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

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

3. 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

4. magnification of background sources
Weak lensing effects
magnification of background sources
coherent shape distortion of background galaxies

5. 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

6. 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)

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

8. 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

9. 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

10. galaxy ellipticities

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

12. 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

13. In the weak lensing regime,
Smoothed shear and convergence

14. 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

15. 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*

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

17. differential and cumulative number density of peaks

18. 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

19. Cumulative number of peaks in 1 deg2

20. with intrinsic alignments for background galaxies

21. 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

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

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

24. Observationally, only can be estimated
from data
With :

25. 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

26. 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

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

28. 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

29. Jing 2002

30. Poisson fluctuation
1σ :
2σ :

31. 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

32. * further studies: the statistics of N(θ)