Intrinsic Alignment of Galaxies and Weak Lensing Cluster Surveys Zuhui Fan Dept. of Astronomy, Peking University

Outline: Introduction Influence of intrinsic alignment on weak lensing effects Constraints on the strength of intrinsic alignment from CFHTLS Deep Discussion

Introduction Gravitational lensing effects “see” the dark matter directly  powerful probes of the distribution of dark matter sensitive to the formation of large-scale structures and the global geometry of the universe  highly promising in dark energy studies

magnification of background sources Weak lensing effects magnification of background sources coherent shape distortion of background galaxies http://www.cita.utoronto.ca/~hoekstra/lensing.html

Weak lensing cluster surveys Searching for clusters of galaxies by their weak lensing effects Avoid the complicated gas physics involved in optical, X-ray and SZ observations  important in cosmological studies with clusters of galaxies

D. Wittman et al. astro-ph/0507606 First Results On Shear-Selected Clusters From the Deep Lens Survey: Optical Imaging, Spectroscopy, and X-ray Followup 8.60 of 200 Deep Lens Survey (DLS)

Gavazzi & Soucail 2006, astro-ph/0605591 CFHTLS Deep (S/N >3.5 14 peaks in ~ 4deg2, 8 of them are secure detections)

Weak lensing cluster surveys: (Tang & Fan 2005, ApJ, 635,60) * projection effects mass distribution along the way can pollute the cluster signal * complicated mass distribution of clusters themselves  not clean mass-selected samples  not truly mass-selected samples ** intrinsic ellipticities of background galaxies

Influence of intrinsic alignment on weak lensing effects The formation and evolution of galaxies are affected by their environments  galaxies are not intrinsically round, and their shapes can be correlated if they are close enough

galaxy ellipticities

Jing, Y.P. 2002, MNRAS, 335, L89 (shapes of dark matter halos at z=1)

intrinsic ellipticities of background galaxies  false peaks in κ-map Effects on weak lensing cluster surveys κ-map peaks  clusters intrinsic ellipticities of background galaxies  false peaks in κ-map  reduce the efficiency of cluster detection  change the true peak height We will discuss how the intrinsic alignment affects the number of false peaks in κ-map

In the weak lensing regime, Smoothed shear and convergence

For the smoothed convergence field, the noise part is If there are no correlations between eαS, then (van Waerbeke 2000, MNRAS,313,524) taking into account the average over the galaxy positions

If there are large enough number of galaxies in the smoothing window (e.g., Ng~10), N(θ) can well be approximated as a Gaussian random field based on the central limit theorem. For a 2-D Gaussian random field, the number of peaks is analytically known, and depends only on two parameters γ and θ*

and (ν is the peak height in unit of σ0)

differential and cumulative number density of peaks

For κ peaks, with a Gaussian smoothing function, in the case of no correlations between eS, we have Thus given a θG, the number of peaks in terms of ν is independent of the value of σ0

Cumulative number of peaks in 1 deg2

with intrinsic alignments for background galaxies

The exact statistics of N(θ) depends on the physical processes that affect of shape and alignment of galaxies, which have not been fully understood yet. tidal field, filaments…… However, since the level of intrinsic alignment is not that large (10-4 – 10-5), the smoothed N(θ) is expected to be approximately Guassian from the central limit theorem

peak number -- γ , θ* (depend on the correlation)

cumulative number of peaks (arcmin-2) θG=1 arcmin Lower set: upper set:

Observationally, only can be estimated from data With :

For relatively high peaks with , the number of peaks is very sensitive to  Npeak depends sensitively on C0 the existence of C0 affects the efficiency E of WLCS dramatically E.g., if E=50% in the case C0=0  E=25% with

If one can separate true and false peaks, (e.g., with lensing tomography or follow-up observations), the number of false peaks can be used to constrain C0 effectively

Constraints on the strength of intrinsic alignment from CFHTLS Deep Gavazzi & Soucail astro-ph/0605591 effective survey area 3.61 deg2 p(z)

There are 14 peaks with S/σ >3.5 Among them, 8 peaks have optical counterparts, and the other 6 are likely false peaks resulting from intrinsic ellipticities of background galaxies

Jing 2002

Poisson fluctuation 1σ : 2σ :

Discussion * with , false peak number depends on C0 sensitively * the existence of C0 reduces the efficiency of WLCS considerably * C0 can be constrained effectively with the number of false peaks ** close to the lower limit predicted by numerical simulations on dark halos  misalignment of baryonic matter and dark matter halos ?? galaxy formation

* further studies: the statistics of N(θ)