The effects of the complex massdistribution of clusters on weak lensing cluster surveys

Zuhui Fan Dept. of Astronomy, Peking University

Radio observations have played important roles in lensing studies

About 40% of the multiple-imaged quasars have been observed in radio band

The first lens system QSO0957+561A,B

VLBI observations show detailed correspondence between various knots of emission in the two radio images

Outline:

Introduction: Clusters as cosmological probes

Gravitational lensing effects Weak lensing selected clusters

Introduction Clusters of galaxies total mass M ~ 1014 –15 Msun

hot gas T ~ a few keV

Largest varialized objects in the universe Gravity plays dominant roles in the formation and evolution of clusters of galaxies Sensitive to cosmological models Strong sources for x-ray, SZ effects, lensing……

As a zoom lens for faint objects

Abell 2218

galaxy z ~7

z ~ 10

Statistically, the cluster number distributionversus redshift z contains much information on cosmological parameters, such as

wm ,, 8

Fan & Chiueh 2001 Fan & Chiueh 2001

Problems in cosmological applications

* theoretically: the abundance of clusters in terms of their mass * observations: the mass of a cluster is usually derived from observable quantities large uncertainties are introduced

For example

X-ray emission or SZ effects are directly associated with intracluster gas Besides gravity, gas physics affects the properties of intracluster gas considerably.

Gravitational lensing effects are directly related to the mass distribution, regardless luminous or dark components

It is expected that lensing cluster surveys can obtain mass-selected cluster samples

Gravitational lensing effects

Strong lensing effects

multiple images giant arcs

central part of galaxies or clusters

weak lensing effects Lensing effects are weak, and statistical studies are necessary.

shape distortion of background galaxies magnitude magnification of background sources

weak lensing effects

http://www.cita.utoronto.ca/~hoekstra/lensing.html

Lensing effects are related to the mass distribution along line of sights between the observer and the sources

If there exists a large cluster in a particular direction, lensing signals are expected to be peaked around the cluster

D. Wittman et al. astro-ph/0507606First Results On Shear-Selected Clusters From the Deep Len

s Survey: Optical Imaging, Spectroscopy, and X-ray Followup

8.60 of 200 Deep Lens Survey (DLS)

convergence map (Tang and Fan 2005, ApJ)

qualitatively, good correlations are seen between massive clusters and peaks in the convergence map

important questions to ask

the efficiency and completeness of lensing cluster surveys

lensing signal mass of clusters lensing-selected cluster sample truly mass-selected??

Weak lensing selected clusters

We particularly concern the quantitative correspondence between the κ value of a peak in the κ map and the mass of its associated halo

concentrate on double primary matches peak < -- > halo

angular smoothing scale θG=1 arcmin (2 arcmin) (Gaussian smoothing window function)

Simulations ( Jing 1998, 2000)

100h-1Mpc, 2563 particles force resolution: 39h-1kpc

convergence map: the Born approximation stacking mass slices

9.0,1,7.0,3.0 8 nm

Spherical NFW model

rs : characteristic scale ρs : characteristic density

given the mass of the halo M < -- > rs (through concentration parameter c=rvir/rs) ρs

one to one correspondence between M and κ at a given redshift

2)/1)(/()(

ss

s

rrrrr

scatter plot of νpeak and νnfw (ν= κ/σnoise)

correlations are seen but with large scatters

statistical distribution of c (dash-dotted line) triaxial shape of halos (dashed line)

* The uncertainty of c contributes a small portion of the dispersion

* The triaxiality contributes additional dispersions, especially at high ν for massive halos

* Still a large part of the dispersion cannot be explained by the triaxiality of halos

* Even more complex mass distribution of halos ? projection effects along the line of sights ?

Isolate the complexity of the mass distribution from the projection effects

generate κ map including only those matched halos

with other particles removed

-- > κsingle or νsingle

comparison

Comparison

dominant part of the dispersion is associated with the complex mass distribution of halos themselves

σtri σsingle σpeak

νnfw=4.5 0.56 1.11 1.29νnfw=5 0.66 1.23 1.39νnfw=6 0.88 1.37 1.53

substructures

triangles: substructures

substructures contribute to the lower-end dispersion

hidden substructures along line of sights

contribute to high-end dispersion as well

results (θG=1 arcmin)

* lensing signals from clusters are far more complex than the spherical NFW model can describe * triaxial mass distribution must be taken into accou

nt * large substructures have important effects * projection effects play minor roles

νnfw=4.5 νnfw=5 νnfw=6

0.25 0.18 0.152/12

single

singlepeak

θG=2 arcmin

comparison

* Projection effects are much more significant than that of θG=1 arcmin

σtri σsingle σpeak

νnfw=4.5 0.44 0.77 1.49νnfw=5 0.49 0.98 1.39νnfw=6 0.61 1.02 1.80

An example

conclusions

* θG=1 arcmin : the lensing signals are dominantly determined by the properties of clusters themselves no simple κ – M correspondence κ-selected not M-selected triaxiality, substructures …

* θG=2 arcmin: projection effects are stronger not preferred in lensing surveys

* the box size of the simulations are relatively small * full ray tracing: evaluate the line-of-sight projection effects more accurately

* the effects of noise: intrinsic non-spherical shape of galaxies

Discussion redshift information:

precise values are not needed applicable to large surveys, such as Planck multi-frequency observations

depending on the cluster-finding algorithm, the final SZE signals are constructed through the weighted average of signals from

different

frequency channels

relativistic effects can be weaker than that

for the v=353 GHz

the flux limit for completeness can be

as high as 200 mJy

Multi-parameter determination

e.g., Ωm, σ8, w

Searching for clusters with weak lensing surveys

Inhomogeneous matter distribution distorts

background source galaxies, and generates correlated distortion signals

Gravitational lensing effect is directly associated with weighted surface mass

distribution κ

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δ: density fluctuation field a: cosmological scale factor ω: comoving radial distance fk: comoving angular diameter distance p(ω): distribution function of source galaxies H0: Hubble constant Ω0: cosmological mass density parameter

Clusters of galaxies are expected to be associated with peaks in κ-map. This is the basic idea of lensing cluster surveys

* Is there a one-to-one correspondence between a peak and a halo? * selection function: mass selected? * completeness and efficiency

halodark

arcmin1oversmoothed

map

al.etHamanaT.

Visually: good correlation theoretically expected κ value from a cluster “observed” κ value ?

mis-matches physical reasons? projection effects

Theoretical modeling:

spherical mass distribution NFW profile one to one correspondence between κ and M mass selected

With simulation data from Dr. Jing et al. analyze the dispersion between the theoretical expected lensing signals with “observed” ones

gGnoise

noise

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n2

22

2

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)arcmin/1(02.0,arcmin30,4.0 2-2Gnoisegn

possible reasons for the dispersion: projection effect nonspherical mass distribution of dark halos high resolution numerical studies of Jing et al. triaxial dark matter halos

orientation

ecb cee ,,

Conclusion statistical uncertainty of the concentration

parameter - account for small part of the dispersion nonsphericity and statistical uncertainty in the axial ratios account for large part of the dispersion especially for the high tail part

Theoretical modeling mass selected

better modeling:

P: probability function

)(lim

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M

halo

halothsGth

dM

zMdndM

d

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dM

zMdnzMHdM

d

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dM

zMdnzMPdM

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dVdzN halo

thsGth

* find P(νth, M, z) * theoretical calculations on the number distribution versus simulations * different cosmological models * understand the projection effect void structures multiple halos * add in noise

On going research and future plans SZ effects clusters detected through gravitational lensing effects dark energy properties: w, dw/dt

LISA: prediction of GW sources from cosmological point of view new window for cosmological studies

Cosmological merging SMBH-galaxy evolution of model -- history - correlations --- binary MBH

# of LISA sources redshift distribution

distribution: orientation of the triaxial halos

ecb cee ,,