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What causes this?<br />

• Choice of cluster center<br />

• Cluster galaxy<br />

(de)contamina@on<br />

• Shear calibra@on<br />

• NFW concentra@on<br />

• Source redshiF<br />

distribu@on<br />

• N-­‐body calibra@on<br />

• …<br />

20 D. E. Applegate et al.<br />

Mean error: 0.77 Mean error: 0.88<br />

My weak lensing mass<br />

Mean error: 0.84 Mean error: 1.38<br />

Your weak lensing mass<br />

Applegate et al. (2012)<br />

Figure 13. Comparison of our mass measurements to results in the literature. Panel a) shows the comparison to Okabe et al. (2010), panel b) to Mahdavi et al.<br />

(2008), panel c) to Bardeau et al. (2007), and panel d) to Pedersen & Dahle (2007). For each comparison, we measure the mass within the overdensity radis r∆<br />

of the respective work. The solid line indicates the one-to-one line, the long-dashed line shows the average of the mass ratios, and the dotted line the median.<br />

For simplicity, the unweighted average is shown, since the measurements are correlated due to overlap in the source galaxy samples.


An observable that scales with mass<br />

What causes this?<br />

It’s not just weak lensing. Systema@c errors in X-­‐ray, SZ, and O/<br />

IR mass-­‐observables propagate through the system to create<br />

(or hide) discrepancies. Lesson: calibrate mass-­‐observables<br />

jointly in fully self-­‐consistent way. If you do this, you find the<br />

field is in a significantly worse state than stated systema9c<br />

errors in previous published works would have you believe.<br />

Planck Collaboration: Planck early results. XII.<br />

Planck Early Results XII (2011)<br />

Your mass calibrated to weak lensing My mass calibrated to weak lensing<br />

. 2. Scaled SZ signal measurements, ˜Y500, binnedbyrichness,N200. Theleft-handpanelpresentstheresultsfortheJohnston et al. (20<br />

00 − N200 relation, the right-hand panel for the Rozo et al. (2009) relation.Ineachcase,thereddiamondsshowthebin-average,redshift-sca<br />

0 calculated as the weighted mean of all individual measurements (e.g., Fig. 1) inthebin,wheretheweightsaretakenfromtheestimatedfi<br />

se. The thick error bars show the corresponding uncertainty on the bin-average SZ signal, while the lighter error bars indicate the uncertai<br />

nd by bootstrap analysis; they are larger due to the presence of intrinsic scatter within the bins, most notable at high richness (see Fig. 4). T<br />

e points represent the model prediction for each bin found by averaging, with the same weights as the data, the SZ signal expected from


Cluster-­‐abundance cosmology<br />

234 G. Mark Voit: Tracing cosmic evolution with clusters of galaxies<br />

• Cosmological parameters:<br />

However, this problem is not as severe as one might<br />

expect because the evolution in the mass function itself<br />

is so dramatic, – Dark especially energyfor equa@on M1. This of state: part of w the =<br />

review discusses P/


ARI 2 August 2011 10:40<br />

Sample size<br />

10 6<br />

10 5<br />

10 4<br />

10 3<br />

10 2<br />

10 1<br />

10 0<br />

Cluster surveys<br />

ACO<br />

B50<br />

EMSS<br />

1990<br />

RCS1<br />

MaxBGC<br />

BCS<br />

REFLEX<br />

400d<br />

MACS<br />

RDCS<br />

ACT<br />

2000<br />

Year<br />

SPT<br />

2010<br />

10 14 M ☉<br />

10 15 M ☉<br />

SPT 2500 deg 2<br />

SPT 720 deg 2<br />

(Reichardt et al., 2012)<br />

Figure 1<br />

Yields from modern surveys of clusters used for cosmological studies are shown, with symbol size<br />

proportional to median redshift. Samples selected at optical ( gray filled circles), X-ray (red squares), and<br />

millimeter (blue triangles) wavelengths are discussed in Section 3.2. Stars and horizontal lines (purple) show<br />

full sky counts of halos expected in the reference CDM cosmology (see Section 2) with masses above 1015 Adapted from Allen, Evrard, & Mantz (2012)<br />

14<br />

MCXC<br />


7<br />

The thermal<br />

Sunyaev-Zel’dovich<br />

effect"<br />

7


photon by roughly kBTe/mec 2 , causing a small (⇥1 mK) distortion in the CMB<br />

spectrum. Figure 1 shows the SZE spectral distortion for a fictional cluster that is<br />

over 1000 times more massive than a typical cluster to illustrate the small effect.<br />

The SZE appears as a decrease in the intensity of the CMB at frequencies below<br />

⇥218 GHz and as an increase at higher frequencies.<br />

The derivation of the SZE can be found in the original papers of Sunyaev &<br />

Zel’dovich (Sunyaev & Zel’dovich 1970, 1972), in several reviews (Sunyaev &<br />

The Sunyaev-­‐Zel’dovich effect<br />

Zel’dovich 1980a, Rephaeli 1995, Birkinshaw 1999), and in a number of more re-<br />

cent contributions that include relativistic corrections (see below for references).<br />

This review discusses the basic features of the SZE that make it a useful cosmological<br />

tool.<br />

Take-­‐home message #1<br />

SZ signal is not an emissive process but a<br />

spectral disor@on, so with beam well<br />

matched to the size of clusters, it’s nearly<br />

redshiF independent.<br />

Figure 1 The cosmic microwave background (CMB) spectrum, undistorted (dashed<br />

line) and distorted by the Sunyaev-Zel’dovich effect (SZE) (solid line). Following<br />

Sunyaev & Zel’dovich (1980a) to illustrate the effect, the SZE distortion shown is for<br />

a fictional cluster 1000 times more massive than a typical massive galaxy cluster. The<br />

SZE causes a decrease in the CMB intensity at frequencies ⇥218 GHz and an increase<br />

at higher frequencies.<br />

Measured SZ spectrum
<br />

of A2163<br />

Take-­‐home message #2<br />

SZ signal is a direct probe of total thermal<br />

energy, and so is a good proxy for cluster<br />

mass.


South Pole Telescope<br />

M500 (10 14 -1<br />

Msun h70) detected clusters<br />

10<br />

SPT-720 deg 2<br />

Planck-ESZ<br />

ROSAT-All sky<br />

Reichardt et al. (2012)<br />

1<br />

0.0 0.5 1.0 1.5<br />

z


Calibra@ng mass-­‐observables with<br />

weak lensing<br />

NDRA CLUSTER COSMOLOGY PROJECT. II. 1047<br />

that the scatter in<br />

in Mtot for a given<br />

X-ray analysis, as<br />

al mass in simulated<br />

robust X-ray mass<br />

YX,isdefinedas<br />

(10)<br />

ng the cluster X-ray<br />

ii 0.15 r500 − 1 r500,<br />

phere r500, derived<br />

otal thermal energy<br />

atedlow-frequency<br />

ich 1972). The total<br />

nstobeaverygood<br />

al. 2004;Motletal.<br />

n the simplest selfes<br />

with the cluster<br />

• Hydrosta@c equilibrium<br />

◌ Weak lensing<br />

Vikhlinin et al. (2009)<br />

Figure 11. Calibration of the Mtot–YX relation. Points with errorbars show<br />

Chandra results from Vikhlinin et al. (2006) withsevenadditionalclusters<br />

(Section 4). The dashed line shows a power law fit (excluding the lowest mass<br />

cluster) with the free slope. The dotted line shows the fit with the slope fixed<br />

at the self-similar value, 3/5 (parametersforbothcasesaregiveninTable3).<br />

Open points show weak lensing measurements from Hoekstra (2007;thesedata


Weak lensing


Weak lensing<br />

Williamson, Oluseyi, & Roe (2007)


SPT targeted weak lensing sample<br />

o 33 clusters at 0.3 < z < 1.3<br />

o Complete SZ, X-­‐ray coverage<br />

o Spectroscopy, Spitzer NIR, and<br />

mul@band OIR from the ground<br />

Ground WL sample<br />

• Magellan/Megacam camera<br />

• 19 clusters at 0.3 < z < 0.6<br />

• Imaging in (u)gri in 2011A+B<br />

Space WL sample<br />

• HST/ACS camera<br />

• 14 clusters at 0.6 < z < 1.3<br />

• Imaging in F606W and F814W<br />

in Cycle 18 and Cycle 19<br />

• Added deep imaging with VLT<br />

• Observa@ons ongoing


SPT-­‐CL J0348-­‐4514, z = 0.39, M 500 = 5.2×10 14 M sun


SPT-­‐CL J0546-­‐5345, z = 1.07, M 500 = 8.0×10 14 M sun


Stellar locus photometric calibra@on<br />

Magellan/IMACS stellar locus<br />

SLR: Stellar Locus Regression<br />

Allows for calibra@on of<br />

colors and magnitudes<br />

without the tradi@onal use<br />

of standard star fields<br />

Successfully used by<br />

Weighing the Giants to<br />

obtain photo-­‐z’s<br />

Adapted from<br />

High et al. (2009)<br />

SLR gives dereddened colors to 0.01−0.03 mag (SDSS)<br />

and magnitudes to 0.05 mag (2MASS).


− i<br />

Stellar locus photometric calibra@on<br />

Magellan/Megacam stellar locus<br />

i − J<br />

g − r r − i<br />

SLR gives dereddened colors to 0.01−0.03 mag (SDSS)<br />

and magnitudes to 0.05 mag (2MASS).


s, in<br />

ation<br />

and<br />

nly a<br />

The<br />

ples,<br />

cribe<br />

and<br />

laxy<br />

stars<br />

f the<br />

hese<br />

from<br />

een<br />

few<br />

is more difficult for smaller or fainter galaxies, and the intrinsic morphology<br />

distribution of galaxies varies as a function of magnitude<br />

in images other than set B, ngals and σ γ are likely to be correlated<br />

in a complicated fashion. Es@ma@ng Galaxy selectionshear effects and weighting<br />

schemes are discussed in Sections 5.6 and 5.7.<br />

4.3 Shear calibration bias and residual shear offset<br />

Shear pipelines that we use:<br />

• ground data: Henk Hoekstra (HH)<br />

• space data: Tim Schrabback (TS)<br />

As with STEP1, we assess the success of each method by comparing<br />

the mean shear measured in each image with the known input shears<br />

γ input<br />

i . We quantify deviations from perfect shear recovery via a<br />

linear fit that incorporates a multiplicative ‘calibration bias’ m and an<br />

additive ‘residual shear offset’ c. With a perfect shear-measurement<br />

method, both of these quantities would be zero. Since the input shear<br />

is now applied in random directions, we measure two components<br />

each of m and c, which correspond to the two components of shear:<br />

Full pipelines blind-­‐tested by the Shear<br />

TesHng Program (STEP: Heymans et al.<br />

2006; Massey et al. 2007). Includes<br />

realis@c point-­‐spread func@ons.<br />

STEP bias sta@s@cs:<br />

〈 ˜γ1〉−γ input<br />

1<br />

〈 ˜γ2〉−γ input<br />

2<br />

= m1γ input<br />

1<br />

= m2γ input<br />

2<br />

+ c1<br />

+ c2.<br />

(43)<br />

Shear code recovers truth with no measurable<br />

C○ 2007 The Authors. Journal compilation C○ 2007 RAS, MNRAS 376, 13–38<br />

Massey et al. (2007)<br />

Figure 6. Comparison of shear-measurement accuracy from different meth-<br />

addi9ve bias (c) and with mul9plica9ve bias<br />

ods, in terms of their mean residual shear offset 〈c〉 and mean shearcalibration<br />

bias (m) 〈m〉. of 2% In the ortop beRer. panel, these parameters have been averaged<br />

over both components of shear and all six sets of images; the bottom panel<br />

includes only image sets A, B, C and F, to avoid the two highly elliptical<br />

PSFs. Note that the entire region of these plots lie inside the grey band that<br />

indicated good performance for methods in Fig. 3 of STEP1. The results<br />

from methods C1, SP, MS1 and ES1 are not shown here.<br />

age set<br />

bias is<br />

elliptic<br />

Strang<br />

pixelliz<br />

betwee<br />

not hav<br />

indeed<br />

succes<br />

Pixe<br />

about t<br />

it may<br />

conseq<br />

able to<br />

objects<br />

high o<br />

galaxie<br />

if Nyqu<br />

etry, bu<br />

pixelliz<br />

seeing,<br />

seeing)<br />

unders<br />

worse<br />

there.<br />

We<br />

lization<br />

ential c<br />

study o<br />

(in pre<br />

bration<br />

pixels,<br />

Becaus<br />

of shea<br />

tics. H<br />

ual clu<br />

The ne<br />

pixel s<br />

mean<br />

promis<br />

method


Magellan/Megacam PSF performance<br />

PSF polariza9on residuals are 0.003 to 0.005 rms,<br />

no appreciable residual in radial bins.<br />

High et al. (2012)


Magellan/Megacam catalogs<br />

Source redshiF distribu@on and<br />

cluster-­‐galaxy decontamina@on<br />

Procedure for ground sample:<br />

o Cut out i > 25 24<br />

o Cut out |z phot − z cluster| < 0.05 region in color-­‐color<br />

space<br />

o Es@mate mean and variance of β from reference<br />

photo-­‐z catalogs using the same cuts<br />

CFHTLS Deep field photo-­‐z catalogs<br />

Coupon et al. 2009<br />

Low contamina9on<br />

near z cluster<br />

High et al. (2012)


Magellan/Megacam catalogs<br />

Source redshiF distribu@on and<br />

cluster-­‐galaxy decontamina@on<br />

Procedure for ground sample:<br />

o Cut out i > 25 24<br />

o Cut out |z phot − z cluster| < 0.05 region in color-­‐color<br />

space<br />

o Es@mate mean and variance of β from reference<br />

photo-­‐z catalogs using the same cuts<br />

Magellan/Megacam catalogs<br />

High et al. (2012)


O/NIR: Magellan/Megacam<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J2145-­‐5644, z = 0.48, M 500 = 6.5×10 14 M sun<br />

White contours: SZ S/N Cyan contours: κ


The results<br />

SPT-­‐CL J2145-­‐5644, z = 0.48, M 500 = 6.5×10 14 M sun


O/NIR: Magellan/Megacam<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J0348-­‐4514, z = 0.39, M 500 = 5.2×10 14 M sun<br />

White contours: SZ S/N Cyan contours: κ


The results<br />

SPT-­‐CL J0348-­‐4514, z = 0.39, M 500 = 5.2×10 14 M sun


O/NIR: VLT/FORS2 & Spitzer<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J0546-­‐5345, z = 1.07, M 500 = 8.0×10 14 M sun<br />

Cyan contours: κ


The results<br />

SPT-­‐CL J0546-­‐5345, z = 1.07, M 500 = 8.0×10 14 M sun


O/NIR: VLT/FORS2<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J2331-­‐5051, z = 0.58, M 500 = 5.1×10 14 M sun<br />

Cyan contours: κ


O/NIR: HST/ACS<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J2331-­‐5051, z = 0.58, M 500 = 5.1×10 14 M sun<br />

Cyan contours: κ


The results<br />

SPT-­‐CL J2331-­‐5051, z = 0.58, M 500 = 5.1×10 14 M sun


O/NIR: HST/ACS & Spitzer<br />

SZ: SPT S/N<br />

κ: Kaiser Squires reconstruc@on<br />

Color scale: SZ S/N Black contours: κ<br />

The results<br />

SPT-­‐CL J2106-­‐5844, z = 1.13, M 500 = 8.4×10 14 M sun<br />

Cyan contours: κ


The results<br />

SPT-­‐CL J2106-­‐5844, z = 1.13, M 500 = 8.4×10 14 M sun


Calibra@on to N-­‐body simula@ons<br />

ArHcle NFW WL mass bias<br />

Becker & Kravtsov<br />

2012<br />

-­‐5% to -­‐10%<br />

Rasia et al. 2012 -­‐5% to -­‐10%<br />

Bahe et al. 2012 -­‐5%<br />

High et al. 2012 -­‐5% to -­‐10%<br />

Our tests:<br />

• Use two flavors of Dark Energy Survey mocks at 220<br />

deg 2 and 5k deg 2 ; fake galaxies with realis@c color,<br />

magnitude, and clustering proper@es (ADDGALS, R.<br />

Wechsler et al.)<br />

• Replicate our color and magnitude selec@on for all<br />

massive 0.25 < z < 0.65 halos<br />

• Also geared up on simula@ons from Becker &<br />

Kravtsov (2012)<br />

WL NFW masses recover truth with overall bias of -­‐5% to -­‐10%.


WL test of joint SZ/X-­‐ray masses<br />

Mean calibraHon from ground<br />

sample: 1.26 ± 0.16<br />

Mean calibraHon from space<br />

sample: 1.16 ± 0.26<br />

High et al. (in prep.)


=0.655 ± 0.02 (1.16)<br />

AWL = 4G<br />

R2 BWL ↵Mpiv 1c2 Dpiv =0.0457 ⇥ (BWL0.13) (±BWL0.06) (1.17)<br />

WL calibraHon of M – YSZ :<br />

A first look at the SPT data<br />

BWL = (1.18)<br />

CWL =1± 0.01 (1.19)<br />

YSZ measured with Rapid Gridded<br />

Likelihood Es@mator (T. Montroy et al.<br />

in prep.).<br />

DWL =0± 0 (fixed) (1.20)<br />

EWL =0± 0 (fixed) (1.21)<br />

Assume self-­‐similar scaling with free<br />

normaliza@on parameter,<br />

Astrophysical scaling relations<br />

M500<br />

10 14 M<br />

= eA<br />

✓<br />

YsphD2 2/3<br />

AE(z) 10 5 Mpc 2<br />

◆3/5<br />

19 SPT-­‐detected clusters used here:<br />

• 7 from space sample<br />

• 12 from ground sample<br />

Aghanim et al. (2012) and Applegate et<br />

al. (2012) have also given evidence for<br />

-­‐30% WL biases in LoCuSS results<br />

(Okabe et al. 2010; Marrone et al.<br />

2012).<br />

(1.22)<br />

These results are preliminary.<br />

High et al. (in prep.)


A SZ<br />

jak 20<br />

at ⇠ > 2. This maximization bias comes from having<br />

maximized ⇠ across possible cluster positions and filters 2<br />

explain<br />

scales, e↵ectively adding three degrees of freedom to the<br />

levels<br />

fit with ⇠ analogous to a 0.5 0.6 0.7 0.8 0.9 1.0 1.1 verse,<br />

at z =<br />

8<br />

Implica@on for cosmology<br />

creasin<br />

of CM<br />

Fig. 5.— Assuming a wCDM cosmology, the two-dimensional<br />

marginalized constraints on ASZ and 8. Contours show the a 95%<br />

68% and 95% confidence regions for the SPTCL +H0+BBN (red) In F<br />

and CMB+BAO+SNe+SPTCL (green) data sets. The horizontal and 8<br />

black dashed line is the center of the theory prior on ASZ.<br />

after13i the ma<br />

that find some evidence for a sterile neutrino species. sumeIt<br />

has been pointed out that these measurements areing most the<br />

wCDM<br />

consistent with two sterile neutrinos and ⌃m⌫& 1.7 ⌃m⌫< eV<br />

SPTCL+H0+BBN (Kopp et al. 2011).<br />

CDM+(m<br />

0.6<br />

Therefore, we >0)<br />

consider the joint Ne↵= cos-<br />

8<br />

CMB+BAO+SNe mological constraints<br />

CMB+H<br />

on Ne↵ 0+BAO<br />

and ⌃m⌫ to compare additio with<br />

+SPT these terrestrial results. CMB+H0+BAO+SPTCL 8 by a<br />

CL 0.5<br />

With only threeCMB+H neutrino 0+SPT species, CL we would expect by a fa<br />

Ne↵= 3.046, a value slightly larger than three because data d<br />

6<br />

0.4<br />

of energy injection from electron-positron annihilation<br />

ized on<br />

at the end of neutrino freeze-out (Dicus et al.<br />

maxim<br />

1982;<br />

Lopez<br />

0.3<br />

⌃m⌫=<br />

et al. 1999; Mangano et al. 2005). As Ne↵ in-<br />

As n<br />

creases, the contribution to the gravitational potential<br />

4<br />

of 0.2<br />

power<br />

the additional neutrino perturbations boosts thevored early<br />

growth of dark matter perturbations (Bashinsky & Seljak<br />

0.1<br />

the ne<br />

2004), which also increases 8 (Hou et al. 2011). its phy As<br />

2<br />

explained in Section 5.2, adding neutrino mass at the<br />

0.0<br />

Ne↵ m<br />

levels considered here only a↵ects the low-redshift theuni mo<br />

0.5 0.6 0.7 0.8 0.9 1.0 1.1 verse, 0.65 suppressing 0.70 structure 0.75 0.80 formation, 0.85 and lowering Keisler 8<br />

at z = 0. Therefore, increasing 8 Ne↵ will also allowthe an in- ex<br />

8<br />

creasing ⌃m⌫. Keisler et al. (2011) used a combination the mo<br />

Fig. 6.— of Assuming CMB+H0+BAO a ⇤CDM cosmology data to withconstrain massive neutrinos, ⌃m⌫< 0.69also eV at w<br />

the two-dimensional a 95% CL, marginalized<br />

8 =0.803 constraints ± 0.056, and on Ne↵= ⌃m⌫ and 3.98 ± 0.43. genera<br />

8. Contours show the 68% and 95% confidence regions for<br />

the CMB+H0+BAO In Figure (gray, 7, dashed), we showCMB+H0+BAO+SPT the constraints on Ne↵, cosmo ⌃m⌫,<br />

CL<br />

(orange, solid), and and 8, usingtheCMB+H0+BAO CMB+H0+SPTCL (blue, dot-dashed) data data set, before8, and wh<br />

sets. The SPT after CLincluding data improves the theSPTCL constraints data. on 8InandTable, ⌃m⌫, 5 we improv give<br />

by factors of 1.8 and 1.4, respectively.<br />

the marginalized constraints. When varying Ne↵ ⌃m⌫ we asc<br />

sume consistency with BBN for our constraints. conser Us-<br />

Recent ing measurements the CMB+H have+BAO+SPT shown a ⇠2 preference data set, for we constrain ical m<br />

2 . Additionally, h⇠i relates to<br />

⇠ by a Gaussian scatter of unit width. Simulations have<br />

been used to verify that these approximations introduce<br />

negligible bias or scatter compared to the Poisson noise<br />

of the sample. For further details we refer the reader to<br />

V10.<br />

We assume a ⇣ M500 relation of the form<br />

✓<br />

M500<br />

⇣ = ASZ<br />

3 ⇥ 1014M h 1<br />

◆BSZ ✓ cally spaced redshifts between 0


Summary<br />

o Weak lensing quality data obtained for 33 clusters<br />

o 19 clusters at 0.3 < z < 0.6 with Magellan/Megacam<br />

o 14 clusters at 0.6 < z < 1.3 with HST/ACS<br />

o full SZ, X-­‐ray, and spectroscopic overlap<br />

o First look at 28 clusters<br />

o provides 14% direct mass calibra@on<br />

o shows weak evidence for low mass es@mates<br />

o Analysis now undergoing refinement and scru@ny<br />

o First<br />

o WL detec@ons using Megacam at Magellan<br />

o direct calibra@on of code used on real data to N-­‐body<br />

simula@ons<br />

o Matching the staHsHcal power of the SPT CL data set will<br />

require a sub-­‐3% calibraHon of mass. SPT CL poised to<br />

achieve δw = 0.035<br />

o Ancillary science<br />

SPT<br />

Magellan<br />

HST


EXTRA SLIDES


asic imaging information for the five<br />

of which has already been transformed to the SDSS<br />

hose be slopes a population are equal to thethat color-term coefficients,<br />

this is not an exhaustive test.<br />

The mean tangential shear as a fun<br />

the plane of the sky at the cluster re<br />

projected surface density, Σ(R), as (M<br />

where c is the speed of light, G is the gravitational constant, and<br />

er the source redshift β ≡ Dls/Ds is the lensing efficiency. Quantities D are angular-<br />

ure ometric is availableerror, in the online δi, journal.) by diameter distances, and l indicates the lens (the cluster) while s<br />

iCFHT > 24 − δi and indicates<br />

Weak<br />

sources.<br />

lensing<br />

photometric accuracy The observable quantity is not the shear but the reduced shear,<br />

basic WL-SZ imaging massinformation ratios at for the g, whichrelatestotheshearas<br />

five<br />

ly stimated subdominant from the to median the magnitude of<br />

-to-noise ematic uncertainties.<br />

ratio is five. Seeing is estimated<br />

Observable quan@ty: reduced shear, g. γ = (1 − κ)g (8)<br />

of photometric zero-point errors on the<br />

ios. Systematic errors in photometry 5 enter<br />

is through theShear estimation relates oftothe mass critical via:<br />

ch cluster (Section 4.2). We estimate this<br />

ly available photometric redshift catalogs<br />

which we apply the same photometric<br />

o the Megacam catalogs. If there is an<br />

i ′ this is the shear component oriented at 45<br />

-band zero point relative to that of the<br />

n we effectively probe a population that<br />

from which we infer the source redshift<br />

the effect of photometric error, δi, by<br />

hoto-z catalogs at iCFHT > 24 − δi and<br />

lysis. The level of photometric accuracy<br />

auses changes in the WL-SZ mass ratios at<br />

which is significantly subdominant to the<br />

and the largest systematic uncertainties.<br />

◦ with respect to γ+.<br />

The azimuthally averaged cross shear 〈γ×〉 as a function of<br />

radius provides a diagnostic for residual systematics, because no<br />

astrophysical effects, including lensing, produce such a signal.<br />

As a consequence, a non-zero 〈γ×〉 indicates the presence of<br />

some types of residual systematic error, though we note that<br />

this is not an exhaustive test.<br />

The mean tangential shear as a function of radial distance in<br />

the plane of the sky at the cluster redshift, R, dependsonthe<br />

projected surface density, Σ(R), as (Miralda-Escude 1995)<br />

〈Σ〉(< R) − Σ(R)<br />

〈γ+〉(R) = . (6)<br />

Σcrit<br />

This depends on the critical surface density,<br />

Σcrit = c2<br />

s the shear component oriented at 45<br />

The signal is a func@on of lens and source redshiFs through: 1<br />

, (7)<br />

4πG Dlβ<br />

where c is the speed of light, G is the gravitational constant, and<br />

β ≡ Dls/Ds is the lensing efficiency. Quantities D are angulardiameter<br />

distances, and l indicates the lens (the cluster) while s<br />

indicates sources.<br />

The observable quantity is not the shear but the reduced shear,<br />

g, whichrelatestotheshearas<br />

γ = (1 − κ)g (8)<br />

5<br />

◦ with respect to γ+.<br />

azimuthally averaged cross shear 〈γ×〉 as a function of<br />

s provides a diagnostic for residual systematics, because no<br />

physical effects, including lensing, produce such a signal.<br />

consequence, a non-zero 〈γ×〉 indicates the presence of<br />

types of residual systematic error, though we note that<br />

s not an exhaustive test.<br />

e mean tangential shear as a function of radial distance in<br />

lane of the sky at the cluster redshift, R, dependsonthe<br />

cted surface density, Σ(R), as (Miralda-Escude 1995)<br />

〈Σ〉(< R) − Σ(R)<br />

〈γ+〉(R) = . (6)<br />

Σcrit<br />

depends on the critical surface density,<br />

Σcrit = c2<br />

estimated from the median magnitude of<br />

l-to-noise ratio is five. Seeing is estimated<br />

t of photometric zero-point errors on the<br />

tios. Systematic errors in photometry enter<br />

sis through the estimation of the critical<br />

ach cluster (Section 4.2). We estimate this<br />

cly available photometric redshift catalogs<br />

o which we apply the same photometric<br />

to the Megacam catalogs. If there is an<br />

m i<br />

1<br />

, (7)<br />

4πG Dlβ<br />

e c is the speed of light, G is the gravitational constant, and<br />

A model for the project mass density,


Advantages<br />

1. Extremely simple theore@cal<br />

rela@onship between total<br />

mass and observables<br />

– A key piece of evidence for<br />

the existence of dark maver<br />

– Independent of maver’s<br />

dynamical state or history<br />

2. Rela@vely straighworward to<br />

realis@cally simulate in the<br />

same N-­‐body simula@ons that<br />

cosmological fixng func@ons<br />

are tuned to<br />

– Ray tracing<br />

– Source selec@on<br />

Weak lensing<br />

Challenges<br />

1. Accurately es@ma@ng<br />

reduced shear<br />

– Correct for the smearing and<br />

shearing by anisotropic point-­‐<br />

spread func@ons<br />

– Cluster galaxies contaminate<br />

shear profiles<br />

2. Accurately es@ma@ng source<br />

redshiF distribu@on<br />

– Photo-­‐z’s are hard!<br />

– Availability of photo-­‐z’s at very<br />

faint magnitudes or very high<br />

redshiF is scant


South Pole Telescope<br />

• (Sub)millimeter wavelength<br />

telescope:<br />

– 10 meter aperture<br />

– 1’ FWHM beam at 150 GHz<br />

– Off-­‐axis Gregorian op@cs design<br />

– 20 micron RMS surface accuracy<br />

– 1 arc-­‐second poin@ng<br />

– Fast scanning, up to 4 deg/sec in<br />

azimuth<br />

• SZ receiver:<br />

– 1 sq. deg FOV<br />

– ~960 background limited pixels<br />

– Observe in 3+ bands between 95-­‐220<br />

GHz simultaneously<br />

– Modular focal plane<br />

• Polarimeters are currently deployed<br />

for CMB polariza@on and deep-­‐SZ<br />

studies (SPTpol)

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