Global MHD Simulations of State Transitions and QPOs in Black Hole Accretion Flows

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Global MHD Simulations of State Transitions and
QPOs in Black Hole Accretion Flows

• Machida Mami (NAOJ)
• Matsumoto Ryoji (Chiba Univ.)

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State transition in GX339-4
Power Spectrum
Hardness Intensity Diagram
Belloni et al. (2006) fig.3
Low/hard state
Hard intermediate state
Belloni et al.(2006) fig.2
Low/hard state Typically, no QPO, break
around 10Hz
sometimes broad low-frequency QPO appears Hard
intermediate state narrow double peak QPO
moves
to higher frequency
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What is the origin of luminous hard state?
Abramowicz et al. (1995) M/Msun10,
r/rg5,a0.1
Mass accretion rate
1LEdd
Q-Q-adv PPgas
Surface density
Maximum luminosity of the ADAF branch when
a0.1 is below 10 of the Eddington luminosity
Maximum luminosity of GX 339-4 in hard state
about 40 of Eddington luminosity
This luminous hard state cannot be explained in
conventional ADAF models.
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Optically thin, luminous low-ßdisk
Isosurface of the plasma ß
M-Srelation obtained from simulations
Thermal equilibrium curve with low-ßbranch
Machida et al. (2006)
Oda et al. (2006)

• In order to study the state transition from
  low/hard state to soft state, we focus on the
  effect of optically thin radiative cooling.
• Due to the vertical contraction of the disk by
  cooling instability, low-ßdisk is formed.
• The low-ßdisk stays in an optically thin,
  thermally stable new equilibrium state supported
  by magnetic pressure.
• The luminosity of low-ßdisk can exceed 10 of
  Eddington luminosity.

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Purpose of this talk

• We focus on the hard state corresponding to the
  radiativelly inefficient accretion flow and its
  low frequency QPOs.
• For this purpose, we carried out global MHD
  simulations of optically thin accretion disk
• High temperature disk model corresponds to ADAF
• Low temperature disk model corresponds to
  cooling-dominated disk.

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Basic Equations
Resistive Magneto-hydrodynamic Equations
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Initial condition
Equilibrium torus threaded by weak toroidal
magnetic fields
(Okada et
al. 1989)
Unit Radius rg1 rg Schwarzschild
radius Velocity c(light speed)1 Density ?01
Length rg 3.0x106(M/10Msun)cm
Velocity c 2.99x1010 cm s-1
Time t0 10-4(M/10Msun) sec
Density ?0 8.3x10-7(M/10Msun)gcm-3
Temperature T0 1.1x1013K
Parameter Radius of the density max. of the
initial torus r0 35, 50 rg Angular momentum
distribution L L0 r0.43 ,L0 The ratio of gas
pressure to magnetic pressure
ßPgas/Pmag100 at rr0
Specific heat ratio ?5/3 Electric
resistivity ?510-4
Sound speed (disk) cs 0.01 c, 0.03c
The density ratio of halo to disk ?h0/?010-4
Critical ion-electron drift velocity vc0.9
Magnetic energy
Density
Z
r
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Snap shots of density distribution
High temperature(HT) model
Low temperature (LT) model
Top panels show the density distribution averaged
in the azimuthal direction. Bottom panels show
the density averaged in vertical direction zlt1.
In the case of HT, the accreting gas froms a
spiral shape. In model LT, inner torus is
formed. The inner torus deforms itself into a
crescent like shape. The inner torus has a
constant angular momentum.
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Time evolution of magneic fields
High temperature
Low temperature
Angular momentum
Radial distribution of specific angular momentum.
BlackHT, Pink LT
Angular momentum distribution depends on the disk
temperature, although the averaged plasma ß does
not depend on the disk temperature.
Top panels Time evolution of plasma ß Bottom
Time evolution of mean radial magnetic field
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PDS of the mass accretion rate
model LT
Right panel shows the power density spectrum
integrated in 3ltrlt6. Black and blue curves show
the model LT and HT, respectively. In model HT,
we can not see the peak around 0.1lt?lt10. But in
model LT, broad peaks appears around 10Hz and
narrow peaks appear around 100Hz and 140Hz.
Left panel shows the r-? distribution of Fourier
Power of mass accretion rate measured during the
time range 55000lttlt61000. In these panels, we
assume a 5.8 solar mass black hole, so 10000t0
corresponds to 0.58sec.
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Conclusion

• Angular momentum transport rate is dependent on
  the disk temperature.
• When the disk temperature becomes low, angular
  momentum transport rate becomes small and a
  constant angular momentum inner trous is formed
  around 4-8rs.
• The crescent-shape non-axisymmetric (m1) density
  distribution grows and disappears
  quasi-periodically.
• When the magnetic field is amplified enough,
  magnetic reconnection takes place and the
  crescent shape is destroyed.
• The inner torus oscillation excites the
  high-frequency QPO around 100Hz when we assume
  5.8 solar mass black hole.