1. No category

長野ブラックホール天文教育研究会（銀中祭り）
2014年11月15日
銀河系中心方向の重力レンズ現象
大西浩次 (長野高専)
0. Introduction
0-1
Photo by Kouji Ohnishi
Lensing toward Galactic Center I
0-2
Microlensing
Observer
Lens
Bulge
Photo by Kouji Ohnishi
Lensing toward Galactic Center II
0-3
Microlensing
Sgr A*
Cluster, Pulsar
Observer
Lens=Black hole, Neutron star,
Photo by Kouji Ohnishi
1. Introduction
Lensing toward Galactic Center IV
0-5
Astrometric Microlensing around Sgr A*
Lens Sgr A*
Source=Star
Observer
Photo by Kouji Ohnishi
2. Gravitational Lens　by Sgr A*
2-1
Einstein Ring
RE
DOS
DOL
原図　大西浩次　作図　星ナビ2007年2月号
2. Gravitational Lens　by Sgr A*
2-2
Lens images
～２０mas
2. Gravitational Lens　by Sgr A*
2-3
Sgr A* の重力レンズの特徴的なサイズ
Sgr A*
Ｍ＝4＊106Ｍｓｕｎ
Ｒ０＝８ｋｐｃ
Photo by Kouji Ohnishi
Schwarzschild半径
Ｒｓ＝２ＧＭ／ｃ２＝１５Ｒｓｕｎ＝６＊１０－２ＡＵ　Θs=Rs/R0=9μas
ΘE　=(2 Rs(DLS/DSDL) )1/2
Einstein Ring
= 1.7” (13600AU @SgrA) @ DLS　è　∞
= 20 mas (160AU @SgrA) @ DLS=1pc
= 0.4 mas (3AU@SgrA)
@ DLS=100AU
Ds
Observer
DL
Sgr A* Star
DLS
2. Gravitational Lens　by Sgr A*
2-3
Sgr A* の重力レンズの特徴的なサイズ
Ｍ＝4＊106Ｍｓｕｎ
Sgr A*
Photo by Kouji Ohnishi
Ｒ０＝８ｋｐｃ
Schwarzschild半径
Ｒｓ＝２ＧＭ／ｃ２＝１５Ｒｓｕｎ＝６＊１０－２ＡＵ　Θs=Rs/R0=9μas
ΘE　=(2 Rs(DLS/DSDL) )1/2
Einstein Ring
= 1.7” (13600AU @SgrA) @ DLS　è　∞
= 20 mas (160AU @SgrA) @ DLS=1pc
= 0.4 mas (3AU@SgrA)
@ DLS=100AU
Sgr A* Star
Ds
Observer
Idea!
DL
DLS
Like a Exoplanet Search by microlensing
6. Lensing toward Galactic Center V
6-1
Macrolens of the Galaxy
QSOｓ
Observer
Photo by Kouji Ohnishi
What is Macro Lens?
Gravitational Deflection in Galactic Center
Individual Star
Astrometric
Microlensing
0-4”
Group of Stars
Macro Lens
This Talk
Lensing toward Galactic Center III
0-4“
Photo by Kouji Ohnishi
Astrometric
Microlensing
@ Distance
Measurement
QSO
Lens=Star
Sgr A*
Observer
Hosokawa,Jauncey,Reynolds, Toioumis, Ohnishi, Fukusima ApJ(2002)
Lensing toward Galactic Center III
0-4
Photo by Kouji Ohnishi
Astrometric
Microlensing
@ Distance
Measurement
QSO
Sgr A*
Lens=Star
Observer
SgrA*
8kpc
Reid et al. ApJ(1999) et al.
Lensing toward Galactic Center III
0-4‘
Detection of Galactic Rotation of Solar System
phase-referenced to QSOs　J1748-291(W109)　J1745-283(W56)
u  Reid et al. 1999
VLBA 43GHz,2yr
u  Backer & Sramek 1999
VLA 4.9GHz, 17yr
u  Reid et al. 2004
VLBA 43GHz,9yr
b 1°
SgrA
*
8kpc
W56
GC441
0.7°=100pc
SgrA*
1°
-1°
W109 -1°
6mas / yr =
220km / s
8kpc
VLBI observation of SgrA* =>6mas/y
Gravitational Deflection by
Axis Symmetric Mass Distribution
Pass of ray
Column Total Mass
Illustration of Shift by Bulge Motion
Lens
Source Plane
Lens Plane
Adopted Galactic Model
Alexander & Sternberg (1999)
Core+Bulge+Disk
ρ core (r ) = 1+3(ρr / r )
o
Characteristic Length Scale
Bulge
Core
0.38pc
667pc
disk
3kpc
c
2
ρ o = 4 × 10 6 M SUM pc −3 ,
rc = 0.38 pc
ρ bu lg e = 3.53 K 0 ( rr ),
b
rb = 3000 pc
Disk contribution is negligible
Effect of Core Motion
b
μc

μc～4μas/10yr
Effect of Bulge Motion
7
b
μ ～2μas/10yr
B

μB
3
Motion of SgrA* referred to QSOs
b
1°
GC441
W56
SgrA*

1°
-1°
W109
100pc
220 km/s
6 mas/yr =
8 kpc
-1°
ç Galactic Rotation
6. Lensing toward Galactic Center V
6-6
Internal Motion
b
+ 2 µas/10 yr

GC441
W56
SgrA*
− 2 µas/10 yr
+ 2 µas/10 yr
W109
1°
コメント：Sgr A*近傍にQSOが見つかると、非常に楽しい。
Parameter Dependence
Effect of Core Motion
⎛ L ⎞
⎟⎟
µc = 4µas/10yr⎜⎜
⎝ 100pc ⎠
−1
⎛
⎞⎛ a ⎞
ρc
⎜⎜
⎟⎜
⎟⎟
6
3 ⎟⎜
⎝ 4 ×10 Msun /pc ⎠⎝ 0.38pc ⎠
2
⎛ V
⎞
⎜
⎟
⎝ 220km/s ⎠
Effect of Bulge Motion
⎛
⎞⎛ V
Σ0
⎞
⎟
µ B = 2µas/10yr⎜⎜
⎟
6
2 ⎟⎜
⎝ 6 ×10 Msun/pc ⎠⎝ 220km/s ⎠
Column Density of Core and Bulge
1. ｴ 10 6
500000.
Core
Msun/
pc^2
100000.
Log Σ 50000
100pc
Column density
Bulge
10000
5000
1
5
10
50 100
500 1000
Log
Log （Impact parameter [pc])
6. Lensing toward Galactic Center V
6-4
Total Effect
10°
0.7°=100pc
10°
-10°
2
⎞⎛ a ⎞ ⎛
⎛ L ⎞⎛
ρc
V
⎞
⎟
⎟⎟⎜⎜
⎜
⎟
µc = 2µas / 10 yr ⎜⎜
⎜
⎟
6
3 ⎟⎜
⎟
⎝ 100 pc ⎠⎝ 4 ×10 M sun / pc ⎠⎝ 0.38 pc ⎠ ⎝ 220km / s ⎠
⎛
⎞
Σ(100 pc )
⎜
⎟
µ B = 2µas / 10 yr ⎜
6
2 ⎟
⎝ 6 ×10 M sun / pc ⎠
6. Lensing toward Galactic Center V
6-5
Total Effect
10° J1700
J1713
J1751
-10°
10°
W56 79mJ@5GHz
J1820
ATCA&VLA, 5GHz,8GHz
Roy, Rao & Subrahmanyan (2006)
4
Apparent Motion
SgrA*
QSOs
Secular
6 mas/yr
Galactic Rotation
Secular
0.6μas/yr
Macro Lens
Periodic
250μas/yr
Annual Parallax
Random (several years)
10μas/yr Microlens
7. Summery
7-1
銀河系中心方向の重力レンズ効果
1．マイクロレンズ効果・・・・MOA Project
èDark matter, 系外惑星探査
2．SgrA*近傍の星質量BH,中性子星、・・によるレンズ。
è SgrA*のDark matterの量、・・・
3.銀河系内の星によるAstrometric microlensingでQSO基準
座標系が揺らぐè意外と高いOptical Depth
4. SgrA*による弱重力近似のレンズ
5．SgrA*による強重力場近似のレンズ
6．銀河系によるマクロな重力レンズ
Photo by Kouji Ohnishi