銀河系中心巨大 BH の強重力における一般相対論の検証– すばる/TMT による重力理論と BH の探求 –SAIDA Hiromi (Daido Univ.) / 斉田浩見 (talk)
NISHIYAMA Shogo (Miyagi U. Edu.) / 西山正吾
+ Collaborators in Theory & Observation⋄ S14A, S15B, S16A, S17AB, S18B, S19A: Normal Programs⋄ S18A: Intensive Program⋄ Nishiyama et al. 2018 PASJ (Subaru obs. before the main event)Do et al. 2019 Science (Test of one peculiar GR eﬀect at 1PN)
Saida et al. 2019 PASJ (Test of whole GR evidence at 1PN)
– Typeset by FoilTEX –• 天文学会, 2019/09/11-13• 物理学会, 2019/09/17-20

1

List of members (in Subaru proposal, S20A):
data analysis & instrumentation

theory & data fitting

S.Nishiyama/西山正吾

H.Saida/斉田浩見

Y.Minowa/美濃和陽典

Y.Takamori/孝森洋介

Students of S.N./

M.Takahashi/高橋真聡

T.Kara, A.Ikki,T.Ohgami/大神隆幸

K.Sakuma, M.Yoshihara

R.Saitou/齋藤亮

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若手の皆さん：興味を持たれたらポスドクなど大歓迎
観測系 → 西山 · 理論系 → 斉田

– Typeset by FoilTEX –2∗

1. Sgr A and GR

1.1 Fact(GR : General Relativity)
Milky Way south partGCS-stars→Sgr A*S0-2 / S2 orbit~2000 AU
Gillessen+09• MSgrA ≃ 4 × 106 M⊙ : Massive BH candidate• S-stars are Test Particles in Grav. of Sgr A∗.
– Typeset by FoilTEX –3

• GR test at Massive BH has just begun
S0-2, S24 have Short Pericenter Distance (rp)⋄ For S0-2:
rp.S0-2 = 113 AU
tp.S0-2 = 2018.39 yr⋄ For S24:
rp.S24 ∼ 800 AU
tp.S24 ∼ 2024.28 yr⋄ BH: RSgrA ≃ 0.1 AU
S0-2 data in 2018 contain Non-Newtonian Eﬀects.
– Typeset by FoilTEX –4

1.2 Our aims, using Subaru/TMT• Facts: Detection of Non-Newtonian Eﬀect→ Do et al. 2019 Science ; Saida et al. 2019 PASJ
• Aim 1: GR or Other Gravity Theory, for SMBH ?
√⋄ PPN parameters, GR test at 1PN√⋄ BH spin measurement, GR test at 1.5PN⋄ Test of Local Position Invariance (Next Talk)• Aim 2: Invisible Mass Distribution around Sgr A∗For these aims, S0-2 and S24 are good probes. We
have been monitoring S0-2 from 2014 with Subaru.
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2. Our Approach

2.1 Obs. quantityPhoto bySean Goebel —• Redshift z of Infra-Red photon
coming from S0-2
λobsz :=−1
λS0-2
• GR evidence ∆zGR is the deviationfrom Newtonian Gravity (NG)zGR = zNG + ∆zGR
– Typeset by FoilTEX –6



2.2 Post-Newtonian (PN) expansion
• PN parameter: (Vp.S0-2 ≃ 0.03c , Vp.S24{ ≃ 0.01c)()−3210for S0-2
GMBHVpε∼ 2≈∼c rpc10−4 for S24

• PN expansion:Taylor expansion of the metric tensor by ε
The metric is a ”multi-comp. grav. potential”(1)(1.5)(2)gµν = ηµν + ε gµν+ ε1.5 gµν+ ε2 gµν+ ···where O(ε) ↔ BH mass , O(ε ) ↔ BH spin
1.5– Typeset by FoilTEX –7• Order estimation of ∆zGR in the unit km/s
PN order
S0-2
S241PN : cεO(102) O(10) ← BH Mass eﬀect
3/2−11.5PN : cεO(1) O(10 ) ← BH Spin eﬀect• Present/Expected obs. uncertainties of cz [km/s]
Tlscp S0-2 S24(S0-2 early type / S24 late type)
Subaru 152 ← From our obs. & NEW LGS
TMT20.2 ← Do et al. 2017
{Subaru detects 1PN eﬀect•
TMT tries 1.5PN eﬀect ← UN-EXPLORED !
– Typeset by FoilTEX –8• Ex. of zGR(t) and ∆zGR(t) at 1PN order⋄ S0-2, the best-fit with observed data

– Typeset by FoilTEX –9czGR1PN [km/s]⋄ S24, a guess based on existing data
2000
1000
0-1000
1850

1900

1950

2000

2050

2100

2150

year

→ Expected GR eﬀect ∆zGR for S24Continues ≈ 30 yr (plot of its central 10yr)– Typeset by FoilTEX –10• 1.5PN formula of the GR eﬀect (∆zGR := zGR − zNG)
c ∆zGR ≈(Subaru)(Subaru)
(TMT)

(RV)
(RV)
VGR − VNG

← Radial velocity

1 2+ VGR ← Special Rel., 1PN
2c
GMSgrA+← GR (grav.), 1PN
c rGR
GMSgrA (RV)
−VGR
← GR, 1.5PN
c rGR

(RV)
Note 1: c zNG = VNG , c zGR = the other terms– Typeset by FoilTEX –11

Note 2: Star’s motion (e.o.m.) at 1.5PN is aﬀectedby the BH spin (appears in the potential terms).
⃗1.5PN = V⃗1.5PN(t, spin)V
r1.5PN = r1.5PN(t, spin)∗TMT’s mission at Sgr ADetermine the parameter of BH spin for Sgr A∗,
which enables us to test the gravity theory at 1.5PN∗
order around Sgr A . (unexplored precision)– Typeset by FoilTEX –

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2.3 Science targets with Subaru/TMT• Parametrized PN/1.5PN :Metric tensor (multi-comp. grav. potential)(1)
1.5 (1.5)2gµν = ηµν + A ε gµν + B ε gµν + O(ε ){ General Rel. : A = 1 and B = 1→
Other Theor. : A ̸= 1 or B ̸= 1

Observational determination of A and B is the testof GR. If GR is rejected, the values of A and B are
the big information for the true gravity theory.
– Typeset by FoilTEX –13• P-PN / P-1.5PN parameter A / B modifies◦ E.O.M. of stars and photons◦ Time evolution of z(t) ← Observable→ Observations of z(t) determine A / B.
(Best-fit search for A / B)
• One science target with Subaru:Measure A at the Massive BH scale• One science target with TMT:
Measure B at the Massive BH scale– Typeset by FoilTEX –14

3. Summary• GR test at Galactic center Sgr A∗has just begun.
• Two of S-stars, S0-2 and S24, are good probes.
• Subaru enables GR test at 1PN,
on going with S0-2, and planning with S24.
◦ Non-NG eﬀect has been found, with S0-2.
◦ Planninng PPN approach with S0-2 and S24,
◦ and Test of ”LPI” with S0-2 and S24 (next page)• TMT enables GR test at 1.5PN,
the highest precision so far.
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⋄ Continue to the next talk (Nishiyama san)Local Position Invariance (LPI) Assumption
At any spacetime position (t, ⃗x),
for any free fall observer (who feels no gravity),
any non-gravitational physics law never changes.

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◦ Two categories of gravity theories exist,
whether nor not the theory assumes LPI.
◦ GR assumes LPI.
◦ As an example of non-grav. physics, we focus on
the photon emission by a given atomic species.

– Typeset by FoilTEX –16