Context. Several semi-analytic models (SAMs) try to explain how galaxies form, evolve, and interact inside the dark matter large-scale structure. These SAMs can be tested by comparing their predictions for galaxy–galaxy–galaxy lensing (G3L), which is weak gravitational lensing around galaxy pairs, with observations. Aims. We evaluate the SAMs by Henriques et al. (2015, MNRAS, 451, 2663, hereafter H15) and by Lagos et al. (2012, MNRAS, 426, 2142, hereafter L12), which were implemented in the Millennium Run, by comparing their predictions for G3L to observations at smaller scales than previous studies and also for pairs of lens galaxies from different populations. Methods. We compared the G3L signal predicted by the SAMs to measurements in the overlap of the Galaxy And Mass Assembly survey (GAMA), the Kilo-Degree Survey (KiDS), and the VISTA Kilo-degree Infrared Galaxy survey (VIKING) by splitting lens galaxies into two colour and five stellar-mass samples. Using an improved G3L estimator, we measured the three-point correlation of the matter distribution with “mixed lens pairs” with galaxies from different samples, and with “unmixed lens pairs” with galaxies from the same sample. Results. Predictions by the H15 SAM for the G3L signal agree with the observations for all colour-selected samples and all but one stellar-mass-selected sample with 95% confidence. Deviations occur for lenses with stellar masses below 9.5 h−2 M⊙ at scales below 0.2 h−1 Mpc. Predictions by the L12 SAM for stellar-mass selected samples and red galaxies are significantly higher than observed, while the predicted signal for blue galaxy pairs is too low. Conclusions. The L12 SAM predicts more pairs of low stellar mass and red galaxies than the H15 SAM and the observations, as well as fewer pairs of blue galaxies. This difference increases towards the centre of the galaxies’ host halos. Likely explanations are different treatments of environmental effects by the SAMs and different models of the initial mass function. We conclude that G3L provides a stringent test for models of galaxy formation and evolution.

In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions Γ(i) and the third-order aperture statistics $ {{\langle{{\mathcal{M}^3_\mathrm{ap}}}\rangle}} $ from the B IHALOFIT bispectrum model and validate these statistics with a series of N-body simulations. We then investigate how to bin the shear three-point correlation functions to achieve an unbiased estimate for third-order aperture statistics in real data. Finally, we perform a cosmological parameter analysis on KiDS1000-like mock data with second- and third-order statistics. In the absence of systematic effects, we recover all cosmological parameters with very little bias. Furthermore, we find that a joint analysis almost doubles the constraining power on S8 and increases the figure of merit in the Ωm-σ8 plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics.

Context. Galaxy-galaxy-galaxy lensing (G3L) is a powerful tool for constraining the three-point correlation between the galaxy and the matter field and thereby models of galaxy evolution. Aims. We propose three improvements to current measurements of G3L, designed to improve the precision and the accuracy by using the galaxies' redshifts and removing biases of the estimator. We further show how to account for lens galaxy magnification by the cosmic large-scale structure and how to convert the G3L signal from angular to physical scales.Methods. The improvements are tested on simple mock data and simulated data based on the Millennium Run with an implemented semi-analytic model of galaxies. Results. Our improvements increase the signal-to-noise ratio by on average 35 % at angular scales between 0. 1 and 10 and physical scales between 0.02 and 2 h −1 Mpc. They also remove the bias of the G3L estimator at angular scales below 1 , which was originally up to 40 %. The signal due to lens magnification is approximately 10 % of the total signal.

Context. Halo models and halo occupation distributions (HODs) are important tools to model the distribution of galaxies and matter. Aims. We present and assess a new method for constraining the parameters of HODs using the mean gravitational lensing shear around galaxy pairs, so-called galaxy-galaxy-galaxy lensing (G3L). In contrast to galaxy-galaxy lensing, G3L is also sensitive to the correlations between the per-halo numbers of galaxies from different populations. We employed our G3L halo model to probe these correlations and test the default hypothesis that they are negligible. Methods. We derived a halo model for G3L and validated it with realistic mock data from the Millennium Simulation and a semianalytic galaxy model. Then, we analysed public data from the Kilo-Degree Survey (KiDS), the VISTA Infrared Kilo-Degree Galaxy Survey (VIKING) and data from the Galaxy And Mass Assembly Survey (GAMA) to infer the HODs of galaxies at z < 0.5 in five different stellar mass bins between 10 8.5 h −2 M and 10 11.5 h −2 M and two colours (red and blue), as well as correlations between satellite numbers. Results. The analysis accurately recovers the true HODs in the simulated data for all galaxy samples within the 68% credibility range. The model best fits agree with the observed G3L signal on the 95% confidence level. The inferred HODs vary significantly with colour and stellar mass. In particular, red galaxies prefer more massive halos 10 12 M , while blue galaxies are present in halos 10 11 M . There is strong evidence (> 3σ) for a high correlation, increasing with halo mass, between the numbers of red and blue satellites and between galaxies with stellar masses below 10 10 M . Conclusions. Our G3L halo model accurately constrains galaxy HODs for lensing surveys of up to 10 3 deg 2 and redshift below 0.5 probed here. Analyses of future surveys may need to include non-Poisson variances of satellite numbers or a revised model for central galaxies. Correlations between satellite numbers are ubiquitous between various galaxy samples and are relevant for halos with masses 10 13 M , that is, of galaxy-group scale and more massive. Possible causes of these correlations are the selection of similar galaxies in different samples, the survey flux limit, or physical mechanisms such as a fixed ratio between the satellite numbers of distinct populations. The decorrelation for halos with smaller masses is probably an effect of shot noise by low-occupancy halos. The inferred HODs can be used to complement galaxy-galaxy lensing or galaxy-clustering HOD studies or as input to cosmological analyses and improved mock galaxy catalogues.

Context. Third-order weak lensing statistics are a promising tool for cosmological analyses since they extract cosmological information in the non-Gaussianity of the cosmic large-scale structure. However, such analyses require precise and accurate models for the covariance of the statistics. Aims. In this second paper of a series on third-order weak lensing statistics, we derive and validate an analytic model for the covariance of the third-order aperture statistics 〈Map3〉. Methods. We derive the covariance model from a real-space estimator for 〈Map3〉, including the Gaussian and non-Gaussian parts. We validate the model by comparing it to estimates from simulated Gaussian random fields (GRFs) and two sets of N-body simulations. Finally, we perform mock cosmological analyses with the model covariance and the simulation estimate to compare the resulting parameter constraints. Results. We find good agreement between the analytic model and the simulations, both for the GRFs and the N-body simulations. The figure of merit in the S8 − Ωm plane from our covariance model is within 3% of the one obtained from the simulated covariances. We also show that our model, which is based on an estimator using convergence maps, can be used to obtain upper and lower bounds for the covariance of an estimator based on three-point shear correlation functions. This second estimator is required to measure 〈Map3〉 in realistic survey data. In our derivation, we find that the covariance of 〈Map3〉 cannot be obtained from the bispectrum covariance and that it includes several ‘finite-field terms’ that do not scale with the inverse survey area. Conclusions. Our covariance model is sufficiently accurate for analysing stage III surveys. Covariances for statistics in Fourier space cannot always be straightforwardly converted into covariance for real-space statistics.