1. Ｒｅｖｉｅｗ ｏｆ Ｇｒａｖｉｔａｔｉｏｎａｌ Ｌｅｎｓｉｎｇ：
Ｒｅｖｉｅｗ　ｏｆ　Ｇｒａｖｉｔａｔｉｏｎａｌ　Ｌｅｎｓｉｎｇ：
T. Futamase,
Kyoto Sangyo University
22nd Dec @ Sendai
Collaborator: many

2. Context History of GL after 1979 Present Status Some ongoing works
Future

3. History of GL research after the discovery of first Lensing event
1979 QSO A,B, Walsh et al
1984 time delay in QSO
　Hubble parameter dependence was pointed out by Refsdal in 1964
1984 Lens Statistics Turner, Ostriker & Gott
1986 Giant Luminous Arc in Abel 370
~1986 MACHO search by Microlensing, Paczynaki
1988 Einstein ring
　predicted in 1924 by Chwolson
1990 Weak Lensing in Abel 1689, CL Tｙson
concept of WL was mentioned in ~1970 by Feynman
2000 Cosmic Shear
2006 Discovery of extrasolar planet by microlensing
2009 Discovery of GRAMOR in MACS J
predicted in 1998

4. Present Status of GL research
Almost all ideaｓ are already known by 1980s and 1990s
New data using new instruments and new surveys
More refinements of theory, in particular weak lensing

5. New Data using new Instruments and new surveys
HST
HFF, CRASH including K.Umetsu
Suprime-Cam Subaru
Cosmic Shear, 　 T. Hamana, S. Miyazaki
Weak Lensing Survey(LoCuSS), 　N. Okabe, M. Takada, K. Umetsu, TF
HSC
　　Cosmic Shear, 　T. Hamana, S. Miyazaki
　Weak Lensing Survey(LoCuSS), 　N. Okabe, M. Takada, K. Umetsu, TF
　　　 Very Nearby Clusters, 　N. Okabe, TF
SDSS
SL images with large separation by Clusters, M.Oguri, N.Inada, I.Kayo
Quasar Statistics, 　M.Oguri

6. Comparison of Field of View
Size of moon on sky

7. Weak Lensing Study of Clusters

8. FOV of HSC 2 full nights in March 2011 2 square degree surcey
seeing ~0.7”
Number density of background galaxies ~50/arcmin^2
18 pointings in Rc band(24.5min) and V band (13.8min)
FOV of HSC
~1.4 Mpc
N.Okabe,T.F, M.Kajisawa, R.Kuroshima (2013)

9. Correspondence between DM subhalos and galaxy groups

10. Mass-to-Light ratio

11. Observed Mass function of Subhalo

12. Power spectrum and Halo Mass function in WDM universe
R.E. Smith & K. Markovic, PRD 2002

13. Classification of subhalos in mass and projected distance from the center

14. Mean distortion profiles of the averaged subhalo in eaｃh class

16. Distance-dependence of subhalo size

17. Main halo
Main halo+Subhalos +LSS

18. Follow-up X ray observation by Suzaku
arXive:
T.Sasaki, K. Matsushita, K.Sato and N. Okabe

19. The subhalo gas mass versus weak-lenisng mass

20. by N. Okabe Subaru Proposal S14A,B, S15A,B, S16A,B
We have already taken all 20 low-z cluster data and waiting the analysis
Results soon coming?
by N. Okabe

21. HFF: MACS J1149.5+2223 A. A.Zitrin & T. Broadhurst, ApJ 2009 z=0544

22. Mechanism to create GRAMOR
Lens mapping
Lens
source
image
Sky
Image Distortion
Magnification
Thus if the density distribution of the lensing cluster is not strongly eccentric, the shear is sufficiently small close to the center of the lens and we expect to have a highly amplified undistorted image

23. Lens model by Smith et al.2009
Density profile A1

24. Lensed Images of a spiral galaxy at z=1.491
The unlensed apparent magnitude in the I-band is
Apparent size of A1.1 corresponds a typical apparent size of galaxy at z=0.1

25. Expected number of GRAMORs by source with
Source distribution
GRAMOR
Arc

26. Expected number of GRAMORs for CRASH clusters

29. Number of GRAMOR is about same order with GLA
GRAMORs are more likely found in Clusters with low concentration
Distribution of source redshift has a sharp peak for GRAMORS in high-z clusters
Distribution of source redshift has a strong dependence on the value of cosmological constant, possibly on the nature of dark energy
Improvement of mass reconstruction for MACS J
Systematic Survey of GRAMORs for high-z clusters combined with other observation such as CMB, SN

30. Future Projects

31. Introduction Ｆｉｔｔｉｎｇ of loght curve SNe Ia intrinsic dispersion
Weak Lensing effect by LSS
z-dep
Non Gaussain
Luminosity distance in flat FLRW universe
Perlmutter et　al. ApJ 1999

32. Theoretical expression for m-z relation in an inhomogeneous universe
Riem = Ricci + Weyl

33. Large scale structure with massive neutrino
Neutrino effect
For

34. HALOFIT
Power spectrum based on halo model with parameters fitted by N-body simulation

35. Result 2 free parameters
Other parameters such as are all fixed (WMAP 5years)

36. High-z
重力波？

37. On going
The above result is obtained by only using minimum information of the expected observation
More information
Shear contribution is not considered by sample selection
Important in small scales

38. Theoretical Refinement

39. Shear measurement convergence shear Ellipticity and shear
in linear order
depends on the def. of ellipticity
After averaging
However the lensed image is not the observed image
due to atmospheric turbulence and so on
Point Spread Function(PSF)
Another problem is that

40. Difficulties in Weak Lensing Analysis
There will be a great progress weak lensing observation from ground as well as from space near future , but it does not automatically means the great progress in the accuracy of weak lensing analysis.
Many systematic errors are not yet fully controlled
PSF correction
We can use only high S/N object

41. PSF correction Point Spread Function(PSF)
Bridle et al.2008
Point Spread Function(PSF)
P is measured at the position of star
Typical number density
Star image in the best seeing
(0.48”) in Hawaii

42. New method of PSF correction(Y.Okura &T.F, 2014,2015)
New PSF correction free from any bias
If P has the same elliticity with I^lensed, then I^Ob has the same ellipticity
The idea is to smear the original PSF again by an appropriate function R to make re-smeared PSF to have the same ellipticity with the lensed galaxy
For this to happen we iteratively solve the equation to find P^(R)

43. New method of PSF correction(ERA)
P(PSF)
P^(R)
Compare
Ellipticity R
Obs
(Observed Image)
I^(R)
If not match
Size is free parameter

44. Iteration result using Simulation
Galaxy
PSF

45. Simulation test : complicated shaped Galaxy
A : GAL = Two Gaussians with e1=0.6, e2=0.0 and e1=0.0, e2=0.6
B : GAL = Gaussian + Arms
PSF = circular Gaussian
shear1 = 0.1, shear2 = 0.0 for 4 images [org, 90rot, x_rev, x_rev+90rot]
error
error A B

46. Pixel Noise correction
Pixel Noise makes additional count and so additional ellipticity

47. Result

48. Comparison between Regaussian in HSC pipeline and ERA

49. New spin 2 ellipticity 0th ellipticity Usual spin 2 ellipticity
Newly defined spin 2 ellipticity
I(θ)

50. Comparison between 2nd and 0th ellipticities using HSC real data.
0th ellipticity
Comparison between 2nd and 0th ellipticities using HSC real data.

51. Conclusion Almost all ideaｓ are already known by 1980s and 1990s
New data using new instruments and new surveys
More and more Many things to do!
More refinements of theory, in particular weak lensing