Ｒｅｖｉｅｗ ｏｆ Ｇｒａｖｉｔａｔｉｏｎａｌ Ｌｅｎｓｉｎｇ： Ｒｅｖｉｅｗ　ｏｆ　Ｇｒａｖｉｔａｔｉｏｎａｌ　Ｌｅｎｓｉｎｇ： T. Futamase, Kyoto Sangyo University 22nd Dec. 2016 @ Sendai Collaborator: many

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

History of GL research after the discovery of first Lensing event 1979 QSO0957+561A,B, Walsh et al 1984 time delay in QSO0957+561 　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, CL1409+53 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 J1149.5+2223 predicted in 1998

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

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

Comparison of Field of View Size of moon on sky

Weak Lensing Study of Clusters

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)

Correspondence between DM subhalos and galaxy groups

Mass-to-Light ratio

Observed Mass function of Subhalo

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

Classification of subhalos in mass and projected distance from the center

Mean distortion profiles of the averaged subhalo in eaｃh class

Distance-dependence of subhalo size

Main halo Main halo+Subhalos +LSS

Follow-up X ray observation by Suzaku arXive:1504.03044 T.Sasaki, K. Matsushita, K.Sato and N. Okabe

The subhalo gas mass versus weak-lenisng mass

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

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

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

Lens model by Smith et al.2009 Density profile A1

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

Expected number of GRAMORs by source with Source distribution GRAMOR Arc

Expected number of GRAMORs for CRASH clusters

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 J1149.5+2223 Systematic Survey of GRAMORs for high-z clusters combined with other observation such as CMB, SN

Future Projects

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

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

Large scale structure with massive neutrino Neutrino effect For

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

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

High-z 重力波？

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

Theoretical Refinement

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

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

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

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)

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

Iteration result using Simulation Galaxy PSF

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

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

Result

Comparison between Regaussian in HSC pipeline and ERA

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

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

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