「銀河系研究会２００６」 2006年2月21日

Macro lens toward the Galactic Center
Kouji Ohnishi
Nagano National College of Technology

Mizuhiko Hosokawa
NiCTToshio Fukushima
NAOJ

1. Introduction
1-1 Detection of Galactic Rotation of Solar Systemphase-referenced to QSOs J1748-291(W109) J1745-283(W56)• Reid et al. 1999
VLBA 43GHz,2yr• Backer & Sramek 1999
VLA 4.9GHz, 17yr
• Reid et al. 2004
VLBA 43GHz,9yr
b 1°
W56

SgrA*

8kpc

0.7°=100pc

SgrA*

1°
W109

GC441

-1°-1°

6mas / yr =220 km / s
8kpc

VLBI observation of SgrA* =>6mas/y

1

1. Introduction
1-2

Various effect in the apparent motion

1. Introduction
1-2

Gravitational Lens effect to the G.C.

Micro Lens effectMacro Lens effectof reference QSOs
by the star near the line ofsight to G.C

of reference QSOs
by galactic potential
near the line of sight to G.C

Individual Star

AstrometricMicrolensing(Hosokawa,et al 2002 )Group of Stars(1) SgrA* (Massive BH)(2) Core(3) Bulge

Macro Lens
(Ohnishi, et al. 2003)

2

2. Astrometric Macro-lens
2-1

Gravitational Deflection byAxis Symmetric Mass Distribution∑ (L)1. Column density

2. Column Total Mass within L

3. Gravitational Deflection

θ =Pass of raym
L

2. Astrometric Macro-lensGravitational Deflection

2-2

θ =Δθm
LLΔLm( L ) ∆θ ( L) =  2πΣ( L) − 2 ∆LL 
If Σ＝Constant∆θ ( L) = πΣ 0 ∆L

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2. Astrometric Macro-lens
2-3

Illustration of Shift by Bulge Motion

Lens
Source Plane
Lens Plane

3. Astrometric Macro-lens in our Galaxy
3-1

Adopted Galactic Model

Core+Bulge+DiskAlexander & Sternberg (1999)

Characteristic Length Scale

CoreBulge

disk

0.38pc

667pc

3kpc

ρ core (r ) = 1+3(ρr / r )oc2

ρ o = 4 × 106 M SUM pc −3 , rc = 0.38 pc

rb = 3000 pc

Disk and Halo contribution is negligible

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A. Astrometric Macro-lens in our Galaxy
A-1

Column Density of Core and Bulge
1. ｴ 10 6Core500000.

Msun/pc^2Log Σ 100000.

100pc

50000

Column density

Bulge

10000
5000

1

51050 100500 1000

Log （Impact parameter [pc])Log

A. Astrometric Macro-lens in our Galaxy
A-2

Total Mass inside the Impact Parameter
1. ｴ 10 1 1bulge

1. ｴ 10 1 0

1. ｴ 10 9core
1. ｴ 10 8

1. ｴ 10 7

disk102050100200500

1000

2000

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3. Astrometric Macro-lens in our Galaxy
Effect of Core Motion

3-2Log Σ Msun/pc^2b

1. ｴ 10 6100000.

10000

φl

1000

151050100500 1000

Log （Impact parameter [pc])Core column density〜4μas/10yr @100pcµ l = µ c (1 − cos 2φ )2

 a  ρcL V 4 ×106 M / pc3  0.38 pc   220km / s pc100sunµ c = 2µas / 10 yr

µ b = µ c ( − sin 2φ )3. Astrometric Macro-lens in our Galaxy
3-3Effect of Core Motion
5°-5°

5°-5°

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3. Astrometric Macro-lens in our Galaxy
Effect of Bulge Motion

3-4bLog Σ Msun/pc^2
1. ｴ 10 6100000.

φ10000l

1000151050 100500 1000

Log （Impact parameter [pc])Bulge column densityµ l = µ B
µ b = 0
Σ (100 pc )62 
 6 × 10 M sun / pc µ B = 2 µ as / 10 yr 〜2μas/10yr

3. Astrometric Macro-lens in our Galaxy
3-5Effect of Bulge Motion
２°

２°
110°

-110°

-1073. Astrometric Macro-lens in our Galaxy
Collective Motionb• Secular proper motion of QSOs

3-7•

J1751-253

λMore than 1000yr!!

GC441

W56

SgrA*

W109

5°

Bulge

6 µas/10 yr

3. Astrometric Macro-lens in our Galaxy
Total Effect

3-610°

10°

-10°

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3. Astrometric Macro-lens in our Galaxy
Total Effect

3-610°
J1700

J1713
J1751
-10°

10°

W56 79mJ@5GHz

J1820
ATCA&VLA, 5GHz,8GHz
Roy, Rao & Subrahmanyan (2006)

3. Astrometric Macro-lens in our Galaxy
Internal Motion

3-8b+ 2 µas/10 yr

λGC441W56
SgrA*− 2 µas/10 yr+ 2 µas/10 yr
W109

1°Core93. Astrometric Macro-lens in our Galaxy
Total Effect

3-610°J1700
J1713
J1751
-10°

10°
J1820

3. Astrometric Macro-lens in our Galaxy
3-9Mass/Luminosity ratiob+ 2 µas/10 yr GC441

λW56− 2 µas/10 yr

SgrA*+ 2 µas/10 yr
W109

1°μas/yr

103. Astrometric Macro-lens in our Galaxy
3-9Mass/Luminosity ratio

5. Conclusion
5-1Summary of MACRO Lens
Macro lens effect of Galaxy is important
Apparent Motion of QSOs

InternalCollectiveCoreCore + Bulge

2μas/10yr

2-6μas/10yr

The collective gravitational deflection by the bulge, that is called MACRO-Lens, are observablemagnitude. This effect reaches 0.6 micro-arcsecond/yr and it has a secular component.

The measurement of these effects will provide us valuable
information on the visible and dark matter density and massfunction of the Galactic Center.

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5. Conclusion
5-2
Summary of MACRO Lens
SgrA*QSOs

Secular
6 mas/yr
Galactic Rotation

Secular0.6μas/yr
Macro Lens

Periodic
250μas/yr
Annual ParallaxRandom(several years)

10μas/yr
Microlensing

3. Astrometric Macro-lens in our Galaxy
3-8

Collective Motion

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