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1 弱い重力レンズの宇宙論と重力理論の検証への応用二間瀬敏史理学部 22 May. 2017

2 内容弱い重力レンズの紹介構造形成理論への応用 Verlinde s Emergent Gravity の検証超新星のm-z 関係とニュートリノ質量

3 重力レンズとは? 観測者銀河団背景銀河 J-P.Kneib. Ph.D thesis

4 なぜ重力レンズが重要なのか? 直接的な質量検出重力のみに依存し質量と明るさの経験的な関係を仮定する必要がない力学状態 m 組成に無関係 X 線 ( 高温 ) ガス光赤外 ( 星 ) などの伝統的な観測と相補的宇宙の幾何学膨張則に依存宇宙論パラメータあらゆる宇宙論的観測に影響雑音ー > 大規模構造の信号自然の望遠鏡原始銀河探査

5 弱い重力レンズ? Background galaxies without lensing Massive object somewhere between us and source galaxies Observed galaxies Coherent deformation of background galaxies ( i, 11,22) 2 Shear γ Convergence κ 1 ˆ 1 ˆ ( k) ˆ( k) D( k) ( (, 11, 22) ) 2,12

6 弱い重力レンズの基礎 Lens equation ( ) (2D)Lensing Potential ls dz N c D 2 s source Projection of Newtonian potential on Sky 2 D image Lens Sky N 4G Surface mass density convergence 2 ( ) ( ) cr with cr 2 c Ds 4GD D l ls

7 レンズ写像 Lens equation defines the mapping between the source plane and image plane ( ) Jacobian of this mapping ( ) where Source plane i i ji j A ij j A( ) ij ij 2 ( ) i 2 i i j convergence shear 2 2 k k2 2ik1k ˆ ( k) 2 k ˆ( 1 2 k ) Image plane (1 )

Q ( s) ij シアの測定法 1) Define background galaxies 2) Measure the ellipticity of background galaxies Q ( obs ) ij obs d 2 d I( ) 2 I( ) 2 d det A( ) A i i j j Q obs obs 11 22 12 1, 2 obs obs obs obs Q11

8 Q ( s) ij シアの測定法 1) Define background galaxies 2) Measure the ellipticity of background galaxies Q ( obs ) ij obs d 2 d I( ) 2 I( ) 2 d det A( ) A i i j j Q obs obs , 2 obs obs obs obs Q11 Q22 Q11 Q22 ik obs Q (0) A k j obs (0) I( ) 2Q 3) Then we have relation between the lensed and intrinsic ellipticity for each background galaxy obs A ik ( A( ) ) (0) Q obs k A j (0) weak lensing limit, 1 obs ( ) s 2 4) Assume that the ellipticities of background galaxies are randomly distributed ( s) ( obs) int ( ) 0 ( ) 2 γ ( ) O int ~ : N Standard deviation of ellipticty

9 Acutally things are not simple! Bridle et al.2008 For stars I star I Obs ( ) d ( ) d ' I 2 ' ( ' 2 ( Lensed ) star ( ') P( ') ) P( ') P( Point Spread Function(PSF) time dependent in ground base telescope star ) nstar 1 arcmin 2 Typical number density of star

10 マウナケア山頂すばる望遠鏡でのベストシーイング

PSF 補正の例 Distribution of Ellipticities ofstars before After PSF anisotropy field Before correction e star -3 star -2 1-3.510, e1-5.

11 PSF 補正の例 Distribution of Ellipticities ofstars before After PSF anisotropy field Before correction e star -3 star , e After correction e e star 1 star 1 ( ) 10 ( ) , Distribution of ellipticity over the field of view Before After

Noise: g true N tot bg / N tot true g true bg : N n' / N n N / N tot tot N n cl true N bg S

12 背景銀河の選択の重要性 Cl (Umetsu et.al. 2010) Dilution Effect Contamination of member galaxies in the sample Lens signal: g' g Noise: g true N tot bg / N tot true g true bg : N n' / N n N / N tot tot N n cl true N bg S N obs S N true N N bg tot S N true 1 1 f ; f N N cl bg Number density distribution Color-color(BRz) selected Cl (z=0.395) Magnitude selected

14 弱い重力レンズを利用した宇宙論研究銀河銀河団の暗黒物質分布観測による構造形成研究レンズ統計による構造形成と暗黒ねねるぎーの研究宇宙シアによる暗黒エネルギー研究強い重力レンズ現象 (Time delay et.al.) を用いた暗黒エネルギー研究銀河団重力レンズによる原始銀河探査赤方偏移 0.15<z<0.3 の 50 個の銀河団に対する暗黒物質ハローの平均質量分布近傍銀河団内の暗黒物質部分ハローの検出

15 Universal Mass Profile (NFW profile) A phenomenological model for DM halos motivated by simulation Boylan-Kolchin+09 r 1 r 3 Navarro+04 r s M vir NFW (r) 4 s r 3 vir 3 s (r /r s )(1 r /r s ) 2, c vir r r vir s Concentration parameter

16 Predicted C-M relation z=0 z=2 z=1 Bhattacharya et.al 2011

17 Subaru Weak Lensing Study for 52 X ray Luminous Clusters ROSAT X-ray All Sky Survey (REFLEX, BCS, ebcs) Okabe, Takada, Umetsu &TF *Redshift~ *volume/flux limited sample *Irrespective of dynamical state

Center the catalogs on the respective BCGs, and stack in

18 Stacked Lensing Analysis Effects of substructure and large Scale Structure are canceled out by stacking Center the catalogs on the respective BCGs, and stack in physical length units across the radial range In 14 log-spaced bins

21 弱い重力レンズによる近傍銀河団内の暗黒物質部分ハロー

22 メインハローとサブハロー A galaxy halo of mass 2 10^12 M_sun A cluster halo of mass 5 10^14 M_sun 300 kpc 2000 kpc

23 近傍銀河団観測の利点髪の毛座銀河団 (z=0.0236) 巨大な見かけの視野 (~3 平方度 ~5Mpc^2) 銀河団内の部分ハローも弱いレンズの分解能以上の大きさ 1 arcmin~28 kpc for h=0.7 at z= 背景銀河の数密度が多く低いレンズ効率を補い統計誤差を改善する 1Mp 以下のスケールでの構造形成理論の検証が可能 Hyper Surpime-Cam

24 DM distribution in Coma cluster(z=0.0236) N. Okabe, T.F, M. Kajsawa ~ 3 Mpc ~1 Mpc

25 Correspondence between DM subhalos and galaxy groups

26 Observed Mas function of Subhalo Expected mass function for fake subhalos

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

28 The sizes of DM subhalos as a function of mass and distance from the center of cluster mass distance

29 Mean distortion profiles of the averaged subhalos in each class

31 Distance-dependence of subhalo size

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

33 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

34 Test of Verlinde s Theory of Emergent Gravity by Weak Lensing

35 Verlinde s interpretation of dark matter Einstein gravity appears from the area law for gravitational entropy The present positive dark energy of the universe leads to a additional volume law contribution to the area law The displacement of dark energy by baryonic matter causes a modification of the standard gravitational law and the modification is interpreted as a dark mattewr

36 Prediction of effective dark matter mass distribution by Emergent Gravity(EG) Apparent Dark Matter Profile is derived by Baryon mass profile Under the following assumptions Isolated, static and spherically symmetric case M 2 D ( r) for ch0r 6G r 2 d 2G ch M b( r) r dr 0 M b ( r), 2kpc, H 0 70 km/s/mpc Example: Point mass model ch C D 6G 0

37 Test of EG using Galaxy-Galaxy Lens(GGL) Galaxy-Galaxy Lens M. M. Brouer, M.R. Visser, A. Dvornik et al.2016 単一の銀河による弱い重力レンズ信号が微弱なので多数の同程度の質量の銀河の信号を重ね合わせる ( obs) int 2 ( ) 2 γ ( ) O int ~ O (10 ) N Lensing galaxies: GAMA(spectroscopic Galaxy And Mass Assembly survey) 1) They are centrals, i.e., not classified as satellites 2) They have stellar masses below 10^11 solar mass 3) They are not affected by massive neighboring groups 180,960 galaxies over 180 square degrees in GAMA -> 33,613 galaxies over 140 square degrees The background galaxies: ikids(kilo-degree Survey)

38 Galaxy-Galaxy Lens(GGL) Excess Surface Density(ESD) ( R) ( R) ( R) ( R) t crit t : tangential shear For Point mass model Total ESD=Baryon+ Effective DM ch C D 6G 0 For point mass model

39 The baryonic masses are determined by stellar mass (using the SDSS and VIKING observation by fitting stellar population synthesis model to spectral energy distributions from 30, ,000nm) and cold gas with some empirical relation

40 EG prediction can be tested by measuring EG b ( r) ( r)

41 Observation galaxies brighter than 19 mag. in R-band 2 red 2 N DOF NFW EG

42 EG prediction A B 1, n 1 GGL observation B NFW best fit EG 予言は弱い重力レンズで測定した銀河の質量分布と矛盾しない

43 このような暗黒物質に対する潮汐効果 EG あるいは他の修正重力理論で説明できるか? 重力レンズの観測では暗黒物質のそのほかの性質も観測されているたとえば銀河団内の部分ハローで観測されている潮汐効果部分ハローの大きさ

44 数年後超大規模サーベイが開始される何ができるか?

45 タイプ Ia 型超新星に対する大規模構造の弱いレンズ効果 Luminosity distance in flat FLRW universe Fitting of loght curve SNe Ia intrinsic dispersion Weak Lensing effect by LSS z-dep Non Gaussain Perlmutter et al. ApJ 1999

46 非一様宇宙における m-z 関係 Riem = Ricci + Weyl

47 大規模構造に対する massive neutrino の効果 Neutrino effect

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

49 Result 2 free parameters Other parameters such as are all fixed (Planck)

50 High-z 重力波?

51 On going The above result is obtained by only using minimum information of the expected observation More information m( z S ) z s 0 dz W ( z S, z) ( z) m N i1 z W ( z i s, z i ) ( z i ) z 1 z N zn m a A ai i i A 1 ai m N a 1,2,, N; i 1,2,, a Shear contribution is not considered by sample selection 2 2, z s 2 m( zs ) dz W ( zs, z) 4G m 0 m( z s ) Important in small scales 2 z, z 0 dw s

52 結論弱い重力レンズは観測的宇宙論重力理論の検証などで重要な役割を果たしている EG 暗黒物質を導入することなしに余分な重力を説明できその予言は弱い重力レンズの観測と矛盾しないしかし暗黒物質は弱い重力レンズの観測結果をもっとも自然に説明する ( 潮汐効果など ) メインハローによる潮汐効果 EG のエントロピー力の伝達速度は?

Ando_JournalClub_160708

Ando_JournalClub_160708 Independent discoveries of a tidally disrupting dwarf galaxy around NGC 253! A Tidally Disrupting Dwarf Galaxy in the Halo of NGC 253 Toloba, E. et al. 2016, ApJL, 816, L5 (hereafter T16, accepted 2015.12.07)