Global MHD Simulations of State Global MHD Simulations of State Transitions and QPOs in Black HolTransitions and QPOs in Black Hol

e Accretion Flowse Accretion Flows

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

State transition in GX339-4State transition in GX339-4

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

Hardness Intensity Diagram Power Spectrum

Belloni et al.(2006) fig.2

Belloni et al. (2006) fig.3

Low/hard state

Hard intermediate state

Time

What is the origin of luminous What is the origin of luminous hard state?hard state?

ADAF

Advection

SADM

Radiation

Q-=Q-rad (BB) P = Pgas

Abramowicz et al. (1995) M/Msun=10, r/rg=5,α=0.1

Surface density

Mass accretion rate

Q-=Q-advP=Pgas

１％ LE ｄｄ

Maximum luminosity of the ADAF branch when α=0.1 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.

Optically thin, luminous low-βdiskOptically thin, luminous low-βdisk

Machida et al. (2006) Oda et al. (2006)Surface density

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-βdisk is formed. • The low-βdisk stays in an optically thin, thermally stable new equilibrium state supported by magnetic pressure. •The luminosity of low-βdisk can exceed 10% of Eddington luminosity.

Isosurface of the plasma β M-Σrelation obtained from simulations Thermal equilibrium curve with low-βbranch

Purpose of this talkPurpose 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.

Basic EquationsBasic Equations

0

y resistivit Anomalous

0on conservatienergy of Eq.

eq.Induction

4

11 motion of Eq.

0on conservati mass of Eq.

20

cd

cdcd

vv

vvvv

vpvt

JBvt

B

BBpvvt

v

vt

Resistive Magneto-hydrodynamic Equations

yresistivit ofonset for the d threshol:

citydrift veloelectron -ion :J/

c

d

v

v

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 　　 β≡Pgas/Pmag ＝ 100 at r=r0

　 Specific heat ratio 　　　　　　　　 γ=5/3 Electric resistivity η=5×10-4

　 Sound speed (disk) 　　　　　　　 　 cs = 0.01 c, 0.03c　 The density ratio of halo to disk 　 ρh0/ρ0=10-4

　 Critical ion-electron drift velocity 　　 vc=0.9

UnitRadius ：　 rg=1 　 rg ： Schwarzschild radiusVelocity ：　 c （ light speed ） =1 　Density ：　 ρ0=1

Initial conditionInitial condition

Length rg 3.0x106(M/10Msun)cm

Velocity c 2.99x1010 cm s-1

Time t0 10-4(M/10Msun) sec

Density ρ0 8.3x10-7(M/10Msun)gcm-3

Temperature T0 1.1x1013K

Density

r

Z

Magnetic energy

Equilibrium torus threaded by weak toroidal magnetic fields 　 （ Okada et al. 　 1989 ）

Snap shots of density Snap shots of density distributiondistributionHigh 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 |z|<1.

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.

Time evolution of magneic fieldsTime evolution of magneic fieldsAngular momentum

Top panels: Time evolution of plasma β

Bottom : Time evolution of mean radial magnetic field

Radial distribution of specific angular momentum. Black:HT, Pink: LT

Angular momentum distribution depends on the disk temperature, although the averaged plasma β does not depend on the disk temperature.

High temperature Low temperature

PDS of the mass accretion PDS of the mass accretion raterate

Left panel shows the r-ν distribution of Fourier Power of mass accretion rate measured during the time range 55000<t<61000. In these panels, we assume a 5.8 solar mass black hole, so 10000t0 corresponds to 0.58sec.

Right panel shows the power density spectrum integrated in 3<r<6. Black and blue curves show the model LT and HT, respectively. In model HT, we can not see the peak around 0.1<ν<10. But in model LT, broad peaks appears around 10Hz and narrow peaks appear around 100Hz and 140Hz.

model LT

ConclusionConclusion• Angular momentum transport rate is dependent on the di

sk temperature. • When the disk temperature becomes low, angular mome

ntum transport rate becomes small and a constant angular momentum inner trous is formed around 4-8rs.

• The crescent-shape non-axisymmetric (m=1) 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.