直接撮像を用いたブラックホールスピン測定 EHT による Sgr A* への落下ガス雲の Kotaro Moriyama 1 , Shin Mineshige 2 , Mareki Honma 3 , Kazu Akiyama 1, 4 1: MIT Haystack observatory, 2: Kyoto university, 3: NAOJ, 4: 2017 Jansky Fellow Moriyama et al. in press, arXiv:1910.10713
Goal and Background Goal ： Observational proof of the black hole spacetime to test of general relativity theory Spacetime is uniquely determined by the black hole mass and spin: ( M, a ) M ： Relatively accurately estimated by observing the motions of stars and gas (e.g., Ozel et al. 2010; Gravity Collaboration et al. 2018; EHT collaboration et al. 2019) EHT collaboration et al. (2019) a ： NOT easy to measure ↑ Important to consider the relativistic effect near the black hole (e.g., Abbott et al. 2017; Broderick et al. 2016; EHT collaboration et al. 2019) � 2 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Sgr A* Imaging: Advantages and Difficulties Sgr A* Quantities Sgr A* M87* 4 × 10 6 6 . 5 × 10 9 Black hole mass [ M � ] EHT 1 . 68 × 10 4 Distance [kpc] 8 50 μ as Apparent size [ µ as] 50 40 Period at ISCO ( a/M = 0) 31 min 37 day Credit: H. Shiokawa (e.g., Gravity Collaboration et al. 2018; EHT collaboration et al. 2019) Advantages: ・ Largest apparent diameter among all black hole candidates (~50 μ as) ・ Relativistic flux variation (~30 min-1hr) → Black hole spin indicator? Lu et al. 2018 � 3 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Gas Cloud Falling Toward the Black Hole Observer Red shifted photon (De-beaming) Blue shifted photon (Beaming) Innermost stable orbit ( r ms ) � 4 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Thickness of the gas Emissivity model Radiation transfer equation relativistic effect frequency Photon cloud (ring or arc) Distance from the central axis of the gas cloud Gas cloud model photon index � − ( R/R 0 ( φ )) 2 � ν Γ +1 j ( ν em )= j 0 exp em � ν obs + ∆ ν ∆ I ( ν obs ) = g 3 j ( ν /g ) ∆ ℓ d ν , ν obs � 5 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Gas clouds falling onto the black hole a / M = 0.9, viewing angle = 75 ∘ inner edge of the disk = r ISCO r g = GM / c 2 r g / c = 20sec (SgrA*) = 0.5day (M87) r g = 5 μ as (SgrA*) = 3.8 μ as (M87) � 6 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Spin Indicator: Photon Rotation and Time Lag Simulated movie r g / c = 20 sec (SgrA*) = 0.4 day (M87*) r g = 5 μ as (SgrA*) = 3.8 μ as (M87*) � 7 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Light curve of a gas ring Simulated movie Light curve of a ring 1 . 0 (a) Normalized flux Total radiation 0 . 8 Direct Secondary 0 . 6 ⟨ g ⟩ 0 . 4 0 . 2 r g / c = 20sec (SgrA*) = 0.5day (M87) 0 . 0 r g = 5 μ as (SgrA*) = 3.8 μ as (M87) 0 10 20 30 40 50 ct/r g � 8 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Light curve of an arc-shaped gas model Single arc gas cloud Various initial phase Align maximum peaks (a) (b) (c) 1 . 0 φ 0 / π = 0 . 0 φ 0 / π = 0 . 0 Total (Ring) φ 0 / π = 0 . 5 φ 0 / π = 0 . 5 Direct (arc) Normalized flux 0 . 8 φ 0 / π = 1 . 0 φ 0 / π = 1 . 0 Secondary 0 . 6 φ 0 / π = 1 . 5 φ 0 / π = 1 . 5 0 . 4 0 . 2 0 . 0 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 ct/r g ct/r g ct/r g � 9 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Spin Dependency of the Echo of Radiation i =75° 3 . 0 45 (a) (b) Time interval 2 . 5 40 a/M = 0 . 98 Photon period Normalized flux 2 . 0 35 c δ t/r g 0 . 9 1 . 5 30 25 1 . 0 0 . 6 20 0 . 5 0 15 0 . 0 0 10 20 30 40 50 60 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 ct/r g a/M Moriyama et al. in press � 10 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Depency of Echo on Other Parameters a/M =0.9 Arc-chord angle Thickness Spectrum index i =75° Rotation velocity Viewing angle Infalling velocity � 11 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
EHT Synthetic Observation (2017-2020) Gas clouds with various initial parameters (u, v) coverage for SgrA* (initial velocities are based on GRMHD/RIAF ) Expected EHT in 2017-2020 r g / c = 20 sec (SgrA*) = 0.4 day (M87*) r g = 5 μ as (SgrA*) = 3.8 μ as (M87*) Moriyama et al. in press � 12 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Spin Dependence of Superposed Light Curve Baseline: ALMA/APEX-JCMT/SMA Synthetic light curve Superposed light curve Align by maximum peaks Unique dependence of the spin a / M = 0.9, viewing angle = 75 ∘ inner edge of the disk = r ISCO Moriyama et al. in press � 13 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Estimated Spin Values and Detectability Baseline: ALMA-JCMT/SMA 100 1 . 0 (a) (b) Detectability (%) 0 . 8 80 a est /M 0 . 6 60 0 . 4 40 0 . 2 20 0 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 a true /M a true /M Other baselines also provides similar estimation for spin values Moriyama et al. in press � 14 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Table 3. Estimated spin value of each baseline baselines a est /M for a true /M = 0 . 2 a true /M = 0 . 6 a true /M = 0 . 9 (1) (2) (3) (4) ALMA-JCMT/SMA 0.39 (0.10-0.66) 0.56 (0.33-0.77) 0.86 (0.82-0.90) ALMA-SMT 0.33 (-0.00-0.62) 0.56 (0.31-0.76) 0.87 (0.82-0.90) JCMT/SMA-SMT 0.34 (0.04-0.62) 0.62 (0.37-0.80) 0.89 (0.83-0.94) ALMA- PV 30 m 0.27 (-0.03-0.59) 0.57 (0.34-0.75) 0.86 (0.82-0.90) ALMA-LMT 0.30 (0.01-0.61) 0.55 (0.31-0.75) 0.86 (0.82-0.90) ALMA-SPT 0.31 (0.01-0.61) 0.54 (0.28-0.73) 0.86 (0.82-0.90) ALMA-NOEMA 0.31 (-0.01-0.62) 0.56 (0.34-0.76) 0.87 (0.82-0.90) LMT-JCMT/SMA 0.33 (0.02-0.63) 0.56 (0.34-0.74) 0.87 (0.84-0.92) LMT- PV 30 m 0.29 (-0.01-0.62) 0.56 (0.34-0.75) 0.86 (0.82-0.90) LMT-SPT 0.33 (0.04-0.62) 0.57 (0.33-0.77) 0.87 (0.84-0.92) LMT-SMT 0.31 (0.02-0.60) 0.57 (0.31-0.75) 0.87 (0.84-0.92) NOEMA-SPT 0.35 (0.03-0.63) 0.58 (0.32-0.77) 0.88 (0.84-0.92) PV 30 m-SPT 0.35 (0.05-0.67) 0.58 (0.34-0.77) 0.88 (0.84-0.92) PV 30 m-NOEMA 0.31 (0.02-0.60) 0.56 (0.31-0.75) 0.87 (0.84-0.92) JCMT/SMA-SPT 0.38 (0.05-0.68) 0.62 (0.36-0.81) 0.89 (0.84-0.94) SMT-SPT 0.39 (0.05-0.69) 0.65 (0.40-0.84) 0.91 (0.85-0.97) Note — Top three lines show the estimated spin values for redundant site, and bottom lines corresponds to other ones.
EHT Movie for Infalling Gas Clouds Synthetic movie using full complex visibility Rotating gas cloud around the black hole (EHT imaging software is SMILI) (1 period = 30 min, Broderick & Loeb (2006) Basic idea: Johnson et al. 2017 � 16 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Summary and Future Issues 3DGRMHD simulation Summary: • Method for black hole spin measurement with EHT observations • Investigate validity of the spin measurement based on 2017-2020 EHT synthetic observation Next issues for GRMHD + Real observations: (Used in EHT Collaboration et al. 2019) • Investigate properties of infalling gas clouds • Investigate the accuracy of the black hole spin estimations Moriyama et al. in press, arXiv:1910.10713 � 17 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
Uncertainty in the inner edge of the accretion disk � 18 32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan
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