational lens system with two source planes. This quantity is independent of the Hubble parameter and directly measures the growth of angular diameter distances as a function of redshift. We investigate the prospects for a single double source plane system and for a forecast population of systems discovered by re-observing a population of single source lenses already known from a photometrically selected catalogue such as CASSOWARY or from a spectroscopically selected catalogue such as SLACS. We find that constraints comparable to current data-sets (15% uncertainty on the dark equation of state at 68%CL) are possible with a handful of double source plane systems. We also find that the method's degeneracy between Omega_M and w is almost orthogonal to that of CMB and BAO measurements, making this method highly complimentary to current probes.

QUANTIFYING THE BIASES OF SPECTROSCOPICALLY SELECTED GRAVITATIONAL LENSES

Spectroscopic selection has been the most productive technique for the selection of galaxy-scale strong gravitational lens systems with known redshifts. Statistically significant samples of strong lenses provide a powerful method for measuring the mass-density parameters of the lensing population, but results can only be generalized to the parent population if the lensing selection biases are sufficiently understood. We perform controlled Monte Carlo simulations of spectroscopic lens surveys in order to quantify the bias of lenses relative to parent galaxies in velocity dispersion, mass axis ratio, and mass density profile. For parameters typical of the SLACS and BELLS surveys, we find: (1) no significant mass axis ratio detection bias of lenses relative to parent galaxies; (2) a very small detection bias toward shallow mass density profiles, which is likely negligible compared to other sources of uncertainty in this parameter; (3) a detection bias towards smaller Einstein radius for systems drawn from parent populations with group- and cluster-scale lensing masses; and (4) a lens-modeling bias towards larger velocity dispersions for systems drawn from parent samples with sub-arcsecond mean Einstein radii. This last finding indicates that the incorporation of velocity-dispersion upper limits of \textit{non-lenses} is an important ingredient for unbiased analyses of spectroscopically selected lens samples. In general we find that the completeness of spectroscopic lens surveys in the plane of Einstein radius and mass-density profile power-law index is quite uniform, up to a sharp drop in the region of large Einstein radius and steep mass density profile, and hence that such surveys are ideally suited to the study of massive field galaxies.

The SWELLS survey - III. Disfavouring ‘heavy’ initial mass functions for spiral lens galaxies

We present gravitational lens models for 20 strong gravitational lens systems observed as part of the Sloan WFC Edge-on Late-type Lens Survey (SWELLS) project. Fifteen of the lenses are taken from paper I while five are newly discovered systems. The systems are galaxy-galaxy lenses where the foreground deflector has an inclined disc, with a wide range of morphological types, from late-type spiral to lenticular. For each system, we compare the total mass inside the critical curve inferred from gravitational lens modelling to the stellar mass inferred from stellar population synthesis (SPS) models, computing the stellar mass fraction f* = M(SPS)/M(lens). We find that, for the lower mass SWELLS systems, adoption of a Salpeter stellar initial mass function (IMF) leads to estimates of f* that exceed 1. This is unphysical, and provides strong evidence against the Salpeter IMF being valid for these systems. Taking the lower mass end of the SWELLS sample sigma(SIE) < 230 km/s, we find that the IMF is lighter (in terms of stellar mass-to-light ratio) than Salpeter with 98% probability, and consistent with the Chabrier IMF and IMFs between the two. This result is consistent with previous studies of spiral galaxies based on independent techniques. In combination with recent studies of massive early-type galaxies that have favoured a heavier Salpeter-like IMF, this result strengthens the evidence against a universal stellar IMF.

THE BOSS EMISSION-LINE LENS SURVEY (BELLS). I. A LARGE SPECTROSCOPICALLY SELECTED SAMPLE OF LENS GALAXIES AT REDSHIFT ∼0.5

We present a catalog of 25 definite and 11 probable strong galaxy-galaxy gravitational lens systems with redshifts 0.4 \lesssim z \lesssim 0.7, discovered spectroscopically by the presence of higher redshift emission-lines within the Baryon Oscillation Spectroscopic Survey (BOSS) of luminous galaxies, and confirmed with high-resolution Hubble Space Telescope (HST) images of 44 candidates. Our survey extends the methodology of the Sloan Lens ACS Survey (SLACS: Bolton et al. 2006; 2008) to higher redshift. We describe the details of the BOSS spectroscopic candidate detections, our HST Adanced Camera for Surveys (ACS) image processing and analysis methods, and our strong gravitational lens modeling procedure. We report BOSS spectroscopic parameters and ACS photometric parameters for all candidates, and mass-distribution parameters for the best-fit singular isothermal ellipsoid models of definite lenses. Our sample to date was selected using only the first six months of BOSS survey-quality spectroscopic data. The full 5-year BOSS database should produce a sample of several hundred strong galaxy-galaxy lenses and in combination with SLACS lenses at lower redshift, strongly constrain the redshift evolution of the structure of elliptical, bulge-dominated galaxies as a function of luminosity, stellar mass, and rest-frame color, thereby providing a powerful test for competing theories of galaxy formation and evolution.

Dynamical masses of early-type galaxies: a comparison to lensing results and implications for the stellar initial mass function and the distribution of dark matter

This work aims to study the distribution of luminous and dark matter in Coma early-type galaxies. Dynamical masses obtained under the assumption that mass follows light do not match with the masses of strong gravitational lens systems of similar velocity dispersions. Instead, dynamical fits with dark matter halos are in good agreement with lensing results. We derive mass-to-light ratios of the stellar populations from Lick absorption line indices, reproducing well the observed galaxy colours. Even in dynamical models with dark matter halos the amount of mass that follows the light increases more rapidly with galaxy velocity dispersion than expected for a constant stellar initial mass function (IMF). While galaxies around sigma ~ 200 km/s are consistent with a Kroupa IMF, the same IMF underpredicts luminous dynamical masses of galaxies with sigma ~ 300 km/s by a factor of two and more. A systematic variation of the stellar IMF with galaxy velocity dispersion could explain this trend with a Salpeter IMF for the most massive galaxies. If the IMF is instead constant, then some of the dark matter in high velocity dispersion galaxies must follow a spatial distribution very similar to that of the light. A combination of both, a varying IMF and a component of dark matter that follows the light is possible as well. For a subsample of galaxies with old stellar populations we show that the tilt in the fundamental plane can be explained by systematic variations of the total (stellar + dark) mass inside the effective radius. We tested commonly used mass estimator formulae, finding them accurate at the 20-30% level.

A compact early-type galaxy at z = 0.6 under a magnifying lens: evidence for inside-out growth

Abstract We use Keck laser guide star adaptive optics imaging and exploit the magnifying effects of strong gravitational lensing (the effective resolution is FWHM ≈ 200 pc) to investigate the sub-kpc scale of an intermediate-redshift (z = 0.63), massive early-type galaxy being lensed by a foreground early-type galaxy; we dub this class of strong gravitational lens systems EELs, i.e. early-type/early-type lenses. We find that the background source is massive (M* = 1010.9 M⊙) and compact (re = 1.1 kpc), and a two-component fit is required to model accurately the surface brightness distribution, including an extended low-surface-brightness component. This extended component may arise from the evolution of higher redshift ‘red nuggets’ or may already be in place at z∼ 2 but is unobservable due to cosmological surface brightness dimming.

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)