Oscillations beats and rotation of the accretion disk around super massive black hole s sgra
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Physics and Astrophysics of Supermassive Black Holes July 10 - July 14, 2006 Santa Fe, New Mexico ( Monday, July 10 th , 4:40 pm – 5:00 pm ). (Oscillations) Beats and Rotation of the Accretion Disk around Super massive Black Hole s SgrA*. Makoto Miyoshi ( NAOJ ).

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Oscillations beats and rotation of the accretion disk around super massive black hole s sgra l.jpg

Physics and Astrophysics of Supermassive Black Holes

July 10 - July 14, 2006 Santa Fe, New Mexico

(Monday, July 10th,4:40 pm – 5:00 pm)

(Oscillations)Beats and Rotation of the Accretion Disk around Super massiveBlack Holes SgrA*

Makoto Miyoshi(NAOJ)

WithZhi-Qiang Shen, T. Oyama , S. Kameno,H. Nagai, A. Doi , R. Takahashi , Y. Kato, & K. Asada

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The most convincing Black Hole today from Density Measurement.

Precise Mass Measurements M~3.6*106Msun

MBH at the Closest Distance ~8kpc

The Largest Apparent SchwarzschildRadius

Rs ~ 8micro-arcsec

Black Hole Shadow

will be observed

soon at SgrA*

(Falcke, Melia et al 00)—Bardeen’s talk

--Mueller’s too

Quasi Periodic Variation at Flare of IR&X-ray

(Genzel03, Eckart06:Aschenbach04)

?Existence of Bright Blob Moving

at the Last Stable Orbit ?

?Does the Period mean an Orbital Period?

Precise Period Determination is important but difficultbecause the Flare is not so Frequent. Also because the Flare Duration is less than about 3 hours.


Motions of Stars at GC.

NIR Observations

(Genzel et al)

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Periodicity was found during NIR flaring of SgrA* P=16.8±2.0 min.(Genzel 03)

P=22 min.( Eckart et al 06)

Genzel et al. 2003

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QPO at X ray too.

Periodicity is also found from X ray flare. P~100 s, 219 s, 700 s, 1150 s, and 2250 s were suggested

(analysis by Achenbach et al. 2004)

–Belanger’s Talk

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1. At Radio SgrA* is always bright enough to observe (1Jy at 43GHz). 2. At mm to sub-mm Radio wave also short time flaring are detected (Miyazaki et al. Zhao et al…). --We can expect to detect similar kinds of QPO in radio wave. We checked the data of SgrA* obtained VLBA. We detected the radio QPO from observations at 43GHz taken at 8th March 2004, just 1.5 days after the millimeter wave short time flare.

↑Example of Radio Flaring of SgrA* ( New detection by Miyazaki).



Shen et al. (2005)

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VLBI gives us high spatial resolution(~0.1mas).So we can also investigate the spatial distributions of QPOs in the image of SgrA* if exist.


(Herrnstein et al 99,

Miyoshi et al 95)

A example of investigations of spatial distributions of water maser line in the image.

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SgrA* image

At 43GHz


(whole time integrations)


We defined 209 rectangular regions

and measured time series of flux densities within the regions from 360 snap shot maps with 5 min integrations.

209(=19×11) in all

Then we check the spatial distributions of the QPOS.

We define these 209 small regions.

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s.n.r.7.8 8.67.7



Time variations of intensity in the 209 rectangulars ( red line=noise level)


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Sum up of 209 rectangulars

Left (0.1 mas east)


Right (0.1 mas west)


Time variations of flux densities in the central 3 rectangulars, & sum-up

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Periods Spectra of the central 3 rectangulars (MEM)
















Left, 0.1mas-east


Right 0.1mas-west

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We show you the statistics of the whole 209 rectangulars

Sum-up amplitude of 209 regions

Central 3 regions

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Statistics on spatial distributions of the periods

Strong confinements occur around P=12.9,17.2,30.1, & 55.8 min.

(also check at P=22.2min)

Sum up 209 rectangulars


P=17.2 m

P=55.8 m

P=12.9 m

P=30.1 m

Period (min)

Distribution size (1sigma)




Period (min)

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We found Periodic Structure Change Patterns

with the 4 Periods

1) We searched periodic structure change patterns around the 5 periods.

2) And found characteristic change patterns of the 4 periods. (P=16.8, 22.2, 31.35, &56.35 min.)

3) First, we show you the mapping method for searching periodic structure change patterns in the next slides.

P=56.35, 31.35, 16.8min

P=22.2 min

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map.wholeobservingtime →

← →oneperiodcircle( P min)

← → sub-divisions (8 phases)

→ phase 1 map

→ phase 2 map

→ phase 3 map

→ phase 4 map

1) This manner will enhance

the periodic structure change pattern

in images.

2) Very similar, almost the same uv- coverages

– free from the instrumental effect of

different synthesized beam shape -

→ phase 5 map

→ phase 6 map

→ phase 7 map

→ phase 8 map

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P=16.80min map.

uv coverage of each phase map

phase 1 phase 2 phase 3 phase 4

phase 5 phase 6 phase 7 phase 8

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We found Periodic Structure Change Patterns map.

with the 4 Periods

P=56.35, 31.35, 16.8min

P=22.2 min

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Periodic Structure map.

change pattern

of the P=56.35 min

① 1 peak

② 2 peaks

③ 2 peaks

2 peaks appear

during the half period.

④ 2 peaks

⑤ 2 peaks

⑥ 1 peak

1 peak appears during

the other half period.

⑦ 1 peak

⑧ 1 peak

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Periodic Structure map.

change pattern

of the P=56.35 min

① 1 peak

② 2 peaks

This seems as if the central intensity of the period is larger than those of next outer radii.

We observe the change with edge-on angle.

③ 2 peaks

④ 2 peaks

⑤ 2 peaks

⑥ 1 peak

⑦ 1 peak

⑧ 1 peak

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Periodic Structure map.

change pattern

of the P=31.35 min

① 2 peaks

② 1 peak

③ 2 peaks



④ 2 peaks

⑤ 1 peak



⑥ 2 peaks

All Phase maps show different opposite peak number

with the corresponding map half periods apart.

⑦ 1 peak

⑧ 1 peak

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Periodic Structure map.

change pattern of

the P=31.35 min

① 2 peaks

This can be explained with 3 bright arms model.

We observe the pattern motion from edge-on angle. Far side is unseen.

② 1 peaks


③ 2 peaks


④ 2 peaks


⑤ 1 peak


⑥ 2 peaks

⑦ 1 peak

⑧ 1 peak

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Periodic Structure map.

change pattern

of the P=22.2 min

Peak is the cross in the figure.

Peak position moves

along east-west direction

with the period.


enlarged images along east-west direction

This become clearer

at P=16.8 min case.

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Periodic Structure map.

change pattern

of the P=16.8 min


① Peak at right side

② Peak at center side

The peak position seems to move with the period.

This can be explained with one arm structure pattern rotating with the period.

And we observe it from edge-on .

③ Peak at left side

④ Peak at left side

⑤ Peak at left side

⑥ Peak at center

⑦ Peak at right side

⑧ Peak at right side

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P=16.80min map.

←Position shift

of the peak

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Change Pattern map.

of the P=16.8 min

Distribution of Amplitude of the P=16.8min

We Fourier-Transformed the Time Series Variations of each Cells in the 8 Phase Maps, derived the Amplitude & Delay Phase of the P=16.8min Change Pattern.

Distribution of Phase Delay of the P=16.8min

If we cut out at the east-west line….

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Phase connected------


Radius from the center (mas)


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They seem in a map.resonance.

P=16.8, 22.2, 31.35, 56.35min

Roughly saying 3:4:6:10

(20:15:10:6 in frequency domain)

P=16.8 & 22.2 min; circular change pattern one-arm (?) structure

P=31.35 min; three-arms (?) structure.

P=56.35 min; confined at the center.

The motion changes are too rapid v > c, light velocity

The changes are not real motion but pattern changes.

These should relate to oscillations of accretion disk!

A Example of Disk Oscillation Modes

Lense-Thirring Precession of Accretion Disks

Draza MarkovicFrederick K. Lamb

University of Illinois at Urbana-Champaign


In real data there are the indications l.jpg

Line of sight velocity map.can be estimated from QPO spectra

In real data there are the indications.

Intrinsic periodic oscillations occurred at the disk will be Doppler shifted by the rotation velocity in the disk when we observe from outside.





Bump moves

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P= 62.15min map.

Intensity Maps of the Periods

P= 62.15min(upper)



The Peak Position Moves

From East to West as Periods

Become Long.

P= 131.6min

P= 224.8min



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P= 5- 80min map.

Intensity Maps of rather wideband periods

(from the top)

P= 5- 80min

P= 80-160min

P= 160-240min

P= 240-320min

P= 320-400min ≒const.

The Peak Position Moves

Towards west as Periods

Become long.

P= 80-160min

P= 160-240min

P= 240-320min

P= 320-400min

If this means the effect

of Doppler shift,

It must be Rotation!

1.9mas,about 193Rs

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↑Displacement of the peak position map.

in P=16.80 min. phase-maps

↑Doppler shift obtained from the tendency of the whole periods (QPO) distributions :

<east> blue shifted --------------------------------- red shifted <west>

Assuming the structural change pattern of P=16.8min has the same direction of the disk rotation, the above two facts mean that the disk is almost edge-on, tilted the north side towards us about some degrees.

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Another View 1 map.


In Stellar Black Hole

1kHz (103Hz) QPO ; BH mass=1 Msun

In Case of SgrA*

P=55.3min(3380sec) ー 3×10-4Hz

means MBH=3.4×106Msun!

--Almost the same as the precise measurements with IR M~3.6×106Msun --

The Confined P=55.3min QPO of SgrA*

should be the similar kind of ‘kHz QPO’

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Another View 2 map.

The intrinsic image is obscured and broadened because of scattering effect by circum-nuclear or inter stellar plasma (∝λ2).

Shen 他(05), Bower他(04) investigated the effect.

Interstellar Plasma Scatters the Radios Image of SgrA* (Scattered Size ∝λobs2).

So VLBI Images of SgrA* are Believed to have No Intrinsic Information so far.

But our results suggest that the image are NOT TOTALLY OBSCURED.

There remain some imprints!

VLBI images of the SgrA*(Lo et al. ’99)

From GC1998.

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Summary of this talk. map.

1. Radio images of SgrA* has some imprints of intrinsic structure at 43GHz (though scattered and broadened).

2. 4 QPO periods ( P=16.8,22.2, 31.15, & 56.35min) are real variation periods. Clear periodic change patterns seen at these 4 periods. These mean disk oscillations.

3. Using Doppler effected QPO spectra, line of sight velocity can be measured.

4. VLBI SgrA* image is almost edge-on rotating disk.

P=56.35, 31.35, 16.8,&22.2min

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QPO observations with spatial resolution will reveal the black hole accretions disk.

But we need the understanding what is QPO in detail.


That’s all.