In this chapter first-time predictions of excess mass maps using the halo model are pre-sented. Trends of excess mass andhN2Mapi(✓) with angular separation, galaxy properties, and redshift are explored by predicting G3L for 29 galaxy samples based on the model
1http://kids.strw.leidenuniv.nl/index.php
2https://www.darkenergysurvey.org
fits to theCFHTLenS G2L. The halo model reproduces the trends found in observations (Simon et al. 2008, Simon+13, Simon+19), i.e. the amplitude of excess mass increases with decreasing lens-lens separation and the signal around pairs of early-type galaxies is more than a factor of ten higher than around late-types. Furthermore, a dependence of G3L on stellar mass and luminosity is found: the amplitude is higher for pairs of more massive and luminous galaxies, indicating that brighter and more massive galaxies inhabit more massive halos. The results indicate that this may also be the case for the least massive and luminous galaxies considered (sm1, L1 and L2), but to establish this finding one would need to account for the e↵ect of di↵erent redshift distributions causing di↵erent lensing efficiencies. The same applies to the increase of G3L with time predicted by the halo model, which may reflect the accretion of matter expected in a⇤CDM universe.
Concerning the contributions of the one-, two- and three-halo terms to the full signal, the model predicts that the one-halo term dominates from the smallest aperture scales up to 10 arcmin, which covers the range tested withCFHTLenS. This is the case for all samples other than the late-type sample, for which the two- and three-halo terms dominate already starting from⇠4 arcmin. The accuracy of approximatinghN2Mapi(✓) by the one-halo term depends on the considered galaxy sample. The deviation is less than 10% up to scales of 3 arcmin for all but the late-type sample. The excess mass map representation reveals that for all samples but the late-type sample the dominance of the one-halo term at a lens-lens separation of 1 arcmin results in the distribution of excess mass in a common halo around the lens pair. For the late-type sample the dominance of the two-halo term results in two peaks of excess mass around the individual lens positions. The one-halo term is suppressed for late-types, which is a consequence of late-types being typically field galaxies, and inhabiting less massive halos for which the probability to find two lenses in one halo is comparatively low.
The sensitivity ofG3Lrelative to±20% variations of theHODparameters is explored.
For the satellite parameter deviations of more than 50% are predicted. For the threshold masses M1 and Mth, and the parameter ↵cen changes of around 10 50% occur depend-ing on the galaxy sample. The changes decrease with stellar mass, which suggests that the low stellar mass samples are better suited to constrain the HOD. Furthermore, the change is largest in the angular range tested byCFHTLenS, except for the late-type sam-ple where the change is largest on scales smaller than 1 arcmin. This could help break parameter degeneracies if future measurements of G3L become reliable on scales smaller than 1 arcmin. Recent work by Laila Linke (priv. comm.) suggests that this will soon be possible. Unfortunately, no identifiable changes in the map features when varying the individualHOD parameters are found.
Excess mass map predictions for a combined sm1-sm6 sample are compared to their observational counterpart to see whether the halo model can explain the map features found withCFHTLenS that the recent SAM by Henriques+15 cannot. A generally good agreement is found: the excess mass peaks around the individual lens positions, and decreases from the centre towards the outer regions of the map by a value of⇠4⇥10 3, corresponding to a drop in the excess surface mass density of ⇠17hM pc 2. Like the SAM, the halo model can not reproduce the vertical bulge found in the observations.
However, the halo model could help test the genuineness of this feature by predictingG3L
88 CHAPTER 5. HALO MODEL PREDICTIONS OF EXCESS MASS MAPS for the scenarios Simon+19 name as possible physical sources: a misalignment between the distribution of the intra-cluster medium and of the dark matter, or between the orientation of lens pairs and of the parent halos.
As a final note, the most interesting results in terms of studying galaxy evolution can be expected from the galaxy-type samples. For all questions pursued in this chapter, the signal for the late-type sample shows a unique behaviour compared to the other samples at low redshifts, which becomes more similar to the ones of the other samples when studying high redshifts.
Testing G3L halo model predictions against CFHTLenS observations
The central question to be answered by this doctoral thesis is whether a ‘standard’ halo model can consistently describe second- and third-order galaxy-dark matter correlations as probed byG2L and G3L. To answer this question, the best-fit models to theCFHTLenS G2L(Chapter4) are used to predictG3Lin terms of the aperture statisticshN2Mapi(✓) for 28 galaxy samples of stellar mass, luminosity, and galaxy-type at two redshifts. The halo model predictions forhN2Mapi(✓) are then confronted with their observational counterpart from CFHTLenS (Simon+13). The results of this quantitative comparison are presented and discussed in this chapter. This work constitutes the next level test for the halo model and thereby puts to test our current understanding of the distribution of galaxies and dark matter in the Universe.
In Chapter 4the halo model is also fitted to theG2Lsignal measured by Saghiha+17 in the Millennium Simulation into which galaxies have been included using the SAM by Henriques+15. In addition to predictions forG2L, Saghiha+17 also published predictions of the G3L aperture statistics for the same stellar mass samples used in this work and compared them to the CFHTLenS G3L observations. The halo model predictions for hN2Mapi(✓) are compared to these SAM predictions, and it is discussed whether the accuracy of the halo model predictions is comparable to the one of theSAM.
The content of this chapter is being prepared for submission to Astronomy & Astro-physics.