Lensed: a code for the forward reconstruction of lenses and sources from strong lensing observations

Robust modelling of strong lensing systems is fundamental to exploit the information they contain about the distribution of matter in galaxies and clusters. In this work, we present Lensed, a new code which performs forward parametric modelling of strong lenses. Lensed takes advantage of a massively parallel ray-tracing kernel to perform the necessary calculations on a modern graphics processing unit (GPU). This makes the precise rendering of the background lensed sources much faster, and allows the simultaneous optimisation of tens of parameters for the selected model. With a single run, the code is able to obtain the full posterior probability distribution for the lens light, the mass distribution and the background source at the same time. Lensed is first tested on mock images which reproduce realistic space-based observations of lensing systems. In this way, we show that it is able to recover unbiased estimates of the lens parameters, even when the sources do not follow exactly the assumed model. Then, we apply it to a subsample of the SLACS lenses, in order to demonstrate its use on real data. The results generally agree with the literature, and highlight the flexibility and robustness of the algorithm.Comment: v2: major revision; accepted by MNRAS; lens reconstruction code available at http://glenco.github.io/lensed

Zooming into the Cosmic Horseshoe: new insights on the lens profile and the source shape

The gravitational lens SDSS J1148+1930, also known as the Cosmic Horseshoe, is one of the biggest and of the most detailed Einstein rings ever observed. We use the forward reconstruction method implemented in the lens fitting code Lensed to investigate with great detail the properties of the lens and of the background source. We model the lens with different mass distributions, focusing in particular on the determination of the slope of the dark matter component. The inherent degeneracy between the lens slope and the source size can be broken when we can isolate separate components of each lensed image, as in this case. For an elliptical power law model, $\kappa(r) \sim r^{-t}$, the results favour a flatter-than-isothermal slope with a maximum-likelihood value t = 0.08. Instead, when we consider the contribution of the baryonic matter separately, the maximum-likelihood value of the slope of the dark matter component is t = 0.31 or t = 0.44, depending on the assumed Initial Mass Function. We discuss the origin of this result by analysing in detail how the images and the sources change when the slope t changes. We also demonstrate that these slope values at the Einstein radius are not inconsistent with recent forecast from the theory of structure formation in the LambdaCDM model.Comment: 13 pages, 9 figures, accepted for publication in MNRA

AMICO: optimised detection of galaxy clusters in photometric surveys

We present AMICO (Adaptive Matched Identifier of Clustered Objects), a new algorithm for the detection of galaxy clusters in photometric surveys. AMICO is based on the Optimal Filtering technique, which allows to maximise the signal-to-noise ratio of the clusters. In this work we focus on the new iterative approach to the extraction of cluster candidates from the map produced by the filter. In particular, we provide a definition of membership probability for the galaxies close to any cluster candidate, which allows us to remove its imprint from the map, allowing the detection of smaller structures. As demonstrated in our tests, this method allows the deblending of close-by and aligned structures in more than $50\%$ of the cases for objects at radial distance equal to $0.5 \times R_{200}$ or redshift distance equal to $2 \times \sigma_z$, being $\sigma_z$ the typical uncertainty of photometric redshifts. Running AMICO on mocks derived from N-body simulations and semi-analytical modelling of the galaxy evolution, we obtain a consistent mass-amplitude relation through the redshift range $0.3 < z < 1$, with a logarithmic slope $\sim 0.55$ and a logarithmic scatter $\sim 0.14$. The fraction of false detections is steeply decreasing with S/N, and negligible at S/N > 5.Comment: 18 pages, accepted for publication in MNRA

AMICO galaxy clusters in KiDS-DR3: sample properties and selection function

We present the first catalogue of galaxy cluster candidates derived from the third data release of the Kilo Degree Survey (KiDS-DR3). The sample of clusters has been produced using the Adaptive Matched Identifier of Clustered Objects (AMICO) algorithm. In this analysis AMICO takes advantage of the luminosity and spatial distribution of galaxies only, not considering colours. In this way, we prevent any selection effect related to the presence or absence of the red-sequence in the clusters. The catalogue contains 7988 candidate galaxy clusters in the redshift range 0.13.5 with a purity approaching 95% over the entire redshift range. In addition to the catalogue of galaxy clusters we also provide a catalogue of galaxies with their probabilistic association to galaxy clusters. We quantify the sample purity, completeness and the uncertainties of the detection properties, such as richness, redshift, and position, by means of mock galaxy catalogues derived directly from the data. This preserves their statistical properties including photo-z uncertainties, unknown absorption across the survey, missing data, spatial correlation of galaxies and galaxy clusters. Being based on the real data, such mock catalogues do not have to rely on the assumptions on which numerical simulations and semi-analytic models are based on. This paper is the first of a series of papers in which we discuss the details and physical properties of the sample presented in this work.Comment: 16 pages, 14 figures, 3 tables, submitted to MNRA

Testing future weak lensing surveys through simulations of observations

Weak lensing experiments such as the future ESA-accepted mission Euclid aim to measure cosmological parameters with unprecedented accuracy. It is important to assess the precision that can be obtained in these measurements by applying analysis software on mock images that contain many sources of noise present in the real data. In this Thesis, we show a method to perform simulations of observations, that produce realistic images of the sky according to characteristics of the instrument and of the survey. We then use these images to test the performances of the Euclid mission. In particular, we concentrate on the precision of the photometric redshift measurements, which are key data to perform cosmic shear tomography. We calculate the fraction of the total observed sample that must be discarded to reach the required level of precision, that is equal to 0.05(1+z) for a galaxy with measured redshift z, with different ancillary ground-based observations. The results highlight the importance of u-band observations, especially to discriminate between low (z < 0.5) and high (z ~ 3) redshifts, and the need for good observing sites, with seeing FWHM < 1. arcsec. We then construct an optimal filter to detect galaxy clusters through photometric catalogues of galaxies, and we test it on the COSMOS field, obtaining 27 lensing-confirmed detections. Applying this algorithm on mock Euclid data, we verify the possibility to detect clusters with mass above 10^14.2 solar masses with a low rate of false detections

AMICO galaxy clusters in KiDS-DR3: weak-lensing mass calibration

We present the mass calibration for galaxy clusters detected with the AMICO code in KiDS DR3 data. The cluster sample comprises $\sim$ 7000 objects and covers the redshift range 0.1 < $z$ < 0.6. We perform a weak lensing stacked analysis by binning the clusters according to redshift and two different mass proxies provided by AMICO, namely the amplitude $A$ (measure of galaxy abundance through an optimal filter) and the richness $\lambda^*$ (sum of membership probabilities in a consistent radial and magnitude range across redshift). For each bin, we model the data as a truncated NFW profile plus a 2-halo term, taking into account uncertainties related to concentration and miscentring. From the retrieved estimates of the mean halo masses, we construct the $A$-$M_{200}$ and the $\lambda^*$-$M_{200}$ relations. The relations extend over more than one order of magnitude in mass, down to $M_{200} \sim 2 (5) \times 10^{13} M_\odot/h$ at $z$ = 0.2 (0.5), with small evolution in redshift. The logarithmic slope is $\sim 2.0$ for the $A$-mass relation, and $\sim 1.7$ for the $\lambda^*$-mass relation, consistent with previous estimations on mock catalogues and coherent with the different nature of the two observables.Comment: 19 pages, 16 figures, accepted by MNRA

CoMaLit -- VI. Intrinsic scatter in stacked relations. The weak lensing AMICO galaxy clusters in KiDS-DR3

Unbiased and precise mass calibration of galaxy clusters is crucial to fully exploit galaxy clusters as cosmological probes. Stacking of weak lensing signal allows us to measure observable-mass relations down to less massive halos halos without extrapolation. We propose a Bayesian inference method to constrain the intrinsic scatter of the mass proxy in stacked analyses. The scatter of the stacked data is rescaled with respect to the individual scatter based on the number of binned clusters. We apply this method to the galaxy clusters detected with the AMICO (Adaptive Matched Identifier of Clustered Objects) algorithm in the third data release of the Kilo-Degree Survey. The results confirm the optical richness as a low scatter mass proxy. Based on the optical richness and the calibrated weak lensing mass-richness relation, mass of individual objects down to ~10^13 solar masses can be estimated with a precision of ~20 per cent.Comment: 12 pages, 6 figures; in press on MNRA

SEAGLE--II: Constraints on feedback models in galaxy formation from massive early type strong lens galaxies

We use nine different galaxy formation scenarios in ten cosmological simulation boxes from the EAGLE suite of {\Lambda}CDM hydrodynamical simulations to assess the impact of feedback mechanisms in galaxy formation and compare these to observed strong gravitational lenses. To compare observations with simulations, we create strong lenses with $M_\star$ > $10^{11}$ $M_\odot$ with the appropriate resolution and noise level, and model them with an elliptical power-law mass model to constrain their total mass density slope. We also obtain the mass-size relation of the simulated lens-galaxy sample. We find significant variation in the total mass density slope at the Einstein radius and in the projected stellar mass-size relation, mainly due to different implementations of stellar and AGN feedback. We find that for lens selected galaxies, models with either too weak or too strong stellar and/or AGN feedback fail to explain the distribution of observed mass-density slopes, with the counter-intuitive trend that increasing the feedback steepens the mass density slope around the Einstein radius ($\approx$ 3-10 kpc). Models in which stellar feedback becomes inefficient at high gas densities, or weaker AGN feedback with a higher duty cycle, produce strong lenses with total mass density slopes close to isothermal (i.e. -d log({\rho})/d log(r) $\approx$ 2.0) and slope distributions statistically agreeing with observed strong lens galaxies in SLACS and BELLS. Agreement is only slightly worse with the more heterogeneous SL2S lens galaxy sample. Observations of strong-lens selected galaxies thus appear to favor models with relatively weak feedback in massive galaxies.Comment: re-submitted to MNRAS, bug fixed, conclusions unchanged, updated appendices and references, 23 pages, 10 Figures, 6 Table

AMICO galaxy clusters in KiDS-DR3: galaxy population properties and their redshift dependence

A catalogue of galaxy clusters was obtained in an area of 414 sq deg up to a redshift $z\sim0.8$ from the Data Release 3 of the Kilo-Degree Survey (KiDS-DR3), using the Adaptive Matched Identifier of Clustered Objects (AMICO) algorithm. The catalogue and the calibration of the richness-mass relation were presented in two companion papers. Here we describe the selection of the cluster central galaxy and the classification of blue and red cluster members, and analyze the main cluster properties, such as the red/blue fraction, cluster mass, brightness and stellar mass of the central galaxy, and their dependence on redshift and cluster richness. We use the Illustris-TNG simulation, which represents the state-of-the-art cosmological simulation of galaxy formation, as a benchmark for the interpretation of the results. A good agreement with simulations is found at low redshifts ($z \le 0.4$), while at higher redshifts the simulations indicate a lower fraction of blue galaxies than what found in the KiDS-AMICO catalogue: we argue that this may be due to an underestimate of star-forming galaxies in the simulations. The selection of clusters with a larger magnitude difference between the two brightest central galaxies, which may indicate a more relaxed cluster dynamical status, improves the agreement between the observed and simulated cluster mass and stellar mass of the central galaxy. We also find that at a given cluster mass the stellar mass of blue central galaxies is lower than that of the red ones.Comment: 14 pages, 16 figures, accepted for publication on MNRA