Noise effects on Weak-lensing Derived Mass-concentration

Relation of Dark Matter Halos

Wei Du

2014.10.11

Wei Du & Zuhui Fan 2014

Tsinghua Large Scale Structure Workshop 2014

National Astronomical Observatory of China

The 2dF Galaxy Redshift Survey

Introduction

The mosaic combines visible-light data from the SDSS.

Coma cluster (Abell 1656, z=0.0231)

"While examining the Coma galaxy cluster in 1933, Zwicky was the first to use the virial theorem to infer the existence of unseen matter, what is now called dark matter."

(from Wiki)

The mosaic combines visible-light data from the SDSS.

Coma cluster (Abell 1656, z=0.0231)

Galaxy clusters: 1, contain ~3% stellar component, ~17% gas and ~80% dark matter 2, 3, A diameter from 2 to 5 Mpc

14 1510 10 Me:

3

2

3

where ( / )(1 / ) 3 ln(1 ) - / (

1 )

4 c = &

3

s critNFW s

s s

crits

c

r r r r c c c

rM r

r

From Phoenix Project; Gao et al. 2012

NFW. 1996, ApJ, 462, 563

0.1 :

M-c relation

Navarro, Frenk & White, 1996,1997

14 1

0.13 0.07

4.6 0.7 for M 10pA h M

e

Mandelbaum et al. 2008

Also see Huanyuan’s work

α ~ -0.4 α ~ -0.45

α ~ -0.59 α ~ -0.8

0.2dz ;

1.1dz ;

Wiesner M.P. et al. 2012

Oguri et al. 2012

Okabe et al. (2010)

Sereno and Covone, 2013

0.46dz ;

0.43dz ;

WL SL+N200

SL+WL SL+WL

Sample variance: narrow mass range, low number of clusters…

Selection effect: more concentrated clusters are more likely to be included in the sample

Physical reasons: baryonic physics, accreting haloes out of equilibrium, ΛCDM?

( )ii,modelp

Mc A

M

Israel, H., Erben, T. et al. 2012; 400d survey, MMT telescope

Coma cluster observed by CFHT

Gavazzi, R., Adami, C. et al. 2009

Noise effect on M-c relation

80

0.2s

g

e

n

30

0.4s

g

e

n

A halo with a low/high true mass can be grouped into a high/low weak lensing-derived mass bin. For those halos, their derived concentrations are systematically lower/higher than their underlying true concentrations.

Bayesian method

en

gn

( , , )lowA M

Bayesian method

~ 0.12in

Where M_{low} indicates selection effect and n(M_T) is the halo mass function taken from Tinker et al. (2008)

For a mass- limited sample:

For a large observational sample of clusters

~ 0.13n

2~ 6 arcmin and 0.4g en

small samples with a limited number of clusters

Okabe et al. (2010) ; 19 clusters

Monte Carlo simulation--Bayesian method

2

0.4

10 ~ 30 arcmin

e

gn

Preliminary result from CFHTLenS

~ 7effn

e.g., W1: Number of bright (<=20 mag) cluster members >=10 147 K2 clusters Further select the clusters without masks within 5 arcmin 114 K2 clusters

Preliminary result from CFHTLenS

~ 7effn

In order to derive an unbiased M-c relation, noise effect should be carefully taken into account.

We introduce a Bayesian method, including the effects of noise and selection bias (i.e., low mass limit), which can give the unbiased prediction.

Summary