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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
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
重力レンズとは?
観測者 銀河団
背景銀河
J-P.Kneib. Ph.D thesis
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
Background galaxies without
lensing
弱い重力レンズ?
Massive object somewhere
between us and source galaxies
Shear γ Convergence κ
)(ˆ)(ˆ1
)(ˆ kDkk
))(2
1( 22,11,
Coherent deformation of background galaxies
Observed galaxies
12,22,11, 2)( i
弱い重力レンズの基礎
)(
Lens
source
image
N
s
ls dzD
D
c
22
2
cr
)()(
lsl
scr
DGD
Dc
4
2
with
convergence
Lens equation
(2D)Lensing Potential
Projection of Newtonian potential on Sky
Sky
GN 4 Surface mass density
レンズ写像
jijjijii A )(
Jacobian of this mapping
Lens equation defines the mapping between the source plane and image plane
)(
ji
ijijA
)()(
2
2212
1211
1
1
12
21
10
01)1(
12221121
2211
2
1
2
1
ii
convergence
shear
where
Source planeImage plane
)(ˆ2
)(ˆ2
21
2
2
2
1 kk
kikkkk
)0()0()()0()0()(det
)(
2
2)(
j
obs
kikjkik
ji
s
ij
AQAIAAAd
IdQ
シアの測定法
1) Define background galaxies
)(2)(
IdQ ji
obs
ij
2) Measure the ellipticity of background galaxies
obsobs
obs
obsobs
obsobsobsobsobs
Q
2211
12
2211
221121
2,
3) Then we have relation between the lensed and
intrinsic ellipticity for each background galaxy
))(( A
2)( sobs
weak lensing limit
1||,
4) Assume that the ellipticities of background galaxies are randomly distributed
0)()(
s
NOobs int)( )(2)(
γ :3.02.0~int Standard deviation
of ellipticty
Acutally things are not simple!
)'()'(')( )(2
PIdI LensedObs
For stars
Point Spread Function(PSF)
Bridle et al.2008
time dependent in ground base telescope
2arcmin 1 starn Typical number density of star
)( )'()'(')( 2
starstar
star PPdI
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
Before After
PSF anisotropy field
Distribution of Ellipticities ofstars
before After-2
1
-3
1 10-5.0 ,10-3.5 starstar ee
Before correction
4-
1
-4
1
101.58)10.2(
,101.18)-0.07(
star
star
e
e
After correction
Distribution of ellipticity over the field of view
背景銀河の選択の重要性
Cl 0024+1654(Umetsu et.al. 2010)
Dilution Effect
bgcltottruetotbgtrue NNNgNNgg :/'
truetotbgtruetotg nNNnNn //'
Contamination of member galaxies in the sample
Lens signal:
Noise:
bg
cl
true
tot
bg
trueobs
N
Nf
fN
S
N
N
N
S
N
S
;
1
1
Cl 0024+1654(z=0.395)
Color-color(BRz) selected Magnitude selectedNumber density distribution
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
Universal Mass Profile (NFW profile)
r1
r3
NFW(r) s
(r /rs)(1 r /rs)2
Navarro+04
Boylan-Kolchin+09
Concentration parameter
rs
A phenomenological model for DM halos motivated by simulation
s
virvirvirsvir
r
rcrM ,
3
4 3
Predicted C-M relation
Bhattacharya et.al 2011
z=0
z=1z=2
Subaru Weak Lensing Study for 52 X ray Luminous Clusters
Okabe, Takada, Umetsu &TFROSAT X-ray All Sky Survey
(REFLEX, BCS, eBCS)
*Redshift~ 0.15 -0.3
*volume/flux limited sample
*Irrespective of dynamical state
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
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
メインハローとサブハロー
A galaxy halo of mass
2×10^12 M_sunA cluster halo of mass
5×10^14 M_sun
300 kpc 2000 kpc
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=0.0236
• 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
DM distribution in Coma cluster(z=0.0236)
N. Okabe, T.F, M. Kajsawa
0
40 41 42 43 44
30
20
10
00
34
24
14
04
31
21
11
01
33
23
13
03
22
12
02
0
~1 Mpc
~ 3 Mpc
Correspondence between DM subhalos and galaxy groups
Observed Mas function of Subhalo
Expected mass
function for fake
subhalos
Power spectrum and Halo Mass function in WDM universe
R.E. Smith & K. Markovic, PRD 2002
The sizes of DM subhalos as a function of mass and distance from the center of cluster
mass
distance
Mean distortion profiles of the averaged subhalos in each class
Distance-dependence of subhalo size
Follow-up X ray observation by Suzaku
arXive:1504.03044
T.Sasaki, K. Matsushita, K.Sato and N. Okabe
by N. Okabe
S14A,B, S15A,B, S16A,B
We have already taken all 20
low-z cluster data and waiting
the analysis
Results soon coming?
Subaru Proposal
Test of Verlinde’s Theory of Emergent Gravity by Weak Lensing
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
Prediction of effective dark matter mass distribution by Emergent Gravity(EG)
km/s/Mpc 70 2kpc,)(2
for
,)(
6)(
0
0
2
02
HrMcH
Gr
dr
rrMd
G
rcHrM
b
bD
Point mass model
Apparent Dark Matter Profile is derived by Baryon mass profile
Under the following assumptions
Isolated, static and spherically symmetric case
Example:
G
cHCD
6
0
Test of EG using Galaxy-Galaxy Lens(GGL)
Lensing galaxies: GAMA(spectroscopic Galaxy And Mass Assembly survey)
M. M. Brouer, M.R. Visser, A. Dvornik et al.2016
Galaxy-Galaxy Lens
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
180,960 galaxies over 180 square degrees in GAMA -> 33,613 galaxies over 140 square degrees
NOobs int)( )(2)(
γ )10( ~ 2
int
O
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
The background galaxies: iKiDs(Kilo-Degree Survey)
crit)()( )()( RRRR t
Excess Surface Density(ESD)
For Point mass model
Total ESD=Baryon+ Effective DM
For point mass model
shear l tangentia:t
Galaxy-Galaxy Lens(GGL)
G
cHCD
6
0
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 30,000-110,000nm) and cold gas with some empirical relation
)(
)(
r
r
b
EG
EG prediction can be tested by measuring
EG 12.1
NFW 933.022
DOF
redN
33613 galaxies brighter than 19 mag. in R-band
Observation
EG prediction 1 ,1 BB nA
GGL observation
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
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
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?
数年後超大規模サーベイが開始される―何ができるか?
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
Perlmutter et al. ApJ 1999
Fitting of loght curve
SNe Ia intrinsic dispersion
Weak Lensing effect by LSS
z-dep
Non Gaussain
非一様宇宙におけるm-z 関係
Riem = Ricci + Weyl
大規模構造に対するmassive neutrino の効果
Neutrino effect
HALOFIT
Power spectrum based on halo model with parameters fitted by N-body simulation
Result
Other parameters such as are all fixed (Planck)
2 free parameters
High-z 重力波?
On going
The above result is obtained by only using minimum information of the
expected observation
More information
)(),()(),( )(10
iis
N
i
imS
z
S zzzWzzzzWdzzms
1z NzNz
Naiiiaia mAAm 1 aiNa ,,2,1 ;,,2,1
Shear contribution is not considered by sample selection
2112
2
2
2
111 , 4
22
Important in small scales
2
0
4),( )( mS
z
S GzzWdzzms
0,)( 2 zzWdzm ss
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?