Gravitational Lensing: Nature’S Weighing Scales

Gravitational lensing: Nature’s weighing scales

Henk Hoekstra Leiden Observatory Nature’s weighing scales

Over the past 30 years (weak) gravitational lensing has developed into a key tool to measure masses of objects, irrespective of their dynamical state.

Another important application of weak lensing is the study of the statistical properties of the matter distribution to constrain cosmological parameters.

With the adoption of Euclid this ﬁeld has an excellent future. Evidence for dark matter

Bullet Cluster

Clowe et al (2006) Lensing by clusters

Abell 223

Weighing the Giants Large cluster samples

We have two options to study cluster samples:

Masses for individual clusters: • study scatter • expensive • only massive clusters

Masses for ensembles of clusters: • cheap • large range in mass (and redshift) • but how to bin? • what about intrinsic scatter? Scaling relations Mahdavi et al. (2013)

Low S0: no intrinsic scatter? No difference between low/high S0 Cosmology with clusters

The number density of clusters as a function of mass and redshift is a sensitive probe of cosmology. Surveys are now ﬁnding unprecedented numbers of clusters.

Planck collaboration, XXIV (2015) Planck & SPT observations A correct interpretation requires accurate knowledge of the masses. This is why lensing measurements have become essential. UpdatedHoekstra CCCP weak lensinget al. masses (2015)23

Figure 21. Left panel:thedeprojectedaperturemassM500 from weak lensing as a function of the hydrostatic mass from Planck PlanckM = (0.76±0.05) M WL Collaboration et al. (2014a). Note that M500 Planckis measured using r500 from the estimateWL of YX ,andM500 is determined using the lensing derived value for r500.TheblackpointsshowourCCCPmeasurements,withthefilledsymbolsindicatingtheclustersdetected by Planck with a signal-to-noise ratio SNR > 7andtheopenpointstheremainderofthesample.Thedashedlineshowsthebest-fit power law model. The WtG results are shown as rosy brown colored points. Right panel:ratioofthehydrostaticandtheweaklensing mass as a function of mass. The dark hatched area indicates the average value of 0.76 0.05 for the CCCP sample, whereas the rosy ± brown colored hatched region is the average for the published WtG measurements, for which we find 0.62 0.04. ±

eters for σ8 and Ωm are in tension with the measurements ter Abell 2163, which corresponds to the right-most point in obtained from the analysis of the primary CMB by Planck Figure 21. There are 20 SNR> 7clustersincommonwith Collaboration et al. (2014b). The results can be reconciled CCCP and these are indicated as filled points in Figure 21, by considering a low value of (1 b) 0.6. whereas the remaining clusters are indicated by the open − ∼ Recently, von der Linden et al. (2014b) estimated the points. We find that the SNR threshold is essentially a se- bias using the lensing masses for the 38 clusters in common lection by mass. For reference, the measurements from von between Planck and WtG. They compared their estimates der Linden et al. (2014b) are indicated by the rosy brown for M500 based on the NFW fits with c200 =4fromAp- colored points. plegate et al. (2014) to the hydrostatic mass estimates from The right panel shows the ratio of the hydrostatic Planck Collaboration et al. (2014a). They obtained an aver- masses from Planck and our weak lensing estimates for all age ratio (1 b)=0.69 0.07, which alleviates the tension. 37 clusters in common. The hatched region indicates our es- − ± As our comparison in 4.1.1 and Fig. 15 shows, the timate for (1 b)=0.76 0.05 (stat) 0.06 (syst), which § − ± Planck± WtG masses are slightly higher than our estimates was obtained from a linear fit to M500 as a function of WL when we follow the same approach, but when we M500 that accounts for intrinsic scatter (Hogg et al. 2010). compare the masses from WtG to our deprojected The systematic error is based on the estimates presented aperture masses, which are more robust and there- in 4.3. We measure an intrinsic scatter of (28 6)%, most § ± fore used here, we find that the agreement is excel- of which can be attributed to the triaxial nature of dark lent. matter halos (e.g. Corless & King 2007; Meneghetti et al. There are 38 clusters in common between CCCP and 2010). If we restrict the comparison to the clusters with the catalog provided by Planck Collaboration et al. (2014a), SNR> 7(blackpoints)weobtain(1 b)=0.78 0.07, − ± although we omit Abell 115 from the comparison as we whereas (1 b)=0.69 0.05 for the remaining clusters. For − ± determine masses for the two separate components of this reference, the rosy brown colored points and hatched region merging cluster. The left panel in Figure 21 shows the depro- indicate the results for WtG, used in von der Linden et al. WL jected aperture mass M500 as a function of the hydrostatic (2014b). We refit these measurements, which yields mass M Planck from Planck Collaboration et al. (2014a). Note (1 b)=0.62 0.04 and an intrinsic scatter of (26 5)%. 500 − ± ± that the observed value for YX was used to estimate the ra- Our measurement of the bias is in agreement with the nom- Planck WL dius r500 used to determine M500 ,whereasM500 is based inal value adopted by Planck Collaboration et al. (2014c) on the value for r500 listed in Table 2. For the cosmological and we conclude that a large bias in the hydrostatic mass analysis, Planck Collaboration et al. (2014c) restricted the estimate is unlikely to be the explanation of the tension of sample to clusters above a SNR threshold of 7 in unmasked the cluster counts and the primary CMB. areas. In our case, the mask only impacts the merging clus- von der Linden et al. (2014b) find modest evidence for

c 0000 RAS, MNRAS 000,000–000 ⃝ Planck & SPT observations Planck collaboration, XXIV (2015)

Perhaps the difference is real!? Testing X-ray masses

Mahdavi et al. (2013)

“cool core”

“disturbed” Stacking results

Johnston et al. (2007) Stacking results

van Uitert et al. (2015) Average scaling relations

Leauthaud et al. (2010) Lensing by galaxies ? ? ? ?

Dynamical and strong lensing studies provide important constraints on the mass distribution on scales of a few tens of kpc.

But what do we know about the mass distribution on scales larger than 100kpc? How can we study this (as a function of redshift)? galaxy-galaxy lensing

RCS2: 800 square degrees (van Uitert et al. 2011) How to interpret the signal?

van Uitert et al. (2011)

clustering

halo mass How to interpret the signal?

The signal (the galaxy-mass cross-correlation function) is the convolution of the dark matter distribution around galaxies and the clustering properties of the lenses.

We have some options to infer information about the properties of the dark matter halos around galaxies:

- interpret the data in the context of a model (simulations/analytical) - deconvolve the correlation function - look at isolated halos

- use the GMCC to learn about cosmology The Halo-Model 4 3 M = 3 (180¯)r

Numerical Simulation view Simulation Numerical

central and Halo Model view Model Halo satellite galaxies The Halo-Model

Ingredients of the model

- galaxies are host or satellite - density proﬁles for hosts & satellites - prescription of the clustering of halos - prescription of the occupation of halos - every dark matter particle resides in a halo

It is statistical in nature:

- it predicts the radial dependence of the signal - it does not make use of the observed positions of lenses - it naturally can account for central and satellite galaxies. A closer look at stacking

StackingHow t oaccordinginterpre tot t anhe observedsignal? galaxy property

Introduction Stacking Galaxy Bias

Conditional Luminosity Function

Galaxy-Galaxy Lensing ! Galaxy-Galaxy Lensing ! The Measurements ! How to interpret the signal? ! Comparison with CLF Predictions ! Cosmological Constraints

Conclusions haloesBecaus eofo fdifferentstacking th emasseslensing signal is difﬁcult to interpret Mixed together Galaxy Transformations central and satellite galaxies

Centrals vs. Satellites ∆Σ(R|L) = R P (M |L)∆Σ(R|M )dM Environment Dependence ∆Σ(R|M ) = (1− fsat)∆Σce}n(R|M )+fsat∆Σsat(R|M ) Conclusions This complicates the interpretation

Extra Material P (M |L) and fsat(L) can be computed from Φ(L|M )

Using Φ(L|M ) constrained from clustering data, we can predict the lensing signal ∆Σ(R|L1, L2)

The Galaxy-Dark Matter Connection - p. 19/39 Modeling the stacking

(r M) (r M) n (r M) dm | dm | s | Convolution of the halo density Dark matter halo density proﬁle and the number density proﬁle distribution of galaxies

+ contributions from the clustering of lenses (2-halo term) Edo van Uitert et al.: The relation between baryons and dark matter

9 Edo van Uitert et al.: The relation between baryons and dark matter

4.1. Lensing signal from the halo model is assumed to follow an NFW profile in the inner regions. The outer regions of the subhalo are tidally stripped of its We now proceed to explain how the lensing signal is com- dark matter by the central halo. Due to this stripping the puted. The ensemble averaged tangential shear is the sum lensing signal is proportional to r−2 at radii larger than the of the signal around central galaxies and satellites, since we truncation radius. Based on good agreement with numerical cannot distinguish between them. We compute each contri- simulations, Mandelbaum et al. (2005b) chose a truncation bution separately, starting with the signal around central radius of 0.4r200, and we use the same. This choice corre- galaxies. It is assumed that the central galaxies are located sponds to roughly 50% of the dark matter being stripped at the centre of the dark matter haloes. Two terms con- from the subhalo. tribute to the lensing signal around central galaxies: the sig- 1h To compute the lensing signal induced by the halo where nal coming from the halo where the galaxy resides (γt,cent), the subhalo resides, we calculate the power spectrum de- 2h and the signal from nearby haloes (γt,cent). Hence the total scribing the correlation between the subhalo and the dark signal around central galaxies is given by matter profile of the central halo: 1h 2h γt,cent = γ + γ . (15) t,cent t,cent 1h 1 P (k, Mh)= dνf(ν)Ns(M,Mh) The density profiles of the central haloes are assumed to sat (2π)3n¯ ! (19) be NFW, which we compute using the mass-concentration ydm(k, M)yg(k, M), relation from Duffy et al. (2008) given by Equation 7. By × picking a central halo mass we can thus compute the tan- withn ¯ the mean galaxy number density, which can be de- gential shear of the central halo term directly, as spectro- Ns(M,Mh) termined usingn ¯ =¯ρ dνf(ν) M ,andyg the ra- scopic redshifts are available for all lenses. dial Fourier transform of the radial distribution of satellites 2h " The calculation of γt,cent requires the power spectrum around the central halo. We assume that the radial distri- describing the correlation between the galaxy in the central bution of satellites follows an NFW profile with a concen- halo and the dark matter of nearby haloes: tration cg, given by the mass-concentration relation from Duffy et al. (2008). To asses the sensitivity to the shape of 2h PNL(k) Pcent(k, Mh,r)=bg(Mh,r) 3 the radial distribution of the satellites, we also calculate the (2π) 1h (16) γt,sat term using a cg that is varied by a factor of two. We Mlim find that this change mainly impacts the model signal at dνf(ν)b(ν,r)ydm(k, M), small scales: for a larger (smaller) concentration, the signal × !0 increases (decreases). At scales larger than a few hundred with bg(Mh,r) the bias of the central galaxy, PNL(k)the kpc, the change of the model signal is negligible. When we non-linear power spectrum from Smith et al. (2003), and fit these adjusted models to the data, we find that the best ydm(k, M) the radial Fourier transform of the central halo fit model parameters do not change significantly. We con- density profile divided by mass: clude that the signal-to-noise of our data currently does not r200 enable us to discriminate between halo models with differ- 1 2 sin(kr) ydm(k, M)= dr4πr ρdm(r, M ) , (17) ent radial distributions of satellite galaxies. M !0 kr Finally we compute the contribution from nearby haloes which we calculate using the analytical formula given in to the lensing signal around satellite galaxies: Pielorz et al. (2010). Mlim The dark matter profiles of adjacent haloes cannot over- 2h PNL(k) Psat(k, Mh,r)= 3 dνf(ν)b(ν,r)ydm(k, M) lap, which is prevented by implementing halo exclusion. (2π) !0 Different approaches to halo exclusion have been used in the ρ¯ Ns(M,Mh) literature. For example, Cacciato et al. (2009) set the two- dνf(ν)b(ν,r) yg(k, M). halo correlation function to zero below r , which leads to ×n¯ ! M 180 (20) a sharp truncation in the halo models. We follow the approach of Tinker et al. (2005), which leads to a more natu- The three power spectra are converted into their respective ral smooth cut-off: the integral in Equation 16 is cut off for Modelingshear signals using Equation the 8, and thestacking contributions from masses greater than Mlim which is chosen such that the r200 the central galaxies and satellites are combined to yield of the central halo does not overlap with the r200 of nearby haloes: r200(Mh)+r200(Mlim)=r. It should be noted that γt =(1 α) γt,cent + αγt,sat, (21) this choice, as any other halo exclusion approach, is an ap- − proximation. Ultimately, numerical simulations should be where α is the fraction of satellites of the sample. The used to provide improved estimates for P 2h . resulting model is compared to the data. cent 6 CFHTLenS The contribution of the satellites to the lensing signal consists of three terms: the signal from the subhalo where The lens sample is selected to cover a range in an ob- compute the 2-halo term, we assume that the dependence of the trunc Velander al. (2013) et the satellite resides (γt,sat ), the signal from the central halo servable, such as luminosity or stellar mass, as the relationgalaxy bias on mass follows the prescription from Sheth et al. in which the subhalo resides (γ1h ), and the signal from between the mean observable and the lensing mass is a use-(2001), incorporating the adjustments described in Tinker et al. t,sat ful constraint for simulations. The dark matter haloes of the nearby haloes (γ2h ). Hence the total signal around satel- (2005). t,sat lenses from such a sample have different masses, however, We model satellite galaxies as residing in subhaloes whose lites is given by and it is therefore important to account for the scatter inspatial distribution follows the dark matter distribution of the trunc 1h 2h the observable-halo mass relation. If the halo mass distri-main halo. The subhaloes have been tidally stripped of dark γt,sat = γt,sat + γt,sat + γt,sat. (18) Following Mandelbaum et al. (2005b) bution is well-known, this can be done by integrating thematter in the outer regions. trunc we adopt a truncated NFW profile, choosing a truncation radius of First we compute the lensing signal of the subhalo, γ , 2 t,sat models over the distribution of halo masses. Unfortunately,0.4r200 beyond which the lensing signal is proportional to r− , following Mandelbaum et al. (2005b). The density profile the distribution is generally not accurately known as thewhere r is the physical distance from the lens. This choice results in about 50% of the subhalo dark matter being stripped, and we acquire a satellite term which supplies signal on small scales. Thus satellite9 galaxies add three further components to the total lensing signal: the contribution from the stripped subhalo (∆Σstrip), the satellite 1-halo term which is off-centred since the satellite galaxy is Figure 3. Illustration of the halo model used in this paper. Here we have 12 1 not at the centre of the main halo, and the 2-halo term from nearby used a halo mass of M200 = 10 h70− M , a stellar mass of M = 10 1 ⊙ ∗ haloes. Just as for the central galaxies, the three terms add to give 5 10 h− M and a satellite fraction of α =0.2. The lens redshift is × 70 ⊙ the satellite lensing signal: zlens =0.5. Dark purple lines represent quantities tied to galaxies which are centrally located in their haloes while light green lines correspond to strip 1h 2h ∆Σsat = ∆Σsat + ∆Σsat + ∆Σsat . (7) satellite quantities. The dark purple dash-dotted line is the baryonic component, the light green dash-dotted line is the stripped satellite halo, dashed There is an additional contribution to the lensing signal, not lines are the 1-halo components induced by the main dark matter halo and yet considered in the above equations. This is the signal induced by dotted lines are the 2-halo components originating from nearby haloes. the lens baryons (∆Σbar). This last term is a refinement to the halo model presented in VU11, necessary since weak lensing measures the total mass of a system and not just the dark matter mass. Fol- plete circular averages and will be present in the observed stacked lowing Leauthaud et al. (2011) we model the baryonic component lensing signal as well. Because of our high sampling of this ran- as a point source with a mass equal to the mean stellar mass of the dom points signal, we can correct the observed signal measured in lenses in the sample: each field by subtracting the signal around the random lenses. This random points test is discussed in more detail in Mandelbaum et al. bar M ∆Σ = ⟨ ∗⟩ . (8) (2005a). πr2 This term is fixed by the stellar mass of the lens, and we do not fit it. Note that we ignore the baryonic term for neighbouring 3.2 The halo model haloes, but their contribution is negligible. To accurately model the weak lensing signal observed around Finally, to obtain the total lensing signal of a galaxy sample galaxy-size haloes, we have to account for the fact that galaxies of which a fraction α are satellites we combine the baryon, central generally reside in clustered environments. In this work we do this and satellite galaxy signals, applying the appropriate proportions: by employing the halo model software first introduced in VU11. bar ∆Σ = ∆Σ +(1 α)∆Σcent + α∆Σsat . (9) For full details on the exact implementation we refer to VU11; here − we give a qualitative overview. All components of our halo model are illustrated in Figure 3. In this 12 1 Our halo model builds on work presented in Guzik & Sel- example the dark matter halo mass is M200 =1 10 h70− M , 10 1 × ⊙ jak (2002) and Mandelbaum et al. (2005b), where the full lensing the stellar mass is M =5 10 h− M , the satellite fraction ∗ × 70 ⊙ signal is modelled by accounting for the central galaxies and their is α =0.2, the lens redshift is zlens =0.5 and Dls/Ds =0.5. On satellites separately. We assume that a fraction (1 α) of our galaxy small scales the 1-halo components are prominent, while on large − sample reside at the centre of a dark matter halo, and the remaining scales the 2-halo components dominate. objects are satellite galaxies surrounded by subhaloes which in turn reside inside a larger halo. In this context α is the satellite fraction of a given sample. The lensing signal induced by central galaxies consists of two 4 LUMINOSITY TREND components: the signal arising from the main dark matter halo (the The luminosity of a galaxy is an easily obtainable indicator of its 1h 1-halo term ∆Σ ) and the contribution from neighbouring haloes baryonic content. To investigate the relation between dark matter 2h (the 2-halo term ∆Σ ). The two components simply add to give halo mass and galaxy mass we therefore split the lenses into 8 bins the lensing signal due to central galaxies: according to MegaCam absolute r′-band magnitudes as detailed in 1h 2h Table 1 and illustrated in Figure 4. The choice of bin limits follow ∆Σcent = ∆Σ + ∆Σ . (6) cent cent the lens selection in VU11. This choice will allow us to compare In our model we assume that all main dark matter haloes are well our results to the results shown in VU11 since the RCS2 data have represented by an NFW density profile (Navarro, Frenk, & White been obtained using the same filters and telescope. We also split 1996) with a mass-concentration relationship as given by Duffy each luminosity bin into red and blue subsamples as described in et al. (2008). The halo model parameters resulting from an analy- Section 2.1 and proceed to measure the galaxy-galaxy lensing sig- sis such as ours (see, for example, Section 4) are not very sensitive nal for each sample, with errors obtained via bootstrapping over the 1 1 to the exact halo concentration, however, as discussed in VU11. To sources. We then fit the signal between 50 h70− kpc and 2 h70− Mpc

c 2012 RAS, MNRAS 000, 1–24 ⃝ CFHTLenS results CFHTLenS: Relation between galaxy DM haloes and baryons 7

Velander et al. (2013)

Figure 5. Galaxy-galaxy lensing signal around lenses which have been split into luminosity bins according to Table 1, modelled using the halo model described in Section 3.2. The dark purple (light green) dots represent the measured differential surface density, ∆Σ, of the red (blue) lenses, and the solid line is the best-ﬁt halo model. Triangles represent negative points that are included unaltered in the model ﬁtting procedure, but that have here been moved up to positive values as a reference. The dotted error bars are the unaltered error bars belonging to the negative points. The squares represent distance bins containing no objects. For a detailed decomposition into the halo model components, please refer to Appendix C.

2 Table 1. Details of the luminosity bins. (1) Absolute magnitude range; (2) elements in the χ fit have significant impact on the best fit pa- Number of lenses; (3) Mean redshift; (4) Fraction of lenses that are blue. rameters. The results are shown in Figure 5 for all luminosity bins and for each red and blue lens sample, with details of the fitted halo model parameters quoted in Table 2. The halo masses quoted in this Sample M (1) n (2) z (3) f (4) r′ lens ⟨ ⟩ blue table have been corrected for various contamination effects as de- L1 [ 21.0, 20.0] 90293 0.30 0.70 tailed in Section 4.1 and Appendix A. Note that the number of blue − − L2 [ 21.5, 21.0] 32271 0.30 0.45 lenses in the two highest-luminosity bins, L7 and L8, is too low to − − L3 [ 22.0, 21.5] 22475 0.30 0.32 constrain the halo mass. In the following sections, these two bins − − L4 [ 22.5, 22.0] 12552 0.30 0.20 have therefore been removed from the analysis of blue lenses. − − L5 [ 23.0, 22.5] 5439 0.30 0.11 − − L6 [ 23.5, 23.0] 1762 0.30 0.06 As expected, the amplitude of the signal increases with lu- − − L7 [ 24.0, 23.5] 349 0.30 0.03 minosity for both red and blue samples indicating an increased − − L8 [ 24.5, 24.0] 77 0.30 0.09 halo mass. In general, for identical luminosity selections blue − − galaxies have less massive haloes than red galaxies. For the red sample, lower luminosity bins display a slight bump at scales of 1 1 h70− Mpc. This is due to the satellite 1-halo term becoming 2 ∼ with our halo model using a χ analysis. Only the halo mass M200 significant and indicates that a large fraction of the galaxies in those and the satellite fraction α are left as free parameters while we keep bins are in fact satellite galaxies inside a larger halo. On the other all other variables fixed. When fitting, we assume that the co- hand, brighter red galaxies are more likely to be centrally located variance matrix of the lensing measurements is diagonal. Off- in a halo. The blue galaxy halo models also display a bump for the diagonal elements are generally present due to cosmic variance lower luminosity bins, but this feature is at larger scales than the and shape noise, but Choi et al. (2012) find that for a lens sam- satellite 1-halo term. The signal breakdown shown in Figure C2 ple at a similar redshift range as our lenses the covariance ma- (Appendix C) reveals that this bump is due to the central 2-halo trix is diagonal up to 1 Mpc, which is about the largest scale term arising from the contribution from nearby haloes. We note, ∼ we include in our fits. Furthermore, Figure 7.2 from the PhD however, that in these low-luminosity blue bins, the model overes- 3 thesis of Jens Rodiger¨ shows that the off-diagonal elements timates the signal at large scales. This may be an indicator that our are rather small. Hence we do not expect that the off-diagonal description of the galaxy bias, while accurate for red lenses, results in too high a bias for blue lenses. Currently we do not have enough data available to investigate this effect in detail, but in the future 3 http://hss.ulb.uni-bonn.de/2009/1790/1790.htm this should be explored further. c 2012 RAS, MNRAS 000, 1–24 ⃝ CFHTLenS results

Velander et al. (2013) KiDS+GAMA: properties of galaxy groups 11

Table 2. Summary of the bin limits used to compute the stacked ESD signal, the number of groups in each bin, the mean redshift of the groups in each bin and the mean stellar mass of the BCG.

BCG 2 Observable Bin limits Number of lenses Mean redshift log( M? [h M ] ) h i 2 log[Lgrp/(h L )] (9.4, 10.9, 11.1, 11.3, 11.5, 11.7, 12.7) (540, 259, 178, 233, 142, 66) (0.13, 0.20, 0.23, 0.26, 0.30, 0.35) (11.00, 11.23, 11.29, 11.37, 11.47, 11.70) 1 /(s km) (0, 225, 325, 375, 466, 610, 1500) (501, 359, 124, 198, 147, 89) (0.15, 0.19, 0.21, 0.23, 0.26, 0.31) (11.05, 11.20, 11.30, 11.36, 11.41, 11.64) Nfof (5, 6, 7, 8, 11, 19, 73) (481, 261, 170, 239, 181, 86) (0.21, 0.21, 0.21, 0.19, 0.18, 0.16) (11.17, 11.23, 11.29, 11.29, 11.35, 11.45) LBCG/Lgrp KiDS(1.0, 0.35, 0.25, 0.18, 0 .13,results0.08, 0) (346, 252, 296, 227, 200, 97) (0.:10, 0.16groups, 0.20, 0.25, 0.29, 0.34) (11.16, 11.19, 11.22, 11.29, 11.36, 11.53)

Figure 7. Stacked ESD profile measured around the groups BCG of the 6 group luminosity bins as a function of distance from the group centre. The group r-bandGAMA luminosity is increases a nearly from left to right complete and from top to bottom. redshift The stacking survey of the signal has down been done using to only m groupsr~19.8, with Nfof and> 5. The error bars on the stacked signal are computed as detailed in section 3.4 and we use dashed bars in the case of negative values of the ESD. The orange and yellow bandsallows represent thefor 68 andthe 95 percentile reliable of the model detection around the median, of while groups. the red line shows The the best fitlensing model. signal around the ~1400 central galaxies is studied in Viola et al. (submitted) For each luminosity bin, a mean halo mass is inferred with a than R200 over this full mass range, these mass measurements are • typical uncertainty on the mean of 0.12 dex. robust and direct as they do not require any extrapolation. The un- ⇠ The relative normalisation of the concentration-halo mass re- certainties on the masses are obtained after marginalising over the • +0.42 lation (see Equation 31) is constrained to be fc =0.84 0.23, in other model parameters. Typically these errors are 15% larger than agreement with the nominal value based on Duffy et al. (2008 ). what would be derived by fitting an NFW profile to the same data, The probability of having an off-centred BCG is po↵ < 0.97 ignoring the scatter in mass inside each luminosity bins. Note that • (2-sigma upper limit), whereas the average amount of mis-centring a simple NFW fit to the data in the 6 luminosity bins, with fixed in terms of the halo scale radius, o↵ , is unconstrained within the concentration (Duffy et al. 2008) would also lead to a bias in the R prior. inferred masses of approximately 25%. The amount of mass at the centre of the stack which con- The inferred halo masses in each luminosity bin are slightly • tributes as a point mass to the ESD profiles is constrained to be correlated due to the assumption that the scatter in halo mass is BCG +1.19 BCG MPM =APM M? =2.06 0.99 M? . constant in different bins of total luminosity. We compute the cor- h i h i relation between the inferred halo masses from their posterior dis- Figure 9 shows the posterior distributions of the halo model tribution, and we show the results in Figure 10. Overall, the correla- parameters and their mutual degeneracies. Table 3 and 4 list the me- tion is at most 20%, and this is accounted for when deriving scaling dian values of the parameters of interest with errors derived from relations (see Section 6). the 16th and 84th percentiles of the posterior distribution. We dis- cuss the constraints on the model parameters in further detail in the remainder of this section. 5.1.2 Concentration and mis-centring

1 The shape of the ESD proﬁle at scales smaller than 200 h kpc 5.1.1 Masses of dark matter haloes ⇠ contains information on the concentration of the halo and on the The dark matter halo masses of the galaxy groups that host the mis-centring of the BCG with respect to the true halo centre. How- stacked galaxy groups analysed in this work span one and a half ever, the relative normalisation of the concentration-halo mass re- 13 14.5 1 orders of magnitude with M [10 ..10 ]h M . Since our lation, fc, and the two mis-centring parameters, po↵ and o↵ are 2 1 R ESD proﬁles extend to large radii, our 2 h Mpc cut-off is larger degenerate with each other. A small value of fc has a similar ef-

c 2015 RAS, MNRAS 000, 000–000 16 Viola M.KiDS et al. results: groups

Figure 13. Left panel: Halo mass as a function of the total group r-band luminosity. The solid black points show the halo masses derived in this work from a haloViola model fit toet the stackedal. ESD(submitted) profile of groups with at: least extending 5 members brighter than scaling the GAMA magnitude relations limit. The vertical to error barslower indicate the 1-sigma uncertainty on the average halo mass after marginalising over the other halo model parameters, while the horizontal error bars indicate the 16th and 84thmasses, percentile of the luminosity but distributionwe can in each bin.also The red study line shows the bestthe fit power-law group to the data members… points. We constrain the slope of the relation to be 1.16 0.13. Our estimate of the 1-sigma dispersion around this relation is shown as the orange area and it accounts for the correlation between the mass ± measurements (see text). The open black circles show the halo masses derived from a lensing analysis of GAMA groups using SDSS galaxies as background sources (Han et al. 2014). Han et al. (2014) have included groups with 3 and 4 members brighter than the GAMA magnitude limits. Right panel: Derived mass-to-light ratio as a function of the group total luminosity from this work (black points), from the GAMA+SDSS analysis (open black circles), from the analysis of the CNOC2 group sample (Parker et al. 2005) (magenta diamonds) and from a lensing analysis of 130000 groups from the MaxBCG catalogue using SDSS imaging (Sheldon et al. 2009, (green crosses)). In blue we show the median relation derived using the 2PIGG catalogue (Eke et al. 2004). The red lines and the orange area correspond to those of the left panel. ity was measured in B-band. Given the small sample of groups, ences in the same mass range, thus showing the imminent potential only two measurements were possible at quite low group luminos- of such measurements. ity. We show their results as the magenta points in Figure 13. Fol- lowing Jee et al. (2014), we applied a 0.8 multiplicative correction to the B-band mass-to-light ratio in order to have an estimate for 6.2 The relation between halo mass and velocity dispersion the mass-to-light ratio in r-band. Only the mass-to-light ratio mea- Next, we focus on the scaling relation between the total halo mass surement in the high luminosity bin of the CNOC2 analysis, which and the group velocity dispersion. Again, we bin the groups in 6 corresponds to our low luminosity bin, can be directly compared to bins according to their velocity dispersion, with the boundaries cho- our analysis, given the luminosity range we probe. We find a good sen so that the signal-to-noise ratios of the stacked ESD profiles are agreement. equal (see Table 2). The halo masses in each bin are then found by The importance of the mass-to-light ratio in constraining the a joint halo model fit to the ESD profile in each velocity dispersion galaxy-dark matter connection has been stressed also in the con- bin. Figure 14 shows the corresponding results. The GAMA groups text of halo occupation distribution studies. For instance, van den span an order of magnitude in velocity dispersion, but most of the Bosch, Mo & Yang (2003) have shown that the Conditional Lumi- constraining power for the scaling relation comes from groups with 1 nosity Function can describe the abundance and large scale cluster- 500km s . This is expected given that the cut imposed on ⇠ ing of galaxies equally well assuming different cosmological pa- group apparent richness excludes the low mass systems from this rameters, provided that one can employ different mass-to-light ra- analysis, and that the survey volume is relatively small, and hence tios at group and cluster scales. In turn, the same notion was used our sample does not contain many very massive galaxy clusters. As in Cacciato et al. (2009) to show that the mass-to-light ratios in- in the case of binning by luminosity, we believe that the apparent ferred from galaxy-galaxy lensing, combined with clustering and richness cut imposed on the GAMA group catalogue will have a abundances, can be used to constrain cosmological parameters. non-neglible effect on the measurement of the average halo mass 1 Cacciato et al. (2009) reported that the same lensing data in the first velocity dispersion bin < 200km s . analysed with cosmological parameters taken from WMAP1 and At low velocity dispersion, we compare our results with those WMAP3 results led to mass-to-light ratios that differed by about from the CNOC2 survey (Carlberg et al. 2001), for which the mass 1 0.1 dex in the mass range 13 < log M/[h M ] < 14. Our data measurements are derived from the dynamical properties of the are on the verge of being able to distinguish between such differ- groups. In Figure 14 we show the average CNOC2 mass measure-

c 2015 RAS, MNRAS 000, 000–000 KiDS results: satellites 8 C. Sif´on,KiDS & GAMA collaborations

100

0.05

50 M h ( sat 0

0.1 1.0 0.1 1.0 0.1 1.0 1 1 1 R (h Mpc) R (h Mpc) R (h Mpc)

1 Figure 5. Excess surface density of satellite galaxies in the three radial bins summarized in Table 1 and shown in the legends in units of h Mpc. Black points show lensing measurements around GAMA group satellites using KiDS data; errorbars correspond to the square root of the diagonal elements of the covarianceSifon matrix. et Theal. solid (submitted) black line is the best-ﬁt model: we where subhaloscan arestart modelled asto having study NFW density observationally proﬁles, and orange and yellow shaded regions mark 68% and 95% credible intervals, respectively. Dashed lines show the contribution of a point mass with a mass equal to the median stellar mass ofthe each bin, dark which is includedmatter in the model. halos in dense environments.

1 488 groups. For comparison, using the same parameterization as we do, 522 rsat,3 = 0.46 h Mpc. At this radius, the average density in groups host +0.42 h i 489 Viola et al. (2015) measured fc = 0.84 0.23. Our smaller error- 523 in the first radial bin is seven times smaller than at rs,1 . h i 490 bars are due to the fact that we do not account for several nui- 524 As mentioned above, our simplistic modelling of groups does 491 sance parameters considered by Viola et al. (2015) in their halo 525 not a↵ect the posterior satellite masses significantly. Therefore it is 492 model implementation. Most notably, accounting for miscentring 526 sucient that our group masses are consistent with the results of 493 significantly increases the uncertainty on the concentration, since 527 Viola et al. (2015), and we do not explore more complex models 494 both a↵ect ⌃ at similar scales (Viola et al. 2015). Indeed, when 528 for the group signal. For a more thorough modelling of the lensing 495 they do not account for miscentring, Viola et al. (2015) measure 529 signal of groups in the KiDS-GAMA overlap region, see Viola et host +0.13 496 fc = 0.59 0.11, consistent with our measurement both in the cen- 530 al. (2015). 497 tral value and the size of the errorbars. While this means that our host 498 estimate of fc is biased, accounting for extra nuisance param- 499 eters such as miscentring is beyond the scope of this work; our 500 aim is to constrain satellite masses and not galaxy group properties. host 501 As shown in Figure 6, fc is not correlated with any of the other host 502 model parameters and therefore this bias in fc does not a↵ect our 531 4.3 The masses of satellite galaxies 503 estimates of the satellite masses.

504 Group masses are consistent with the results from Viola et al. 532 We detect the signal from satellites with significances >99% in all 505 (2015) (with the same caveat that the small errorbars are an artifact 533 three radial bins. Satellite masses are consistent across radial bins. 506 produced by our simplistic modelling of the host groups). Specif- 534 We show the marginalized posterior estimates and 68% credible 507 ically, our average mass-to-light ratios follow the mass-luminosity 535 intervals in Figure 7 as a function of 3-dimensional group-centric 508 relation found by Viola et al. (2015). As shown in Figure 6, group 536 distance, rsat (in units of the group radius r200). 509 masses are slightly correlated because they are forced to follow 537 Figure 7 also shows the subhalo mass as a function of 3- 510 the same mass-concentration relation determined by Equation 10. 538 dimensional separation from the group centre found in numeri- 511 Groups in the third bin are on average 3.4 0.8 times more ⇠ ± 539 cal simulations by Gao et al. (2004). Our data points are broadly 512 massive than groups in the first radial bin. This is a selection ef- 540 consistent with this trend. The bottom panel shows the average 513 fect, arising because groups in each bin must be big enough to 541 stellar mass fractions, which are also consistent with each other, 1 514 host a significant number of satellites at the characteristic radius 542 M?,sat/Msub 0.04 h . 6 h i⇠ 515 of each bin. For example, groups in the first radial bin have 543 We also show in Figure 7 the results obtained for the 1 +0.06 516 log Mhost,1/(h M ) = 13.46 0.06 and c1 3.3, which imply a 544 truncated theoretical model. The di↵erence between each pair h i 1 h i⇡ 517 = . scale radius rs,1 0 19 h Mpc, beyond which the density drops 545 of points depends on the posterior rt estimated in each 3 h i 518 as ⇢ r (cf. Equation 8). The average 3-dimensional distance / 546 bin through Equation 13. Specifically, we estimate rt = 519 of satellites to the group centre (obtained by randomly drawing +0.02 +0.03 +0.04 1 h i 547 (0.04 0.01, 0.06 0.02, 0.09 0.02) h Mpc. To illustrate this we also 520 such distances from NFW profiles with a lower limit given by the 548 show in Figure 7 the masses obtained by integrating the posterior 521 measured 2-dimentional distance, Rsat) in the third radial bin is 549 NFW models up to said truncation radii, shown by the dashed line, 550 which are fully consistent with the truncated model. This implies 551 that the truncated model produces the same results as the full NFW 6 Throughout, we quote masses and radii for a given radial bin by adding 552 model except we integrate the density profile up to di↵erent radii an index from 1 to 3 to the subscript of each value. 553 rt.

MNRAS 000, 1–?? (2015) KiDS results10 C. Sif´on,KiDS & GAMA: collaborationssatellites

opposed to one measured at the time of infall) SHMF proposed by van den Bosch et al. (2005), dN 1 (/ )↵ exp ( /) , (17)

) d / 12 10 where ↵ = 0.9 and = 0.13, and calculate the average subhalo M

1 mass (in units of the host mass), max 1 max h dN dN ( = d d , (18) h i d d "Z min # Z min sub 3 580 where min 10 is approximately the minimum fractional satel-

M ⇡ 581 lite mass we observe, and max = 1 is the maximum fractional satel- host 2/3 582 lite mass by deﬁnition. Integrating in this range gives = 0.0052. Msub (rsat/r200 ) h i 11 583 There are many uncertainties involved in choosing a min rep- ) 10 584 resentative of our sample, such as survey incompleteness and the

sub 0.08 585 conversion between stellar and total mass; we defer a proper mod- 0.06 586 elling of these uncertainties to future work. For reference, changing 587 by a factor 5 modiﬁes the predicted by a factor 3. Con-

hM min

( h i ⇠ 0.04 588 sidering the uncertainties involved, all we can say at present is that / 0.02 589 our results are consistent with ⇤CDM predictions. sat , 0.00

M 0.0 0.2 0.4 0.6 0.8 host 590 5 DISCUSSION & CONCLUSIONS rsat/r200 2 2 591 We used an e↵ective area of 68.5 deg over 100 deg of optical Figure 7. Top: Marginalized posterior mass estimates of satellite galaxies 592 imaging from KiDS to measure the lensing signal around spec- Sifon etfrom al. the full(submitted) NFW (black, large circles): andwe truncated need NFW (grey, more small 593 data!troscopically confirmed satellite galaxies from the GAMA galaxy circles) models, and the dashed black line shows the NFW masses within 594 group catalogue. We model the signal assuming NFW profiles for r t for comparison. Horizontal errorbars are 68% ranges in (3-dimensional) 595 both host groups and satellite galaxies, including the contribution rsat/r200 per bin. The black solid line shows the radial dependence of sub- 596 from the stellar mass for the latter, in the form of a point source. halo mass predicted by the numerical simulations of Gao et al. (2004) with 597 Taking advantage of the combination of statistical power and high an arbitrary normalization. Bottom: Stellar-to-total mass ratios in each bin. 598 image quality we split the satellite population into three bins in 599 projected separation from the group centre, which serves as a (high- 600 scatter) proxy for time-since-infall. We fit the data with a model that 554 4.4 The average subhalo mass 601 includes the satellite and group contributions using an MCMC (see 555 We can link the above results to predictions from numerical simula- 602 Section 3 and Figure 5), fully accounting for the data covariance. 556 tions. Comparisons of the satellite populations of observed galaxies 603 As a consistency check, we find group masses in good agreement 557 (or groups) provide valuable insights as to the relevant physical pro- 604 with the weak lensing study of GAMA galaxy groups by Viola et 558 cesses that dominate galaxy formation, as highlighted by the well 605 al. (2015), even though we do not account for e↵ects such as mis- 559 known “missing satellites” (Klypin et al. 1999; Moore et al. 1999) 606 centring or the contribution from stars in the BCG. 560 and “too big to fail” (Boylan-Kolchin et al. 2011) problems, which 607 We model both host groups and satellite galaxies with NFW. 2 561 suggest either that our Universe is not well described by a ⇤CDM 608 This model fits the data well, with /d.o.f. = 0.85 (PTE = 0.69). 562 cosmology, or that using numerical simulations to predict observa- 609 We are able to constrain total satellite masses to within 0.3 dex or ⇠ 563 tions is more complicated than anticipated. While the former may 610 better. Satellite galaxies have similar masses across group-centric 564 in fact be true, the latter is now well established, as the formation 611 distance, consistent with what is found in numerical simulations 565 of galaxies inside dark matter halos depends strongly on baryonic 612 (accounting for the measured uncertainties). Satellite masses as a 566 physics not included in N-body simulations, and the influence of 613 function of group-centric distance are influenced by a number of 567 baryons tends to alleviate these problems (Zolotov et al. 2012). 614 e↵ects. Tidal stripping acts more eciently closer to the group cen- 568 Here we specifically compare the average subhalo-to-host 615 tre, but on the other hand dynamical friction makes massive galax- 569 mass ratio, M /M , to ⇤CDM predictions through the sub- 616 ies sink to the center more eciently, an e↵ect referred to as mass ⌘ sub host 570 halo mass function (SHMF), which describes the mass distributions 617 segregation (e.g., Frenk et al. 1996). In addition, by binning the 571 of subhalos for a given dark matter halo mass. In numerical simu- 618 sample in (projected) group-centric distance we are introducing a 572 lations, the resulting SHMF is a function only of (e.g., van den 619 selection e↵ect such that outer bins include generally more massive 573 Bosch et al. 2005; Jiang & van den Bosch 2014). As summarized 620 groups, which will then host more massive satellites on average. 574 in Table 2, we find typical subhalo-to-host mass ratios in the range 621 Future studies with increased precision may be able to shed light 575 0.005 . . 0.025, statistically consistent across group-centric 622 on the interplay between these e↵ects by, for instance, selecting h i 576 distance. We obtain these values by taking the ratio Msub/Mhost at 623 samples residing in the same host groups or in bins of stellar mass. 577 every evaluation in the MCMC. For comparison, the values we ob- 624 As a proof of concept, we compare our results to predic- 578 tain using the truncated model are in 0.005, also consis- 625 tions from N-body simulations. These predict that the subhalo h tNFWi⇡ 579 tent across radial bins. 626 mass function is a function only of the fractional subhalo mass, We compare our results to the analytical evolved (that is, mea- 627 M /M . Our binning in satellite group-centric distance pro- ⌘ sub host sured after the subhalos have become satellites of the host halo, as 628 duces a selection e↵ect on host groups, such that each bin probes

MNRAS 000, 1–?? (2015) Cosmic shear weak lensing by large scale structure Ellipticity correlations Lensing by LSS

Born approximation: to ﬁrst order in the potential, the distortion can be approximated by the integral along the unperturbed light ray, with correction of order Φ2 (precision ~few %).

Analogous to 2D lensing we deﬁne the deﬂection potential Lensing by LSS

The 3-d Poisson equation in comoving coordinates is:

2 2 3H Ω ∇ Φ = 0 m δ 2a which yields a convergence: Lensing by LSS

How can we relate this to the measurements and the cosmological model? Limber’s equation Convergence power spectrum

geometry cosmology

But we do not measure κ... convergence vs shear Convergence power spectrum

Recall: shear and convergence are related; this allowed us to make mass reconstructions. Convergence power spectrum

The convergence and shear have the same power spectrum:

We can use the observed shear statistics to directly constrain the convergence power spectrum! shear variance How to quantify?

The cosmic shear signal is mainly a measurement of the variance in the density ﬂuctuations.

Little bit of matter, large ﬂuctuations

Lot of matter, small ﬂuctuations Same “lensing” signal Same Measuring variance Top-hat variance

Problems: mixes power on different scales and cannot properly account for gaps in the data. Measuring variance Ellipticity correlations

The shapes of galaxies become aligned as their light rays are deﬂected by common structures along the line-of-sight.

φ −2iφ −2iφ γt = −ℜ[γe ] and γ× = −ℑ[γe ]

ξ± (θ) = γt (ϑ )γt (ϑ +θ) ± γ x (ϑ )γ x (ϑ +θ) Ellipticity correlations

The ellipticity correlation functions are more convenient to use in practice: Slicing the universe

We need to measure the matter distribution as a function of redshift: in addition to the shapes, weak lensing tomography requires redshift information for the sources. Slicing the universe

The lensing kernel is most sensitive to structure halfway between the observer and the source. But the kernel is broad: we do not need precise redshifts for the sources. Slicing the universe Cosmic shear is sensitive to everything along the line-of-sight... Slicing the universe Slicing the universe

Tomography allows us to break the inherent degeneracy between normalization and matter density!

constrain the growth of structure

- test GR on cosmological scales - constrain dark energy properties Slicing the universe

MaHuterer et al. et al.(2006) (2006)

Because the kernel is broad the tomographic bins are very correlated. The gain saturates quickly with number of bins. Intrinsic alignments

Gravitational lensing is not the only source of shape alignments.The local gravitational tidal field generates torques and shear forces. Intrinsic alignments

As a result shapes and angular momenta of galaxies are intrinsically aligned and lead to additional contributions to the ellipticity correlation function:

Courtesy B. Joachimi Intrinsic alignments

not so easy

“easy”

Can we use the different redshift dependence? Intrinsic alignments Intrinsic alignments Joachimi & Bridle (2010)

Observable Intrinsic alignments Joachimi & Bridle (2010) Predicted power spectrum matter power spectrum

The largest contribution to the weak lensing power spectrum comes from scales that correspond to groups of galaxies, i.e. non-linear structures. To relate the observations to cosmological parameters we need very accurate predictions from numerical simulations (see talk by Romain Teyssier tomorrow).

The lensing signal is sensitive to the total matter power spectrum, not just that of dark matter. If baryons trace the dark matter perfectly then “simple” n-body simulations might be sufficient, but recent work suggests that feedback processes can redistribute a large fraction of the baryons.

Hydro-simulations to infer “real” C(l)

Recipe to convert n-body into “real” C(l) e.g. Semboloni et al. (2011)

Requires better modeling of feedback: Euclid data will be extremely useful! matter power spectrum

van Daalen et al. (2011): feedback processes can modify the matter power spectrum signiﬁcantly on scales that are important for cosmic shear. cannot ignore feedback

Semboloni et al. (2011): ignoring feedback may lead to large biases. We cannot just use bigger dark matter-only simulations. quantify feedback

Current simple halo model where: - galaxies are point masses with a luminosity - gas follows beta-model with some fraction removed model the feedback

Semboloni et al. (2011): biases can be reduced

Ignoring feedback Accounting for feedback Higher order statistics

Semboloni et al. (2013)

Comparison of 2- and 3-point statistics can be used to test the ﬁdelity of the feedback model (or perhaps even help to calibrate) Cosmic shear results Exponential growth

Dark energy physics

Dark energy constraints Ì Measurement

Detection First results

The ﬁrst cosmic shear detections were reported in Spring 2000: four groups (nearly) simultaneously put papers of astro-ph. Importantly the results agreed well (although the errors were large).

Bacon et al. (2000) Kaiser et al. (2000) van Waerbeke et al. (2000) Wittman et al. (2000) Observational tests

Kaiser & Squires (1993): Observational tests

This is now referred to as E-B mode decomposition Observational tests

E-mode (curl-free)

B-mode (curl) Observational tests

Here Q is a compensated ﬁlter (Schneider et al. 1998) No large-scale B-modes!

Hoekstra et al. (2002) Improved VIRMOS results

Van Waerbeke et al. (2005) CFHT Legacy Survey Uses 5 yrs of data from the Deep, Wide and Pre-survey components of the CFHT Legacy Survey

State-of-the-art cosmological survey with 154 deg2 uniquely covered - lensing analysis used the 7 i-band images (seeing <0.85”) - ugriz to i<24.7 (7σ extended source) - 4 ﬁelds CFHTLenS: the approach

Accurate cosmology is difﬁcult: we have to make sure we do not bias the analysis to a “desired” result.

Heymans et al. (2012): we ﬁrst employed a number of tests of the analysis that do not rely on cosmology. Star-galaxy correlation

The star-galaxy correlation function provides a cosmology independent way to assess the level and signiﬁcance of PSF-related systematics

Star-galaxy correlation: Tests on simulated data

CFHTLenS image simulations are created to match the observed properties of galaxies and the PSF. Miller al. (2013) et Tests on simulated data

Simulations show a S/N dependent multiplicative bias, which is accounted for (also see Melchior & Viola, 2012).

Miller et al. (2013) Signal vs source redshift

To test the redshift dependence we examine the galaxy- galaxy lensing signal (very weak cosmology dependence) Heymans al. (2012) et CFHT LenS: results

Van Waerbeke et al. (in prep.) Signal looks good!

Kilbinger et al. (2013) CFHT LenS: tomography

Heymans et al. (2013): narrower bins which means we cannot ignore the intrinsic alignment signal CFHT LenS: testing GR

For a linearly perturbed metric: dτ 2 = (c2 + 2ѱΦ)dt 2 − (1− 2Φ / c2 )ds2

Ψ is potential experienced by non-relativistic particles, such as galaxies; measured from redshift space distortions.

(Φ+ Ψ) is the potential experienced by relativistic particles, such as photons; measured using gravitational lensing

If we can decouple the potentials we can distinguish between dark energy and modiﬁed gravity. CFHT LenS: testing GR Simpson et al. (2013) The future looks great!

Dark energy physics

Dark energy constraints Ì Measurement

Detection KiloDegree Survey

The Kilo Degree Survey (KiDS) is the ﬁrst cosmic shear survey that can provide dark energy constraints without the need of priors from other probes! Observations have started and the survey will be completed in a couple of years. survey area: 1500 deg2 ﬁlter coverage: ugri ZYJHK

~10% error in w Dark Energy Survey 4m Blanco Telescope equipped with a new wide ﬁeld corrector+camera: 2.2 deg2 ﬁeld of view

525 nights: g,r,i,z: 5000 deg2 HyperSuprimeCamera Survey

8m Subaru equipped with a new wide ﬁeld corrector+camera:

~1.8 deg2 ﬁeld of view 300 nights: deep grizy survey of 1400 deg2

870 megapixels! Large Synoptic Survey Telescope

Proposed new 8m telescope designed for weak lensing

FoV: 10 deg2

cover the sky twice each week! Euclid

Euclid has been selected for adoption by the European Space Agency. Its primary cosmology probes, which drive the Eucliddesign, hasare: been selected by ESA

- Weak lensing by large scale structure - Clustering of galaxies - launch in ~6 years Euclid will image the - will observe 15000 deg2 - best 1/3 of the sky (15000 deg2) - will- similar push resolution everything at HST in optical to the limit - NIR imaging in 3 filters - Images for 2x109 galaxies

and carry out an unprecedented redshift survey with

- NIR spectra for 5x107 galaxies (0.7

Radiation in the form of ions, mostly Solar protons, causes damage to the lattice structure of the CCD, which traps electrons while they are being transferred in the readout process.

TRAPPING

RELEASE Euclid: new problems Euclid: performance

FoM > 400 (e.g. wp~0.016 and wa~0.16) Euclid: combining probes

As an example we can combine weak lensing, galaxy clustering and redshift space distortion measurements to get rid of astrophysical quantities (galaxy bias) to test theories of gravity:

which is nothing else than:

b Ω Ω ∝ M 0 ≈ M 0 f b f where f is the growth rate.

€ Euclid: cosmology machine

(09/2011)

Euclid addresses many aspects of the current cosmological paradigm! Euclid: strong lensing

Euclid will:

- Increase the number of strong lensing galaxy systems to ~300,000 compared to a few hundred known today. This allows for population studies, but also provides interesting numbers of rare events (double rings, high magnification). - Increase the number cluster strong lenses to ~5000.

Simulated Euclid image (VIS+NIR) Rare lensing event Euclid: strong lensing

100% of SLACS FromEuclid: curiosity to a multi-purpose strong tool for unique galaxy lensingstructure & formation studies

SLACS (2010) 2%EUCLID ofEUCLID Euclid (2020+) (2020) lenses…

Credit: Leon Koopmans Conclusions

The coming decade is going to be an exciting time to be working on weak gravitational lensing projects.

The rapidly increasing precision will require increased effort in understanding and dealing with systematic errors, both observationally and theoretically.