Can the halo model describe 2<sup>nd</sup>- and 3<sup>rd</sup>-order correlation functions of gravitational lensing consistently?

To understand and model the distribution of and the relation between baryonic and dark matter in the Universe is one of the key challenges in contemporary astrophysics. A well-established theoretical description is given by the semi-analytical <em>halo model</em>, which combines the <em>dark matter halo model </em>and <em>the halo occupation distribution</em> (HOD). Whereas the former reduces the complex distribution of dark matter to the clustering of dark matter halos on large scales and the radial distribution of dark matter within these halos on small scales, the latter incorporates galaxies based on the assumption that galaxies can only form and live within dark matter halos. The validity of the halo model is determined by how well its predictions match ever-newer observations. <br /> A unique tool to map the matter distribution in the Universe is the <em>gravitational lensing effect</em>, the phenomenon that light rays emitted from distant objects get differentially deflected by the gravitational potential of the intervening matter distribution, visible or dark. As statistical applications of the weak gravitational lensing effect, <em>galaxy-galaxy lensing</em> (G2L) and <em>galaxy-galaxy-galaxy lensing</em> (G3L) probe the average matter density profile about galaxies and pairs of galaxies, respectively, thereby revealing the relation between galaxies and their dark host halos. The halo model is known to provide a good description of second-order statistics as G2L, but so far neither a quantitative comparison of halo model predictions for G3L to observations nor direct model fits to observations of G3L are available. <br /> The main goal of this doctoral thesis is to test whether the halo model can describe measurements of G2L and G3L consistently. To this end halo model fits are performed to the G2L signal measured from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) for 29 galaxy samples of stellar mass (5 × 10<sup>9</sup> M<sub>⊙</sub> ≤ M<sub>*</sub> ≤ 2 × 10<sup>11</sup> M<sub>⊙</sub>), luminosity (-23 ≤ M<sub>r</sub> ≤ -18) and galaxy-type, further differentiating between low (0.2 ≤ z<sub>ph</sub> < 0.44) and high redshift (0.44 ≤ z<sub>ph</sub> < 0.6) samples. Based on the best-fit models, predictions of G3L in terms of the <em>aperture statistics</em> 〈 N<sup>2</sup> M<sub>ap</sub> 〉(<em>Θ</em>) are generated, which are confronted with their observational counterparts from CFHTLenS. The comparison shows that the halo model can successfully describe G3L at a level of accuracy that is on par with that of dark matter simulations into which baryonic physics is incorporated using a semi-analytical model (SAM). <br /> Moreover, first-time halo model predictions of the more intuitive representation of G3L as <em>excess mass maps</em> are presented. Trends of excess mass with lens-lens separation, galaxy properties, and redshift are studied and are discussed together with the respective predictions for the aperture statistics 〈 N<sup>2</sup> M<sub>ap</sub> 〉(<em>Θ</em>). The results suggest that excess mass increases with stellar mass and luminosity, and decreases with redshift. The results confirm the observation of excess mass to increases with decreasing lens-lens separation, and to be more than one order of magnitude higher around pairs of early-type compared to late-type galaxies. Additionally, the dependence of excess mass on halo model properties is explored; i.e. the contributions of the one-, two-, and three-halo terms are quantified. For a projected lens-lens separation of 1 arcmin the one-halo term is found to be suppressed for late-type galaxies as a consequence of them being typically field galaxies. The results for 〈 N<sup>2</sup> M<sub>ap</sub> 〉(<em>Θ</em>) show that for all other samples the one-halo term clearly dominates up to aperture scales of 10arcmin. A sensitivity analysis regarding the dependence of G3L on individual HOD parameters shows that, first, changes are maximal in the range probed by CFHTLenS (1-10arcmin). Second, changes in G3L exceed 20% for four out of five parameters when varied individually by ±20% around their best-fit values, indicating that simultaneous model fits to G2L and G3L will help to constrain the HOD. Finally, it is tested whether the halo model can describe map features observed with CFHTLenS, in particular a vertical bulge-like feature that is absent in predictions of SAMs. Although the halo model cannot reproduce the feature, the predictions match the observations regarding the amplitude of the signal around the lenses and the rate of drop-off of the signal towards the outer regions of the map.

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