1.0

1.5

2.0

2.5

3.0

tim

e [1

04 r

s /

c]

0.5

10 20 30 40 10 20 30 40

r / rs r / rs(a) (b)

-0.001 -0.0005 0.0 0.0005 0.001 -0.001 -0.0005 0.0 0.0005 0.001mr(r, t).

mz(r, t).

1.0

1.5

2.0

2.5

3.0

0.5

tim

e [(

M/1

0 M

) s

]

2 2

Waves propagate outward

Radial Oscillations Vertical Oscillations

Fig. 2. Radial and vertical oscillations in spact-time diagram. Thehorizontal axis is the radius and the vertical axis is the time.Gray-scale indicates the mass fluxes at each cells.

10 20 30 40r / rs

1

10

100

1000-4.4 -4.2 -4.0 -3.8 -3.6 -3.4

10 20 30 40r / rs

-4.4 -4.2 -4.0 -3.8 -3.6 -3.4log10 νP(r, ν) log10 νP(r, ν)

(b)(a)

ν [(

10M

/

M)

Hz]

2 2

Global Disk Oscillation

Patterned Oscillations

Inner Torus Oscillation

Trapped Oscillation

Radial Oscillations Vertical Oscillations

Fig. 3. Power Spectrum Density (PSD) of the radial and the verticaloscillations. The horizontal axis is the radius and the vertical axisis the time. Gray-scale indicates the mass fluxes at each cells.

the simulation and is ended 3 sec and the sampling dura-tion is 2 sec in total. The first 1 sec is called as the earlyphase and the last 1 sec is called as the late phase in thisstudy. The mass fluxes are displayed in gray-scale.

2.2. Global disk oscillations

The figure 3 shows PSDs of the radial and the verticaloscillations as a function of radius. The power of os-cillations is shown by gray-scale. A dashed line and asolid line indicate Keplerian frequency and epicyclic fre-quency as a function of radius, respectively. In radialoscillations, we found some global oscillations. In verti-cal oscillations, we found several patterned oscillations.One of them is located at 6rs. In addition, we found weaktrapped oscillations inside the radius where the epicyclicfrequency become maximum and also weak oscillationsof inner torus located around 10rs.

2.3. Twin HF-QPOs

Integrated PSD over the radius is shown in figure 4. Wefound two twin QPOs. One is transient twin QPOs onlyin early phase and theother is persistent twin QPOs inboth early and late phase of MHD accretion flows.

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

10 100 1000-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

10 100 1000

log 1

0 P

(ν)

log 1

0 P

(ν)

ν−1

ν−2

ν−1

ν−2

ν−1

ν−2

ν−1

ν−2

νu1νl1

νu2

νl2

νu2

νl2

νκ1 νK1 νκ1+νK1

ν [(10M / M) Hz] ν [(10M / M) Hz]

(a) (b)

(c) (d)

νκ2 νK2 νκ2+νK2

Early Phase

Late Phase

Radial Oscillations Vertical Oscillations

Fig. 4. Integrated PSD of the radial and the vertical oscillation.

In twin QPOs in radial oscillations, the lower peakfrequency corresponds to the Kepler frequency and thehigher peak frequency corresponds to the sum of Keperfrequency and epicyclic frequency at the resonant radiuswhere the ratio of Kepler and epicyclic frequency is closeto 2 in the Schwartzchild black hole. Radial oscillation isexcited at the resonant radius and it propagate the accre-tion disk globally. We have discovered for the first timeresonant global disk oscillations in magnetized accretiondisks.

2.4. Short Summary

We have found twin QPOs in the integrated PSD of vari-abilities in the magnetized accretion flows. Frequenciesof QPOs corresponds to the resonant frequencies at theresonant radius. These QPOs are likely to be excitedat the resonant radius where the ratio of the Kepler fre-quency and the epicyclic frequency is 2:1. This may becaused by the wave-warp resonance (see S. Kato 2004 indetail; see also Abramowicz 2003, Rebusco 2004). Theratio of resultant upper and lower frequencies of QPOsis close to 3:2 which is consistent with the observed ratio(Remillard et al. 2002).

3. Radiation Transfer Calculations

We compute radiation properties of our 3-D MHD sim-ulation data and compare our result with the spec-tral energy distribution (SED) of the Galactic centersource, Sgr A*. For a radiative transfer calculation, thereare three parameters, normalization density, black holemass, and electron temperature. The normalization den-

sity is leave as a free parameter in order to fit the ob-served SED and the electron temperature is estimated bythe gas temperature in the MHD simulation. The blackhole mass is fixed as 3.6 × 106M¯ (Eckert et al. 2005).For radiative process, Synchrotron emision/absorption,inverse-Compton scattering, and Bremsstrahlung emis-sion/absorption by thermal electrons (e.g., Narayan &Yi 1995; Manmoto 2000) are taken into consideration inthis study.

3.1. Emergent SED

In figure 5, we plot SEDs of MHD accretion flows. Theemergent SED is consistent with the observed SED ofSgr A* from radio to gamma-ray in quiescent state.Radio band consist of self-absorbed synchrotron emis-sion. From submillimeter to optical band consist of syn-chrotron self-compton emission. Above X-ray band con-sist of Bremsstrahlung emission.

8 10 12 14 16 18 20

28

30

32

34

36

38

log10 ν [Hz]

log

10 ν

Lν [

erg

/sec

]

quiscent state

flaring state

Fig. 5. Spectral Energy Distribution (SED) of MHD accretion flowsranging from radio to gamma-ray. Solid and dashed lines indicatethe emergent spectra and the emitted spectra, respectively. Barsindicate the time variation. Cross points and “bow ties” indicatethe observed spectra in the Galactic center (Narayan et al. 1998;Eckart et al. 2006; Baganoff 2001; Belandger et al. 2005)

3.2. Synthesis Images

We created images of centimeter, submillimeter, and in-frared bands by using the ray-tracing calculation dis-played in figure 6. We found that the size of a coreemission region in the centimeter and the submillimeterbands is about 30 rs around a black hole. In the infraredband, we found that a disk like emission region extendsmore than 100 rs. Direction of magnetic vectors in cen-timeter and submillimeter bands is similar but that ofinfrared band is different from the others.

4. Future Prospects

Radiation transfer studies of MHD data will be a key-stone between theory and observation. Intensive timinganalysis both on variable emissions in MHD accretion

1011

≤ v < 1012

[Hz]

-100 -50 0 50 100-100 -50 0 50 100

26 28 30 32 34

log10 ∫ v Lv dlog v [erg/sec]10

10 ≤ v < 10

11 [Hz]

-100

-50

0

50

100

V [

r s]

≈ (

MB

H/

10

6 M

)

[20 m

as]

1012

≤ v < 1014

[Hz]

-100 -50 0 50 100

U [rs] ≈ (MBH/ 106 M ) [20 mas]

-100

-50

0

50

100

V [

r s]

≈ (

MB

H/

10

6 M

)

[20 m

as]

Fig. 6. Synthesis images in centimeter, submillimeter, and infraredbands. White arrows indicate the magnetic vector which is per-pendicular to the polarization vector.

flows and on X-ray brightness oscillations in X-ray bi-naries will provide a crucial information on the origin ofQPOs.

References

Abramowicz, M. A. et al. 2003 PASJ, 55, 467Baganoff, F. K., et al. 2001 Nature, 413, 45Baganoff, F. K., et al. 2003 ApJ, 591, 891Belanger, G., et al. 2006 ApJ, 636, 275Eckart, A. et al. 2005 The Evolution of Starbursts, 783,

17Eckart, A., et al. 2006, A&A, 450, 535Kato, S. 2004 PASJ, 56, 905Kato, Y. 2004 PASJ, 56, 931Manmoto, T. 2000 ApJ, 534, 734Narayan, R., & Yi, I. 1995 ApJ, 452, 710Narayan, R. et al. 1998 ApJ, 492, 554Rebusco, P. 2004 PASJ, 56, 553Remillard, R. A. et al. 2002 ApJ, 580, 1030Remillard, R. A. 2005 Astronomische Nachrichten, 326,

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