L4 high-z samples in Fig. 5.6, an increase of the amplitude with luminosity is visible, particularly for small aperture scales and high-z.
ThehN2Mapi(✓) signal of the early-type sample dominates over that of the late-types on all scales and for both redshift samples. The deviation reaches up to two orders of magnitude, for low-zaround✓⇠3 arcmin and for high-zon the smallest scales considered of ✓ ⇠ 0.1 arcmin. In contrast to the late-type sample, the early-type sample is found to resemble the signal of a typical stellar mass or luminosity sample, i.e. sm3/sm4 and L5/L6, in terms of amplitude and shape.
The preceding discussion suggests that the stellar mass and luminosity samples show a similar qualitative behaviour. Therefore, the following discussion of the excess mass maps is restricted to the stellar mass samples sm1 to sm6 and the galaxy-type samples. Addi-tionally, for conciseness only excess mass maps for a lens-lens separation of 1 arcmin are presented, which corresponds roughly to the separation explored in theCFHTLenSexcess mass maps. With respect to the aperture statistics, the discussion will focus exemplarily on the early- and late-type samples, as the former resembles a typical stellar mass sample and the latter is found to behave uniquely compared to all other samples.
76 CHAPTER 5. HALO MODEL PREDICTIONS OF EXCESS MASS MAPS
sm 1 1h sm 1 2h sm 1 3h
sm 2 1h sm 2 2h sm 2 3h
sm 3 1h sm 3 2h sm 3 3h
sm 4 1h sm 4 2h sm 4 3h
sm 5 1h sm 5 2h sm 5 3h
sm 6 1h sm 6 2h sm 6 3h
ETG 1h ETG 2h ETG 3h
LTG 1h LTG 2h LTG 3h
0% 20% 40% 60% 80% 100%
:: low-z ::
sm 1 1h sm 1 2h sm 1 3h
sm 2 1h sm 2 2h sm 2 3h
sm 3 1h sm 3 2h sm 3 3h
sm 4 1h sm 4 2h sm 4 3h
sm 5 1h sm 5 2h sm 5 3h
sm 6 1h sm 6 2h sm 6 3h
ETG 1h ETG 2h ETG 3h
LTG 1h LTG 2h LTG 3h
0% 20% 40% 60% 80% 100%
:: high-z ::
Figure 5.7: Relative contributions of the one-, two- and three-halo term (left to right) in the excess mass maps in percent for the stellar mass and galaxy-type samples (top to bottom). In the left plot the low-z results are shown, in the right plot the high-z results. All maps are for a lens-lens separation of 1 arcmin.
The lens positions are indicated by stars. The size of each map is 4⇥4 arcmin2.
from the same halo are suppressed, but correlations originating from di↵erent halos are enhanced.
Regarding redshift, a slight shift in contribution from the two-halo to the one-halo term is found for the late-type sample. In contrast, for the stellar mass and the early-type samples the relative contribution of the one-halo term decreases slightly with redshift, whereas the relative contributions of the two- and three-halo term increase. This could indicate that the excess mass of the common halo about pairs of galaxies from the sm1 to sm6, and the early-type samples increases with time, and vice versa for the late-type sample. Whether this finding reflects a physical trend can only be answered by comparing the maps at a fixed physical instead of angular separation.
The trends found for the early- and late-type galaxies become even clearer when ex-amining the aperture statistics predictions (Fig. 5.8). First of all, the crossover between the dominance of the one-halo term and the dominance of the two/three-halo terms hap-pens for the early-type low-zsample only at an aperture scale of approximately 10 arcmin, whereas for the late-type low-z sample the three-halo term starts to dominate already around 4 arcmin. Being typically cluster galaxies, early-type galaxies live in more ex-tended halos, which allows to find pairs of early-types sharing the same halo even at comparably large lens-lens separations. Therefore, the one-halo term contributes to much larger radii than in the case of late-types. Second, the crossover point shifts for early-types towards smaller aperture scales with increasing redshift. The observed increase of the influence of the one-halo term towards larger scales with time is partially due to ob-jects getting smaller with redshift. Partially, it may also reflect the bottom-up scenario of structure formation in a⇤CDM universe, where large structures are assumed to form by mergers of smaller structures. For the late-type sample the crossover point between one-and three-halo term stays roughly at the same aperture radius with changing redshift, but the two-halo term dominates over the one-halo term only at larger aperture scales for high-z. Third, the total amplitude increases with time: for the early-type sample partic-ularly on scales larger than 1 arcmin and for the late-type sample on scales smaller than 4 arcmin. This is to some extent due to the e↵ect of the samples having di↵erent redshift distributions. Additionally, this may reflect the accretion of mass with time in a cold dark matter model. Finally, Fig.5.8shows that, although the two-halo term adds a significant contribution to the signal particularly in the range tested by CFHTLenS, it is actually never the dominant term among the three halo terms.
As a final note, the computation of the fullG3L signal is computationally very expen-sive. This is also why in this work it is refrained from fitting the model simultaneously to G2LandG3Lto constrain theHOD. A possible approximation ofhN2Mapi(✓) by the sum of the one-halo term and the large-scale limit of the three-halo term is discussed inR¨odiger (2009). The results presented here are in agreement with R¨odiger (2009): the one-halo term is generally a good approximation up to scales of 2 3 arcmin. However, care must be taking for the late-type sample. Whereas the signal for the early-type and stellar mass samples is with a maximal deviation of 10% well approximated by the one-halo term up to scales of 3 arcmin, for late-types deviations of 10% occur already for 0.1 arcmin in the high-z case due to the suppression of the one-halo term.
78 CHAPTER 5. HALO MODEL PREDICTIONS OF EXCESS MASS MAPS
<
N2 Map>
θ [ arcmin ]
:: low−z ::
ETG
10−7 10−6 10−5 10−4 10−3 10−2
1 10
θ [ arcmin ] :: low−z ::
ETG total LTG
1h 2h 3h
1 10
<
N2 Map>
θ [ arcmin ]
:: high−z ::
ETG
10−7 10−6 10−5 10−4 10−3 10−2
1 10
θ [ arcmin ] :: high−z ::
ETG total LTG
1h 2h 3h
1 10
Figure 5.8: Contributions of the one-, two- and three-halo term to hN2Mapi(✓) for the early-type (left) and the late-type (right) samples as a function of aperture scale radius✓. Shown are the low-z (top), and the high-z results (bottom). The vertical lines indicate the range considered in the analysis in Chapter6.