Theoretical/Numerical predictionsfor weak lensing cluster search

Outline1. Basics of WL cluster search

2. Analytic model predictions

3. Survey power

4. Noise and scatter

5. WL & Spec, demonstrative results fromSuprime33

6. Summary

Takashi HamanaNAOJ

Miyazaki’s talk for observational aspects

1. Weak lensing survey with Hyper-Suprime is avery efficient way to locate massive clusters, ifthe seeing is less than 0.7”.

2. Weak lensing survey is complementary to X-raysurvey (Optical, SZ, as well)

3. >1/3 of high peaks on the weak lensing mass map(cluster candidates) are false signals.

4. Projection effects makes WL cluster massestimation uncertain.

5. Spectroscopic follow-up very nicely screens outfalse signals and improves the mass estimation.

Conclusions

Basics of weak lensingcluster search

Gravitational lensingUnlensed Lensed

3.0

1014

==

z

MM sun

Mass distributionof a cluster

coherent distortionin backgroundgalaxy images

Weak lensing

Weak lensing mass reconstruction

grav. potentialtidal field

(1) basics

Weak lensing mass reconstruction(1) basics

Recipes:(1) Taking imaging data(2) Object detection(3) Shape measurement(4) WL mass reconstruction

Imaging dataWL mass map

All we need for WLis imaging data

Signal & noise(1) basics

S

LSLSL

SL

D

DDzzf

zzf

=

∝

),(

),(MassSignal 1/3

<zS>

Signal = the peak height on the WL mass map

Signal & noise(1) basics

densitynumber galaxy :iesellipticitgalaxy of RMS:

/

gal

e

galelensingobs

intrinsiclensingobs

n

nee

eee

σσ+=

+=

2gal arcmin/30

4.0~)0.7"FWHM (seeingobs Cam-Suprime Typical

≥

<

neσ

Detection S/N is basicallydetermined by the number densityof the “usable galaxies” ngal

Usable galaxies(1) basics

Stars(seeing size)

usable galaxies

Not all detected galaxies areusable for weak lensing.Seeing erases the lensing signalof small galaxies (size<seeing).Only the large galaxies(size>seeing) are usable for WL.

Number of usable galaxies islimited by the seeing.Good seeing (<0.7”) is essentialfor weak lensing survey.

WL signal lost

Analytic predictions fromsimple models

Detectable clusters(2) predictions

1 arcmin/30

4.0~ parameters Obs*

profileNFW universe LCDM

:Models

2gal

==

**

S

e

znσ

Significant detection

02.0noise =σ

NOT mass selected(2) predictions

Undetectable

Weak lensing clusters areNOT “mass selected”but the “weak lensing signalselected”

The detectable minimum mass is redshift dependent

Number counts(2) predictions

function mass PS1

arcmin/30 4.0~

parameters Obs*profileNFW

universe LCDM:Models

2gal

*=

≥

**

S

e

znσ

N~5/sq deg for S/N>4N~/10sq deg for S/N>3

Survey power

WL VS X-ray(3) survey power

X-ray cluster counts

Rosati et al (2002)

])//[(NewtonXMMdeg1/10~)10(

ROSATdeg1/1~)10(

2

214

213

scmergffNfN

X

XX

XX

−‹>‹>

−

−N~5/sq deg for S/N>4N~10/sq deg for S/N>3

WL cluster counts

Exposure time

by Suprime-Cam

X-ray surveyby XMM-Newton

4 pointings to cover 1deg2

1/4 deg2 FOV each (Suprime-Cam) 9 pointings/1 deg 2(XMM-LSS design)

1 pointing 3.1 deg 2

2lim

deg1/5~)4S/N(mag26

hours21800s4

>=

=×

WLNR

2lim,

214-lim,

deg1/10~)(s/erg/cm1e

hours25ks109

XX

X

fNf

>=

=×

(3) survey power

Weak lensing surveysby Hyper-Suprime

2lim

deg1/5~)4S/N(mag26

hours5.01800s1

>=

=×

WLNR

1 cluster/2.5h 1 cluster/0.4h 1 cluster/0.03h

(1)Weak lensing survey is a very efficient way to

locate massive clusters.

Requirements:

(i) Very wide FOV camera <= Hyper-Suprime

(ii) Very good seeing condition <= Mauna-kea

(2) Weak lensing is complementary to X-ray:

X-ray misses X-ray faint massive clusters,

WL misses less massive X-ray bright clusters.

Conclusions (1)

Mock simulation with realistic noises

Completeness & contaminationof weak lensing survey

TH, Takada & Yoshida,(2004)

Lensing mass map from WL surveyHalos within 0.1<z<0.8 from N-body sim.

Large symbols: M>3e14small: 3e14>M14>8e13dots: 8e13>M14>1e13

Mock numerical simulation(4) simulation

02.0noise =σ

How many missing clusters ?

How many contaminations ?

Completeness & contamination(4) simulation

peakshigh of #

signals false of #clusters of #

clusters detected of #

Lowering the threshold S/N gives us a high completeness at aprice of a lot of contaminations (false signals). Screening out thefalse signals is key to a WL halo catalog being useful.

(1) Contaminations False signals from the random noise Projection of less massive halos

(2) Scatters in WL signal Random noise (positive or negative) Projection with structures in the same LOS (i) large-scale structures : RMS~0.01 (~0.5 x Noise RMS) unavoidable but weak effect (ii) surrounding structures: make the signal greater (in general) unavoidable a hint from a spectroscopic follow-up (iii)clusters/groups : unavoidable but very rare easily identifiable by a spectroscopic follow-up

Source of contaminants & scatter(4) simulation

*The projection effect makes WL mass estimate uncertain

somethingSignalSignal clusterobs +=

(3) A high completeness can be obtained by

lowering the threshold S/N (~3) but at a price

of a high contamination rate.

*False signals mainly arise from the noise

and partly from chance projections.

*The projection effect makes WL mass

estimate uncertain.

Conclusions (2)

How does the combinationof WL mass map and Spec. work ?

Screening out false signalsand getting better mass estimation

(4) Screening out the false signals is key to a WL

halo catalog being useful.

Spectroscopic follow-up is very important.

Requirements:

30-50 galaxies/cluster (3-5arcmin radius)

=>~1 galaxy/arcmin2

Conclusions (3)

(1)Weak lensing survey with Hyper-Suprime is a

very efficient way to locate massive clusters

(2) Weak lensing survey is complementary to

X-ray survey (Optical, SZ, as well)

(3) A high completeness can be obtained by

lowering the threshold S/N (~3) but at a price

of a high contamination rate.

(4) Spectroscopic follow-up very nicely screens

out false signals and improves the mass

estimation.

Summary

end