EHT Sgr A* - - PowerPoint PPT Presentation

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EHT Sgr A* - - PowerPoint PPT Presentation

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EHT Sgr A* Kotaro Moriyama 1 , Shin Mineshige 2 , Mareki Honma 3 , Kazu Akiyama 1, 4 1: MIT Haystack observatory, 2: Kyoto university,

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EHTによるSgr A*への落下ガス雲の
 直接撮像を用いたブラックホールスピン測定

Kotaro Moriyama1, Shin Mineshige2, 
 Mareki Honma3, Kazu Akiyama1, 4 


1: MIT Haystack observatory, 
 2: Kyoto university, 
 3: NAOJ, 
 4: 2017 Jansky Fellow


Moriyama et al. in press, arXiv:1910.10713

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan 2

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)


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)

Goal： Observational proof of the black hole spacetime to test of general relativity theory

EHT collaboration et al. (2019)

Goal and Background

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Sgr A* Imaging: Advantages and Difficulties

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Credit: H. Shiokawa

50μas

EHT

Sgr A*

Quantities Sgr A* M87* Black hole mass [M] 4 × 106 6.5 × 109 Distance [kpc] 8 1.68 × 104 Apparent size [µas] 50 40 Period at ISCO (a/M = 0) 31 min 37 day

(e.g., Gravity Collaboration et al. 2018; EHT collaboration et al. 2019)

Advantages:

・Largest apparent diameter among all black hole candidates (~50 μas) ・Relativistic flux variation (~30 min-1hr) → Black hole spin indicator?

Lu et al. 2018

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Gas Cloud Falling Toward the Black Hole

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Observer

Innermost stable orbit (rms)

Blue shifted photon (Beaming) Red shifted photon (De-beaming)

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Gas cloud model

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j(νem)= j0 exp

  • − (R/R0(φ))2

νΓ+1

em

Distance from the central axis

  • f the gas cloud

Emissivity model

Thickness of the gas cloud (ring or arc) Photon frequency

∆I(νobs) = g3 νobs+∆ν

νobs

j(ν/g)∆ℓdν,

relativistic effect

Radiation transfer equation

photon index

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Gas clouds falling onto the black hole

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rg = GM/c2

a/M = 0.9, viewing angle = 75∘ inner edge of the disk = rISCO

rg/c = 20sec (SgrA*) = 0.5day (M87)

rg = 5μas (SgrA*) = 3.8μas (M87)

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Spin Indicator: Photon Rotation and Time Lag

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Simulated movie

rg/c = 20 sec (SgrA*) = 0.4 day (M87*) rg = 5 μas (SgrA*) = 3.8 μas (M87*)

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Light curve of a gas ring

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Light curve of a ring Simulated movie

rg/c = 20sec (SgrA*) = 0.5day (M87) rg = 5μas (SgrA*) = 3.8μas (M87)

0.0 0.2 0.4 0.6 0.8 1.0

Normalized flux

Total radiation Direct Secondary (a)

⟨g⟩

10 20 30 40 50

ct/rg

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Light curve of an arc-shaped gas model

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10 20 30 40 50

ct/rg

0.0 0.2 0.4 0.6 0.8 1.0

Normalized flux (a) Total (Ring) Direct (arc) Secondary

10 20 30 40 50

ct/rg (b) φ0/π = 0.0 φ0/π = 0.5 φ0/π = 1.0 φ0/π = 1.5

10 20 30 40 50

ct/rg (c) φ0/π = 0.0 φ0/π = 0.5 φ0/π = 1.0 φ0/π = 1.5

Single arc gas cloud Various initial phase Align maximum peaks

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Spin Dependency of the Echo of Radiation

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10 20 30 40 50 60

ct/rg

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Normalized flux

(a) a/M = 0.98 0.9 0.6

0.0 0.2 0.4 0.6 0.8 1.0

a/M

15 20 25 30 35 40 45

cδt/rg

(b)

Time interval Photon period

Moriyama et al. in press

i=75°

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Depency of Echo on Other Parameters

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Thickness Spectrum index Arc-chord angle Viewing angle Infalling velocity Rotation velocity

a/M=0.9 i=75°

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

EHT Synthetic Observation (2017-2020)

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(u, v) coverage for SgrA*

Expected EHT in 2017-2020

Gas clouds with various initial parameters


(initial velocities are based on GRMHD/RIAF )

rg/c = 20 sec (SgrA*) = 0.4 day (M87*) rg = 5 μas (SgrA*) = 3.8 μas (M87*)

Moriyama et al. in press

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Spin Dependence of Superposed Light Curve

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Baseline: ALMA/APEX-JCMT/SMA

a/M = 0.9, viewing angle = 75∘ inner edge of the disk = rISCO

Synthetic light curve

Align by maximum peaks

Superposed light curve

Moriyama et al. in press Unique dependence 


  • f the spin
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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Estimated Spin Values and Detectability

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Other baselines also provides similar estimation for spin values

0.0 0.2 0.4 0.6 0.8 1.0 atrue/M 0.0 0.2 0.4 0.6 0.8 1.0 aest/M

(a)

0.0 0.2 0.4 0.6 0.8 1.0 atrue/M 20 40 60 80 100 Detectability (%)

(b)

Baseline: ALMA-JCMT/SMA

Moriyama et al. in press

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Table 3. Estimated spin value of each baseline baselines aest/M for atrue/M = 0.2 atrue/M = 0.6 atrue/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.

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

EHT Movie for Infalling Gas Clouds

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Rotating gas cloud around the black hole
 (1 period = 30 min, Broderick & Loeb (2006)

Synthetic movie using full complex visibility
 (EHT imaging software is SMILI)

Basic idea: 
 Johnson et al. 2017

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Summary and Future Issues

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  • Method for black hole spin measurement with EHT
  • bservations
  • Investigate validity of the spin measurement based on

2017-2020 EHT synthetic observation

  • Investigate properties of infalling gas clouds
  • Investigate the accuracy of the black hole spin estimations

Summary: Next issues for GRMHD + Real observations:

Moriyama et al. in press, arXiv:1910.10713

3DGRMHD simulation 


(Used in EHT Collaboration et al. 2019)

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32th Rironkon Symposium, 12/25, 2019, NAOJ Mitaka, Tokyo, Japan

Uncertainty in the inner edge of the accretion disk

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