Lensing Galaxy Research Articles

Complex angular structure of three elliptical galaxies from high-resolution ALMA observations of strong gravitational lenses

The large-scale mass distributions of galaxy-scale strong lenses have long been assumed to be well described by a singular ellipsoidal power-law density profile with external shear. However, the inflexibility of this model could lead to systematic errors in astrophysical parameters inferred with gravitational lensing observables. Here, we present observations with the Atacama Large (sub-)Millimetre Array (ALMA) of three strongly lensed dusty star-forming galaxies at $ mas angular resolution and investigate the sensitivity of these data to angular structure in the lensing galaxies. We jointly infer the lensing mass distribution and the full surface brightness of the lensed sources with multipole expansions of the power-law density profile up to the fourth order using a technique developed for interferometric data. All three datasets strongly favour third and fourth-order multipole amplitudes of $ percent of the convergence. While the infrared stellar isophotes and isodensity shapes agree for one lens system, for the other two the isophotes disagree to varying extents, suggesting contributions to the angular structure from dark matter intrinsic or extrinsic to the lensing galaxy.

Correction to: Subaru HSC weak lensing of SDSS redMaPPer cluster satellite galaxies: empirical upper limit on orphan fractions

Correction to: Subaru HSC weak lensing of SDSS redMaPPer cluster satellite galaxies: empirical upper limit on orphan fractions

The powerful lens galaxy cluster PLCK G287.0+32.9 (θE ∼ 43″)

Aims. We present a new high-precision strong-lensing model of PLCK G287.0+32.9, a massive lens galaxy cluster at z = 0.383, with the aim of obtaining an accurate estimation of its effective Einstein radius and total mass distribution. We also present a spectroscopic catalog containing accurate redshift measurements for close to 500 objects up to redshift z = 6, including multiply lensed sources and cluster member galaxies. Methods. We exploited high-quality spectroscopic data from the Multi Unit Spectroscopic Explorer (MUSE), covering a central 3 arcmin2 region of the cluster. We supplemented the spectroscopic catalog by including redshift measurements from VIsible MultiObject Spectrograph (VIMOS) and DEep Imaging Multi-Object Spectrograph (DEIMOS). We identified 129 spectroscopic cluster member galaxies with redshift values of 0.360 ≤ z ≤ 0.405, and mF160W ≤ 21. We complemented this galaxy cluster member sample with 24 photometric members identified with a convolutional neural network (CNN) approach. We also identified 114 multiple images from 28 background sources, of which 84 images from 16 sources are new and the remaining ones have already been identified in previous works. From these, we extracted “golden sample” of 47 secure multiple images and used them, together with the selected cluster member, to build and optimize several strong-lensing models with the software lenstool. Results. The best-fitting lens model shows a root mean square (RMS) separation value between the predicted and observed positions of the multiple images of 0.″75. Using its predictive power, we found three new multiple images and we confirm the configuration of three systems of multiple images that were not used for the optimization of the model. For a source at a redshift of zs = 2, we found a cluster with an Einstein radius of θE = 43.4″ ± 0.1″. This value is in agreement with previous estimates and corresponds to a total mass enclosed in the critical curve of ME = 3.33−0.07+0.02 × 1014 M⊙. Conclusions. The combined application of ancillary Hubble Space Telescope (HST) imaging, VIMOS and DEIMOS data, and the new MUSE spectroscopic observations allowed us to build a new lens model of the galaxy cluster PLCK G287.0+32.9, with an improvement in terms of reconstructing the observed positions of the multiple images of a factor of 2.5 with respect to previous models. The derived total mass distribution confirms this cluster to be a very prominent gravitational lens, with an effective Einstein radius of θE ∼ 43″. We were also able to construct an extensive spectroscopic catalog containing 490 objects, of which 153 are bright cluster members with mF160W ≤ 21, and 114 are multiple images.

General multipoles and their implications for dark matter inference

ABSTRACT The flux ratios of strongly lensed quasars have previously been used to infer the properties of dark matter. In these analyses, it is crucial to separate the effect of the main lensing galaxy and the low-mass dark matter halo population. In this work, we investigate flux-ratio perturbations resulting from general third- and fourth-order multipole perturbations to the main lensing galaxy’s mass profile. We simulate four lens systems, each with a different lensing configuration, without multipoles. The simulated flux ratios are perturbed by 10–40 per cent by a population of low-mass haloes consistent with cold dark matter and, in one case, also a satellite galaxy. This level of perturbation is comparable to the magnitude of flux-ratio anomalies in real data that has been previously analysed. We then attempt to fit the simulated systems using multipoles instead of low-mass haloes. We find that multipoles with amplitudes of 0.01 or less can produce flux-ratio perturbations in excess of 40 per cent. In all cases, third- or fourth-order multipoles can individually reduce the magnitude of, if not eliminate, flux-ratio anomalies. When both multipole orders are jointly included, all simulated flux ratios can be fit to within the observational uncertainty. Our results indicate that low-mass haloes and multipoles are highly degenerate when modelling quadruply imaged quasars based just on image positions and flux ratios. In the presence of this degeneracy, flux-ratio anomalies in lensed quasars alone cannot be used to place strong constraints on the properties of dark matter without additional information that can inform our priors.

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

The missing quasar image in the gravitationally lensed quasar HE0230−2130: Implications for the cored lens mass distribution and dark satellites

Strongly lensed systems with peculiar configurations allow us to probe the local properties of the deflecting lens mass while simultaneously testing general profile assumptions. The quasar HE0230−2130 is lensed by two galaxies at similar redshifts (Δz ∼ 0.003) into four observed images. Using modeled quasar positions from fitting the brightness of the quasar images in ground-based imaging data from the Magellan telescope, we find that lens-mass models where each of these two galaxies is parametrized with a singular power-law (PL) profile predict five quasar images. One of the predicted images is unobserved despite it being distinctively offset from the lensing galaxies and likely bright enough to be observable. This missing image gives rise to new opportunities to study the mass distribution of these galaxies. To interpret the quad configuration of the system, we tested 12 different profile assumptions with the aim of obtaining lens-mass models that correctly predict only four observed images. We tested the effects of adopting: cored profiles for the lensing galaxies; external shear; and additional profiles to represent a dark matter clump. We find that half of our model classes can produce the correct image multiplicity. By comparing the Bayesian evidence of different model parametrizations, we favor two model classes: (i) one that incorporates two singular PL profiles for the lensing galaxies and a cored isothermal sphere in the region of the previously predicted fifth image (rNIS profile), and (ii) one with a bigger lensing galaxy parametrized by a singular PL profile and the smaller galaxy by a cored PL profile with external shear. We estimated the mass of the rNIS clump for each candidate model of our final Markov chain Monte Carlo sample, and find that only 2% are in the range of 106 M⊙ ≤ MrNIS ≤ 109 M⊙, which is the predicted mass range of dark matter subhalos in cold dark matter simulations, or the mass of dark-matter-dominated and low-surface-brightness galaxies. We therefore favor the models with a cored mass distribution for the lens galaxy close to the predicted fifth image. Our study further demonstrates that lensed quasar images are sensitive to the dark matter structure in the gravitational lens. We are able to describe this exotic lensing configuration with relatively simple models, which demonstrates the power of strong lensing for studying galaxies and lens substructure.

Inferring Properties of Dark Galactic Halos Using Strongly Lensed Gravitational Waves

Abstract Gravitational waves (GWs) can be deflected, similarly to electromagnetic (EM) waves, by massive objects through the phenomenon of gravitational lensing. The importance of GW lensing for GW astronomy is becoming increasingly apparent in the GW detection era, in which nearly 100 events have already been detected. As current ground-based interferometers reach their design sensitivities, it is anticipated that these detectors may observe a few GW signals that are strongly lensed by the dark halos of intervening galaxies or galaxy clusters. Analyzing the strong lensing effects on GW signals is, thus, becoming important to understand the lens’ properties and correctly infer the intrinsic GW source parameters. However, one cannot accurately infer lens parameters for complex lens models with only GW observations because there are strong degeneracies between the parameters of lensed waveforms. In this paper, we discuss how to conduct parameter estimation of strongly lensed GW signals and infer the lens parameters using additional EM information, including the lens galaxy’s axis ratio and the GW source-hosting galaxy’s lensed images. We find that for simple spherically symmetric lens models, the lens parameters can be well recovered using only GW information. On the other hand, recovering the lens parameters requires systems in which four or more GW images are detected with additional EM observations for nonaxially symmetric lens models. Combinations of GW and EM observations can further improve the inference of the lens parameters.

Towards quantifying the impact of triaxiality on optical signatures of galaxy clusters: weak lensing and galaxy distributions

ABSTRACT We present observational evidence of the impact of triaxiality on radial profiles that extend to 40 Mpc from galaxy cluster centres in optical measurements. We perform a stacked profile analysis from a sample of thousands of nearly relaxed galaxy clusters from public data releases of the Dark Energy Survey and the Dark Energy Camera Legacy Survey. Using the central galaxy elliptical orientation angle as a proxy for galaxy cluster orientation, we measure cluster weak lensing and excess galaxy density axis-aligned profiles, extracted along the central galaxy’s major or minor axes on the plane of the sky. Our measurements show a ≳ 2σ–3σ difference per radial bin between the normalized axis-aligned profiles. The profile difference between each axis-aligned profile and the azimuthally averaged profile ($\sim \pm 10\,\rm per\ cent-20~{{\ \rm per\ cent}}$ along major/minor axis) appears inside the clusters (∼0.4 Mpc) and extends to the large-scale structure regime (∼10–20 Mpc). The magnitude of the difference appears to be relatively insensitive to cluster richness and redshift, and extends further out in the weak lensing surface mass density than in the galaxy overdensity. Looking forward, this measurement can easily be applied to other observational or simulation data sets and can inform the systematics in cluster mass modelling related to triaxiality. We expect imminent upcoming wide-area deep surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, to improve our quantification of optical signatures of cluster triaxiality.

Cosmography with supernova Refsdal through time-delay cluster lensing: Independent measurements of the Hubble constant and geometry of the Universe

We present new measurements of the values of the Hubble constant, matter density, dark energy density, and dark energy density equation-of-state (EoS) parameters. These results have been obtained from a full strong-lensing analysis of the observed positions of 89 multiple images and 4 measured time delays of the supernova (SN) Refsdal in the Hubble Frontier Fields galaxy cluster MACS J1149.5+2223. By strictly following the identical modelling methodology (as done in our previous work undertaken before time delays were available), our cosmographic measurements are essentially blind, based on the frozen procedure. Without using any priors from other cosmological experiments, in an open wCDM cosmological model and via our reference cluster mass model, we measure the following values: H0 = 65.1−3.4+3.5 km s−1 Mpc−1, ΩDE = 0.76−0.10+0.15, and w = −0.92−0.21+0.15 (at the 68.3% confidence level). No other single cosmological probe has been able to simultaneously measure all these parameters. Remarkably, our estimated values of the cosmological parameters, in particular that of H0, are very robust and do not significantly depend on the assumed cosmological model or the cluster mass modelling details. The latter aspect introduces systematic uncertainties on the values of H0 and w, which are found to be largely subdominant compared to the statistical errors. The results of this study demonstrate that the combination of time delays in lens galaxy clusters with extensive photometric and spectroscopic information offers a novel and competitive cosmological tool.

Measurement of the size of the gamma-ray source in blazar B0218+357 based on microlensing at the 100 GeV energy band

Context. Observations of the effect of microlensing in gravitationally lensed quasars can be used to study the structure of active galactic nuclei on distance scales down to the sizes of a supermassive black hole’s powering source activity. Aims. We searched for a microlensing effect in the signal from a gravitationally lensed blazar, B0218+357, in a very-high-energy γ-ray band. Methods. We combined observations of a bright flare of the source in 2014 by the Fermi Large Area Telescope and MAGIC telescopes in the 0.1 − 300 GeV and 65 − 175 GeV energy ranges, respectively. Using the time-delayed leading and trailing signals from two gravitationally lensed images of the source, we measured the magnification factor at the moment of the flare. We used the scaling of the maximal magnification factor with the source size to constrain the size of the γ-ray emission region in the wide 0.1 − 175 GeV energy range. Results. The magnification factor in the very-high-energy band that we derived from our comparison of Fermi/LAT and MAGIC data is μVHE = 25−17+38, which is substantially larger than the factor found in the radio band. This suggests one of the source images is strongly affected by microlensing at the moment of the flare. Assuming that the microlensing is produced by a stellar mass object in the lens galaxy, we constrained the size of the emission region in the E > 100 GeV band to be RVHE = 6.6−5.6+69 × 1014 cm. We note that the spectrum of the microlensed source was unusually hard at the moment of the flare, and we speculate that this hardening may be due to the energy-dependent microlensing effect. This interpretation suggests that the source size decreases with energy in the entire 0.1 − 175 GeV energy range we studied.

Under Einstein’s Microscope: Measuring Properties of Individual Rotating Massive Stars from Extragalactic Microcaustic Crossings

Highly magnified stars residing in caustic crossing lensed galaxies at z ≃ 0.7–1.5 in galaxy cluster lensing fields inevitably exhibit recurrent brightening events as they traverse a microcaustic network cast down by foreground intracluster stars. The detectable ones belong to nature’s most massive and luminous class of stars, with evolved blue supergiants being the brightest ones at optical wavelengths. Considering single stars in this work, we study to what extent intrinsic stellar parameters are measurable from multifilter light curves, which can be obtained with optical/near-IR space telescopes during one or multiple caustic crossing events. We adopt a realistic model for the axisymmetric surface brightness profiles of rotating O/B stars and develop a numerical lensing code that treats finite source size effects. With a single microcaustic crossing, the ratio of the surface rotation velocity to the breakup value is measurable to a precision of ∼0.1–0.2 for feasible observation parameters with current space telescopes, with all unknown intrinsic and extrinsic parameters marginalized over and without a degeneracy with inclination. Equatorial radius and bolometric luminosity can be measured to 1/3 and 2/3 of the fractional uncertainty in the microcaustic strength, for which the value is not known at each crossing but an informative prior can be obtained from theory. Parameter inference precision may be further improved if multiple caustic crossing events for the same lensed star are jointly analyzed. Our results imply new opportunities to survey individual massive stars in star formation sites at z ≃ 0.7–1.5 or beyond.

Project Dinos I: A joint lensing–dynamics constraint on the deviation from the power law in the mass profile of massive ellipticals

ABSTRACT The mass distribution in massive elliptical galaxies encodes their evolutionary history, thus providing an avenue to constrain the baryonic astrophysics in their evolution. The power-law assumption for the radial mass profile in ellipticals has been sufficient to describe several observables to the noise level, including strong lensing and stellar dynamics. In this paper, we quantitatively constrained any deviation, or the lack thereof, from the power-law mass profile in massive ellipticals through joint lensing–dynamics analysis of a large statistical sample with 77 galaxy–galaxy lens systems. We performed an improved and uniform lens modelling of these systems from archival Hubble Space Telescope imaging using the automated lens modelling pipeline dolphin. We combined the lens model posteriors with the stellar dynamics to constrain the deviation from the power law after accounting for the line-of-sight lensing effects, a first for analyses on galaxy–galaxy lenses. We find that the Sloan Lens ACS Survey lens galaxies with a mean redshift of 0.2 are consistent with the power-law profile within 1.1σ (2.8σ) and the Strong Lensing Legacy Survey lens galaxies with a mean redshift of 0.6 are consistent within 0.8σ (2.1σ), for a spatially constant (Osipkov–Merritt) stellar anisotropy profile. We adopted the spatially constant anisotropy profile as our baseline choice based on previous dynamical observables of local ellipticals. However, spatially resolved stellar kinematics of lens galaxies are necessary to differentiate between the two anisotropy models. Future studies will use our lens models to constrain the mass distribution individually in the dark matter and baryonic components.

Properties of the brightest young stellar clumps in extremely lensed galaxies at redshifts 4 to 5

ABSTRACT We study the populations of stellar clumps in three high-redshift galaxies, at z = 4.92, 4.88, and 4.03, gravitationally lensed by the foreground galaxy clusters MS1358, RCS0224, and MACS0940, respectively. The lensed galaxies consist of multiple counter-images with large magnifications, mostly above $\mu > 5$ and in some cases reaching $\mu > 20$. We use rest-frame UV observations from the HST to extract and analyse their clump populations, counting 10, 3, and 11 unique sources, respectively. Most of the clumps have derived effective radii in the range $R_{\rm eff}=10\!-\!100$ pc, with the smallest one down to 6 pc, i.e. consistent with the sizes of individual stellar clusters. Their UV magnitudes correspond to $\rm SFR_{UV}$ mostly in the range $0.1\!-\!1\ {\rm M_\odot \, yr}^{-1}$; the most extreme ones, reaching ${\rm SFR_{UV}}=5\ {\rm M_\odot \, yr}^{-1}$ are among the UV-brightest compact ($R_{\rm eff} < 100$ pc) star-forming regions observed at any redshift. Clump masses span a broad range from 106 to $10^9\,{\rm M}_\odot$; stellar mass surface densities are comparable and in many cases larger than the ones of local stellar clusters, while being typically 10 times larger in size. By compiling published properties of clump populations at similar spatial resolution between redshifts 0 and 5, we find a tentative evolution of $\Sigma_{\rm SFR}$ and $\Sigma _{M_\star }$ with redshift, especially when very compact clumps ($R_{\rm eff}\leqslant 20$ pc) are considered. We suggest that these trends with redshift reflect the changes in the host galaxy environments where clumps form. Comparisons with the local universe clumps/star clusters shows that, although rare, conditions for elevated clump $\Sigma_{\rm SFR}$ and $\Sigma _{M_\star }$ can be found.

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2 reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude σ 8 = 0.819 ± 0.015 at 1.8% precision, S8≡σ8(Ωm/0.3)0.5=0.840±0.028 , and the Hubble constant H 0 = (68.3 ± 1.1) km s−1 Mpc−1 at 1.6% precision. A joint constraint with Planck CMB lensing yields σ 8 = 0.812 ± 0.013, S8≡σ8(Ωm/0.3)0.5=0.831±0.023 , and H 0 = (68.1 ± 1.0) km s−1 Mpc−1. These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find that S 8 from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probing z ∼ 0.5–5 on mostly linear scales and galaxy lensing at z ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m ν < 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys.

Euclid: Validation of the MontePython forecasting tools

Context. The Euclid mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. Aims. We expand and adjust the mock Euclid likelihoods of the MontePython software in order to match the exact recipes used in previous Euclid Fisher matrix forecasts for several probes: weak lensing cosmic shear, photometric galaxy clustering, the cross-correlation between the latter observables, and spectroscopic galaxy clustering. We also establish which precision settings are required when running the Einstein–Boltzmann solvers CLASS and CAMB in the context of Euclid. Methods. For the minimal cosmological model, extended to include dynamical dark energy, we perform Fisher matrix forecasts based directly on a numerical evaluation of second derivatives of the likelihood with respect to model parameters. We compare our results with those of previously validated Fisher codes using an independent method based on first derivatives of the Euclid observables. Results. We show that such MontePython forecasts agree very well with previous Fisher forecasts published by the Euclid Collab oration, and also, with new forecasts produced by the CosmicFish code, now interfaced directly with the two Einstein–Boltzmann solvers CAMB and CLASS. Moreover, to establish the validity of the Gaussian approximation, we show that the Fisher matrix marginal error contours coincide with the credible regions obtained when running Monte Carlo Markov chains with MontePython while using the exact same mock likelihoods. Conclusions. The new Euclid forecast pipelines presented here are ready for use with additional cosmological parameters, in order to explore extended cosmological models.

A Malmquist-like Bias in the Inferred Areas of Diamond Caustics and Consequences for the Inferred Time Delays of Gravitationally Lensed Quasars

Quasars are quadruply lensed only when they lie within the diamond caustic of a lensing galaxy. This precondition produces a Malmquist-like selection effect in observed populations of quadruply lensed quasars, overestimating the true caustic area. The bias toward high values of the inferred logarithmic area, lnAinf , is proportional to the square of the error in that area, σlnA2 . In effect, Malmquist’s correction compensates posthoc for a failure to incorporate a prior into parameter optimization. Inferred time delays are proportional to the square root of the inferred caustic area of the lensing galaxy. Model time delays are biased long, leading to overestimates of the Hubble constant. Crude estimates of σlnA for a sample of 13 quadruple systems give a median value of 0.16. We identify a second effect, an “inferred magnification bias,” resulting from the combination of selection by apparent magnitude and errors in model magnification. It is strongly anticorrelated with caustic area bias, and almost always leads to underestimates of the Hubble constant. Malmquist’s scheme can be adapted to priors on multiple parameters, but for quad lenses, the negative covariances between caustic area and absolute magnitude are poorly known. Inferred magnification bias may even cancel out caustic area bias, depending upon (among other things) the slope of the number–magnitude relation for the sample. Proper correction for these combined effects can, in principle, be built into Bayesian modeling schemes as priors, eliminating the need for a Malmquist-style approximation, but is likely to be challenging in practice.

Flat-sky angular power spectra revisited

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. For the case of projections with broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the commonly adopted Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables in a flat ΛCDM universe. In the case of galaxy clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the cases of lensing, we show on the full-sky that the angular power spectrum of the lensing convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales. We further analyse the clustering and lensing angular power spectra by isolating the projection effects due to the observable- and survey-specific window functions, separating them from the effects due to integration along the line of sight and unequal-time mixing in the 3D power spectrum. All of the angular power spectrum results presented in this paper are obtained using a Python code implementation, which we make publicly available.

Synchronize your chrono-brane: testing a variable brane tension model with strong gravitational lensing

Brane world models have shown to be promising to understand the late cosmic acceleration, in particular because such acceleration can be naturally derived, mimicking the dark energy behaviour just with a five dimensional geometry. In this paper we present a strong lensing joint analysis using a compilation of early-type galaxies acting as a lenses, united with the power of the well studied strong lensing galaxy cluster Abell 1689. We use the strong lensing constraints to investigate a brane model with variable brane tension as a function of the redshift. In our joint analysis we found a value n=7.8-0.5+0.9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n = 7.8^{+0.9}_{-0.5}$$\\end{document}, for the exponent related to the brane tension, showing that n deviates from a Cosmological Constant (CC) scenario (n=6). We obtain a value for the deceleration parameter, q(z) today, q(0)=-1.2-0.8+0.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q(0)=-1.2^{+0.6}_{-0.8}$$\\end{document}, and a transition redshift, zt=0.60±0.06\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_t=0.60\\pm 0.06$$\\end{document} (when the Universe change from an decelerated phase to an accelerated one). These results are in contrast with previous work that favors CC scenario, nevertheless our lensing analysis is in agreement with a formerly reported conclusion suggesting that the variable brane tension model is able to source a late cosmic acceleration without an extra fluid as in the standard one.

Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies

We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combines time-delay cosmography in lens galaxy clusters with pure samples of ‘cosmic chronometers’ by probing the member galaxies. The former makes use of the measured time delays between the multiple images of time-varying sources strongly lensed by galaxy clusters, while the latter exploits the most massive and passive cluster member galaxies to measure the differential time evolution of the Universe. We applied two different statistical techniques, adopting realistic errors on the measured quantities, to assess the accuracy and the gain in precision on the values of the cosmological parameters. We demonstrate that the proposed combined method allows for a robust and accurate measurement of the value of the Hubble constant. In addition, this provides valuable information on the other cosmological parameters thanks to the complementarity between the two different probes in breaking parameter degeneracies. Finally, we showcased the immediate observational feasibility of the proposed joint method by taking advantage of the existing high-quality spectro-photometric data for several lens galaxy clusters.

Two-dimensional kinematics and dynamical modelling of the ‘Jackpot’ gravitational lens from deep MUSE observations

ABSTRACT We present results from the first spatially resolved kinematic and dynamical modelling analysis of the unique SDSSJ0946+1006 (‘Jackpot’) triple-source lens system, where a single massive foreground $z\, =\, 0.222$ galaxy multiple-images three background sources at different redshifts. Deep integral field unit spectroscopic data were obtained using the MUSE instrument on the VLT, which, compared to previous single-slit observations, provides full azimuthal area coverage, high sensitivity (5 h integration) and high angular resolution (0.5 arcsec full width at half-maximum). To account for the strong continuum contributions from the $z\, =\, 0.609$ source, a multiple-component stellar template fitting technique is adopted to fit to the spectra of both the lens galaxy and the bright lensed background arc simultaneously. Through this, we robustly measure the first and second moments of the 2D stellar kinematics out to about 10 kpc from the centre of the lens, as well as resolving the inner profile inwards to ∼1 kpc. The 2D kinematic maps show a steep velocity dispersion gradient and a clear rotational component. We constrain the characteristic properties of the stellar and dark matter (DM) mass components with a sufficiently flexible parametrised dynamical model and an imposed lensing mass and find a DM density slope of $\gamma \, =\, 1.73\substack{+0.17 \\ -0.26}$, i.e. significantly steeper than an unmodified NFW profile ($\gamma \, =\, 1$) and consistent with a contracted DM halo. Our fitted models have a lensing-equivalent density slope of $\eta \, =\, 0.96\pm 0.02$, and thus we confirm most pure lensing results in finding a near isothermal profile for this galaxy.