Steady Models of Steady Models of Black Hole Accretion Black Hole Accretion

Disks including Disks including Azimuthal Magnetic Azimuthal Magnetic

FieldsFields Hiroshi Oda (Chiba Univ)

Mami Machida (NAOJ)Kenji Nakamura (Matsue)

Ryoji Matsumoto (Chiba Univ)

YITP Workshop on ldquoQuasi-Periodic Oscillations and Time Variabilities of Accretion Flowsrdquo Kyoto Nov 20-22 2007

(Ref Oda et al 2007 PASJ 59 457)

IntroductionIntroduction X-ray observational data shows four spectral statX-ray observational data shows four spectral stat

eses HighSoft State Slim Disk State LowHard State Very High (Intermediate) State

HFQPOs amp LFQPOs are prominent BrightHard stateBrightHard state (eg Miyakawa et al 2007)

observed during the rising phase (up to ~02LEdd) ~177 Ecut ~ 40-200keV (L-074)

This means that Te decreases as L increases LFQPOs are prominent

In my presentation I focus on the BrightHard state

Hard-to-Soft transition ( eg Gierliński amp Newton 2006)

Brightslow transition Slow Occurring at 03 LEdd or more

Darkfast transition Fast Occurring at le 01 LEdd

Energy [ keV ]

Slim

VH(IM)LH

HS

BH

Gierliński amp Newton 2006

01LEdd

03LEdd

Miyakawa et al 2007

X-ray spectrum

GX339-4

Theoretical Models of Accretion Theoretical Models of Accretion DisksDisks

These conventional models do not include the magnetic fieldsThese conventional models do not include the magnetic fields Hard-to-Soft transition occurs at the critical mass accretion rate for tHard-to-Soft transition occurs at the critical mass accretion rate for t

he existence of the ADAF and this corresponds to ~04he existence of the ADAF and this corresponds to ~0422LEdd (Esin e (Esin et al 1997)t al 1997) This luminosity can not explain Brightslow transition unless This luminosity can not explain Brightslow transition unless ~1~1

Surface Density

Mass

Acc

reti

on

Rate

Thermal Equilibrium Curves

LcritLEdd~042

Advection

Advection

Hard X-RaySoft X-Ray

Soft X-Ray

ADAF

Slim

Standard

SLE

Numerical Simulations of Accretion Numerical Simulations of Accretion DisksDisks

Local 3D MHD (eg Hawley et al 1995)Local 3D MHD (eg Hawley et al 1995) MRI excites and maintains magnetic turbulence The Maxwell stress transports the angular momentum

Global 3D MHD including the radiative cooling Global 3D MHD including the radiative cooling (eg Machida et al 2006)(eg Machida et al 2006)

A radiatively inefficient Torus rarrAn optically thin hot disk is formed rarrThe cooling instability takes place rarrThe disk shrinks in the vertical direction rarrThe magnetic pressure becomes dominant rarrThe quasi-equilibrium cool state The Maxwell stress is proportional to the total pressure

The total dissipative heating rate is due to the thermalization of the magnetic energy

Aim amp Assumption for One Temperature Model

Our aimTo construct steady models of the

magnetically supported accretion disks Assumption

The magnetic fields inside the disk are turbulent and dominated by azimuthal component

Total stress is dominated by Maxwell stress and is proportional to the total pressure

The disk is heated by the dissipation of the magnetic energy

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

IntroductionIntroduction X-ray observational data shows four spectral statX-ray observational data shows four spectral stat

eses HighSoft State Slim Disk State LowHard State Very High (Intermediate) State

HFQPOs amp LFQPOs are prominent BrightHard stateBrightHard state (eg Miyakawa et al 2007)

observed during the rising phase (up to ~02LEdd) ~177 Ecut ~ 40-200keV (L-074)

This means that Te decreases as L increases LFQPOs are prominent

In my presentation I focus on the BrightHard state

Hard-to-Soft transition ( eg Gierliński amp Newton 2006)

Brightslow transition Slow Occurring at 03 LEdd or more

Darkfast transition Fast Occurring at le 01 LEdd

Energy [ keV ]

Slim

VH(IM)LH

HS

BH

Gierliński amp Newton 2006

01LEdd

03LEdd

Miyakawa et al 2007

X-ray spectrum

GX339-4

Theoretical Models of Accretion Theoretical Models of Accretion DisksDisks

These conventional models do not include the magnetic fieldsThese conventional models do not include the magnetic fields Hard-to-Soft transition occurs at the critical mass accretion rate for tHard-to-Soft transition occurs at the critical mass accretion rate for t

he existence of the ADAF and this corresponds to ~04he existence of the ADAF and this corresponds to ~0422LEdd (Esin e (Esin et al 1997)t al 1997) This luminosity can not explain Brightslow transition unless This luminosity can not explain Brightslow transition unless ~1~1

Surface Density

Mass

Acc

reti

on

Rate

Thermal Equilibrium Curves

LcritLEdd~042

Advection

Advection

Hard X-RaySoft X-Ray

Soft X-Ray

ADAF

Slim

Standard

SLE

Numerical Simulations of Accretion Numerical Simulations of Accretion DisksDisks

Local 3D MHD (eg Hawley et al 1995)Local 3D MHD (eg Hawley et al 1995) MRI excites and maintains magnetic turbulence The Maxwell stress transports the angular momentum

Global 3D MHD including the radiative cooling Global 3D MHD including the radiative cooling (eg Machida et al 2006)(eg Machida et al 2006)

A radiatively inefficient Torus rarrAn optically thin hot disk is formed rarrThe cooling instability takes place rarrThe disk shrinks in the vertical direction rarrThe magnetic pressure becomes dominant rarrThe quasi-equilibrium cool state The Maxwell stress is proportional to the total pressure

The total dissipative heating rate is due to the thermalization of the magnetic energy

Aim amp Assumption for One Temperature Model

Our aimTo construct steady models of the

magnetically supported accretion disks Assumption

The magnetic fields inside the disk are turbulent and dominated by azimuthal component

Total stress is dominated by Maxwell stress and is proportional to the total pressure

The disk is heated by the dissipation of the magnetic energy

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

Theoretical Models of Accretion Theoretical Models of Accretion DisksDisks

These conventional models do not include the magnetic fieldsThese conventional models do not include the magnetic fields Hard-to-Soft transition occurs at the critical mass accretion rate for tHard-to-Soft transition occurs at the critical mass accretion rate for t

he existence of the ADAF and this corresponds to ~04he existence of the ADAF and this corresponds to ~0422LEdd (Esin e (Esin et al 1997)t al 1997) This luminosity can not explain Brightslow transition unless This luminosity can not explain Brightslow transition unless ~1~1

Surface Density

Mass

Acc

reti

on

Rate

Thermal Equilibrium Curves

LcritLEdd~042

Advection

Advection

Hard X-RaySoft X-Ray

Soft X-Ray

ADAF

Slim

Standard

SLE

Numerical Simulations of Accretion Numerical Simulations of Accretion DisksDisks

Local 3D MHD (eg Hawley et al 1995)Local 3D MHD (eg Hawley et al 1995) MRI excites and maintains magnetic turbulence The Maxwell stress transports the angular momentum

Global 3D MHD including the radiative cooling Global 3D MHD including the radiative cooling (eg Machida et al 2006)(eg Machida et al 2006)

A radiatively inefficient Torus rarrAn optically thin hot disk is formed rarrThe cooling instability takes place rarrThe disk shrinks in the vertical direction rarrThe magnetic pressure becomes dominant rarrThe quasi-equilibrium cool state The Maxwell stress is proportional to the total pressure

The total dissipative heating rate is due to the thermalization of the magnetic energy

Aim amp Assumption for One Temperature Model

Our aimTo construct steady models of the

magnetically supported accretion disks Assumption

The magnetic fields inside the disk are turbulent and dominated by azimuthal component

Total stress is dominated by Maxwell stress and is proportional to the total pressure

The disk is heated by the dissipation of the magnetic energy

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

Numerical Simulations of Accretion Numerical Simulations of Accretion DisksDisks

Local 3D MHD (eg Hawley et al 1995)Local 3D MHD (eg Hawley et al 1995) MRI excites and maintains magnetic turbulence The Maxwell stress transports the angular momentum

Global 3D MHD including the radiative cooling Global 3D MHD including the radiative cooling (eg Machida et al 2006)(eg Machida et al 2006)

A radiatively inefficient Torus rarrAn optically thin hot disk is formed rarrThe cooling instability takes place rarrThe disk shrinks in the vertical direction rarrThe magnetic pressure becomes dominant rarrThe quasi-equilibrium cool state The Maxwell stress is proportional to the total pressure

The total dissipative heating rate is due to the thermalization of the magnetic energy

Aim amp Assumption for One Temperature Model

Our aimTo construct steady models of the

magnetically supported accretion disks Assumption

The magnetic fields inside the disk are turbulent and dominated by azimuthal component

Total stress is dominated by Maxwell stress and is proportional to the total pressure

The disk is heated by the dissipation of the magnetic energy

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

Aim amp Assumption for One Temperature Model

Our aimTo construct steady models of the

magnetically supported accretion disks Assumption

The magnetic fields inside the disk are turbulent and dominated by azimuthal component

Total stress is dominated by Maxwell stress and is proportional to the total pressure

The disk is heated by the dissipation of the magnetic energy

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

BasicEquations

Heating cooling and Advection term

Prescription of the magnetic flux advection rate

Parameters We fixed Now free parameters are and

mass conservation

angular momentumconservation

energy eq

( ) entropy gradientparameter

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

Results Thermal Equilibrium Curves

A new branch appears in the thermal equilibrium curves On this branch the disk is supported by magnetic

pressure and cooler than the ADAF solution but hotter than the Standard disk

We call this ldquolow- branchrdquo The low- branches connect optically thin and thick

branches The optically thin part can emit hard X-ray The optically thick part can emit soft X-ray

The low- branches extends to above ~02

ADAF

Slim

Standard

SLE

ADAF

Slim

Standard

SLE

Low -

Low -

Low

-Low

-

red extremely smallthin smallthick large

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

ADAF

Slim

Standard

SLE

Low

-Low

-

Discussion Why does the low- branch appears

Q+~Qadv

Wtot~Wgas

Q+~Q-rad

Wtot~Wgas

Q+~Q-rad

Wtot~Wmag

Q+~Q-rad

Wtot~Wmag

Q+~Qadv

Wtot~Wrad

We set the heating rate as Although the gas pressure becomes small due to

the radiative cooling (and the disk thickness becomes smaller than the ADAF) the magnetic pressure can become large due to the magnetic flux

conservation

Thus the magnetically enhanced heating balances with the radiative cooling

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

red extremely smallthin smallthick large

Discussion Hard-to-Soft Transition

Gierliński amp Newton 2006

ADAFADAF

Low-Low-

Slim orStandard

Slim orStandardBS

DF

Note In the outer region the critical mass accretion rate for the existence of the ADAF is lower and the temperature is cooler

Hard (Low Ecut)Hard

ADAFOpt thin

Low-Slim

Soft

Opt thickLow-

Slim

Note For smaller B the critical mass accretion rate for the existence of the ADAF is lower

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

At low M (low L) T is independent of M (or L) At high M (high L) Anti-correlation between T and M This can lead the anti-correlation between L and T (or Ecut)

ADAF

Slim

Standard

SLELow

-Low

-

Discussion BrightHard State

The Low- branch seems to be a good candidate for the BrightHard

state

Miyakawa et al 2007BH state of GX339-4 (anti-correlation L-Ecut kTe)

Thermal equilibrium curveon M-T plane

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

The Slim disk evolves to the Low- disk

If the magnetic flux escapes from the disk due to the buoyancy Parker instability jet etchellip

The Low- disk could undergo transition to the standard disk

ADAF

Slim

StandardSL

E

Low -

Low -

Discussion Slim rarr Low-rarrStandard Transition

Advection

Soft X-Ray

Soft X-Ray

Soft X-Ray

The limit cycle of GRS 1915+105

Paul et al 1998

A typical profile of outburst

didipp

Slim

Low-

Standard

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

SummarySummary

We obtained the thermal equilibrium curves incluWe obtained the thermal equilibrium curves including azimuthal magnetic fields based on results ding azimuthal magnetic fields based on results of numerical simulationsof numerical simulations The low-The low- branch appears in the optically thin and thic branch appears in the optically thin and thic

k regionk region The low-The low- disk is radiatively cooled and magnetically supporte disk is radiatively cooled and magnetically supporte

dd This thermal equilibrium state can explain both the BrightHarThis thermal equilibrium state can explain both the BrightHar

d state and the Brightslow transitiond state and the Brightslow transition and suggest that the existence of the optically thick magnetiand suggest that the existence of the optically thick magneti

cally supported disk during the slim cally supported disk during the slim rarr standard transitionrarr standard transition

ENDEND

ENDEND