The effects of the complex mass distribution 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 QSO A,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 ~ – 15 M sun 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 distribution versus redshift z contains much information on cosmological parameters, such as 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

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/ First Results On Shear-Selected Clusters From the Deep Lens Survey: Optical Imaging, Spectroscopy, and X-ray Followup of 20 0 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 θ G =1 arcmin (2 arcmin) (Gaussian smoothing window function)

Simulations ( Jing 1998, 2000) 100h -1 Mpc, particles force resolution: 39h -1 kpc convergence map: the Born approximation stacking mass slices

Spherical NFW model r s : characteristic scale ρ s : characteristic density given the mass of the halo M r s (through concentration parameter c=r vir /r s ) ρ s one to one correspondence between M and κ at a given redshift

scatter plot of ν peak and ν nfw (ν= κ/σ noise ) 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 -- > κ single or ν single

comparison

Comparison  dominant part of the dispersion is associated with the complex mass distribution of halos themselves σ tri σ single σ peak ν nfw = ν nfw = ν nfw =

substructures

triangles: substructures substructures contribute to the lower-end dispersion

hidden substructures along line of sights contribute to high-end dispersion as well

results (θ G =1 arcmin) * lensing signals from clusters are far more complex than the spherical NFW model can describe * triaxial mass distribution must be taken into account * large substructures have important effects * projection effects play minor roles ν nfw =4.5ν nfw =5ν nfw =

θ G =2 arcmin

comparison * Projection effects are much more significant than that of θ G =1 arcmin σ tri σ single σ peak ν nfw = ν nfw = ν nfw =

An example

conclusions * θ G =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 … * θ G =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., Ω m, σ 8, 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

δ: density fluctuation field a: cosmological scale factor ω: comoving radial distance f k : comoving angular diameter distance p(ω): distribution function of source galaxies H 0 : Hubble constant Ω 0 : 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

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

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

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

* find P(ν th, 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