Context. Strong lensing mass measurements require the knowledge of the redshift of both the lens and the source galaxy. Traditionally, spectroscopic redshifts are used for this purpose. Upcoming surveys, however, will lead to the discovery of ∼105 strong lenses, and it will be very difficult to obtain spectroscopic redshifts for most of them. Photometric redshift measurements will also be very challenging due to the blending between lens and source light. Aims: The goal of this work is to demonstrate how to carry out an inference of the structural properties of the galaxy population from the analysis of a set of strong lenses with no individual source redshift measurements, and to assess the loss in precision compared to the case in which spectroscopic redshifts are available. Methods: Building on the formalism introduced in Paper III, I developed a method that allows a statistical strong lensing inference to be carried out while marginalising over the source redshifts. This method, which relies on the knowledge of the properties of the unlensed background source population and of the selection function of the survey, generalises an approach known as photogeometric redshift, originally introduced by the Strong Lensing Legacy Survey collaboration. I tested the method on simulated data consisting of a subset of 137 strong lenses that is complete above a cut in observational space. Results: The method recovers the properties of the galaxy population with a precision that is comparable to that attainable in the case in which individual source redshifts are known. Conclusions: The photogeometric redshift method is a viable approach for the analysis of large sets of strong lenses provided that the background source population properties and lens selection function are well known. less

How hot is the Universe today? How hot was it before? We report on the result of the observational determination of the mean temperature of hot gas in the Universe. We find that the mean gas temperature has increased ten times over the last 8 billion years, to reach about 2 million Kelvin today. As cosmic structures form, matter density fluctuations collapse gravitationally and baryonic matter is shock-heated and thermalized. We therefore expect a connection between the mean gravitational potential energy of collapsed halos and the mean thermal energy of baryons. Our result provides quantitative verification of such a connection via cosmic shock-heating. less

Context. Existing samples of strong lenses have been assembled by giving priority to sample size, but this is often at the cost of a complex selection function. However, with the advent of the next generation of wide-field photometric surveys, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness. Aims: There are two main advantages of working with a complete sample of lenses. First, such completeness makes possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. The present work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features. Methods: I introduce a general formalism for the statistical analysis of a sample of strong lenses with known selection function, and then test it on simulated data. The simulation consists of a population of 105 galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of ∼103 strong lenses, which form a complete sample above an observational cut. Results: The method allows the user to recover the distribution of the galaxy population in Einstein radius and mass density slope in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available. Conclusions: Complete samples of lenses are a powerful asset with which to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population. less

The observed pattern of linear polarization of the cosmic microwave background (CMB) photons is a sensitive probe of physics violating parity symmetry under inversion of spatial coordinates. A new parity-violating interaction might have rotated the plane of linear polarization by an angle β as the CMB photons have been traveling for more than 13 billion years. This effect is known as "cosmic birefringence." In this paper, we present new measurements of cosmic birefringence from a joint analysis of polarization data from two space missions, Planck and WMAP. This dataset covers a wide range of frequencies from 23 to 353 GHz. We measure β=0.342°+0.094°−0.091° (68% C.L.) for nearly full-sky data, which excludes β=0 at 99.987% C.L. This corresponds to the statistical significance of 3.6σ. There is no evidence for frequency dependence of β. We find a similar result, albeit with a larger uncertainty, when removing the Galactic plane from the analysis. less

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, αsps , defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of 0.5′′ , the strong lensing bias in αsps is 10% , while that in the central dark matter mass is 5% . The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Quadruply imaged quasar lenses, however, are biased towards higher ellipticity galaxies. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. less

Context. The Sérsic profile is a widely used model for describing the surface brightness distribution of galaxies. Spiral galaxies, however, are qualitatively different from a Sérsic model. Aims: The goal of this study is to assess how accurately the total flux and half-light radius of a galaxy with spiral arms can be recovered when fitted with a Sérsic profile. Methods: I selected a sample of bulge-dominated galaxies with spiral arms. Using photometric data from the Hyper Suprime-Cam survey, I estimated the contribution of the spiral arms to their total flux. Then I generated simulated images of galaxies with similar characteristics, fitted them with a Sérsic model, and quantified the error on the determination of the total flux and half-light radius. Results: Spiral arms can introduce biases on the photometry of galaxies in a way that depends on the underlying smooth surface brightness profile, the location of the arms, and the depth of the photometric data. A set of spiral arms accounting for 10% of the flux of a bulge-dominated galaxy typically causes the total flux and the half-light radius to be overestimated by 15% and 30%, respectively. This bias, however, is much smaller if the galaxy is disk-dominated. Conclusions: Galaxies with a prominent bulge and a non-zero contribution from spiral arms are the most susceptible to biases in the total flux and half-light radius when fitted with a Sérsic profile. If photometric measurements with high accuracy are required, then measurements over finite apertures are to be preferred over global estimates of the flux. less

We search for evidence of parity-violating physics in the Planck 2018 polarization data, and report on a new measurement of the cosmic birefringence angle, β. The previous measurements are limited by the systematic uncertainty in the absolute polarization angles of the Planck detectors. We mitigate this systematic uncertainty completely by simultaneously determining β and the angle miscalibration using the observed cross-correlation of the E- and B-mode polarization of the cosmic microwave background and the Galactic foreground emission. We show that the systematic errors are effectively mitigated and achieve a factor-of-2 smaller uncertainty than the previous measurement, finding β=0.35±0.14° (68% C.L.), which excludes β=0 at 99.2% C.L. This corresponds to the statistical significance of 2.4σ. less

Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H0. However, in order to obtain an accurate estimate of H0 from a sample of time-delay lenses, very good knowledge of the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H0 and the lens model parameters on a single object basis. Aims: The goal of this study is to determine whether it is possible to break the H0-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data with no stellar kinematics information. Methods: I simulated a set of 100 lenses with doubly imaged quasars and related time-delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results: The sample of 100 lenses on its own provides a measurement of H0 with 3% precision, but with a −4% bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a 1% level inference. Moreover, the 100 lenses allow for a 0.03 dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions: Breaking the H0-lens model degeneracy with lensing data alone is possible, but 1% measurements of H0 require either many more than 100 time-delay lenses or knowledge of the structural parameter distribution of the lens population from a separate sample of lenses. less

Context. The number of known strong gravitational lenses is expected to grow substantially in the next few years. The combination of large samples of lenses has the potential to provide strong constraints on the inner structure of galaxies. Aims: We investigate the extent to which we can calibrate stellar mass measurements and constrain the average dark matter density profile of galaxies by combining strong lensing data from thousands of lenses. Methods: We generated mock samples of axisymmetric lenses. We assume that, for each lens, we have measurements of two image positions of a strongly lensed background source, as well as magnification information from full surface brightness modelling, and a stellar-population-synthesis-based estimate of the lens stellar mass. We then fitted models describing the distribution of the stellar population synthesis mismatch parameter αsps (the ratio between the true stellar mass and the stellar-population-synthesis-based estimate) and the dark matter density profile of the population of lenses to an ensemble of 1000 mock lenses. Results: We obtain the average αsps, projected dark matter mass, and dark matter density slope with greater precision and accuracy compared with current constraints. A flexible model and knowledge of the lens detection efficiency as a function of image configuration are required in order to avoid a biased inference. Conclusions: Statistical strong lensing inferences from upcoming surveys provide a way to calibrate stellar mass measurements and to constrain the inner dark matter density profile of massive galaxies. less

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims: We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods: We selected 2409 central massive elliptical galaxies (log M*/M⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u − g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, Lr, 10, and the light-weighted surface brightness slope, Γ10. Results: We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with Lr, 10 and anti-correlates with Γ10. At fixed redshift, Lr, 10 and Γ10, the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass. less