1. Steady Models of Magnetically Supported Black Hole Accretion Disks and their Application to Bright/Hard State and Bright/Slow Transition Hiroshi Oda The Group Meeting @ The ITC Lounge Table of Contents ‣ Background Information ✓ Basic Picture and General Aspects ✓ Conventional Theory of BH Accretion Disks ‣ Motivation ✓ Bright/Hard state & Bright/Slow transition ✓ Recent MHD/Rad.-MHD simulations ➡ Importance of magnetic fields in accretion disks ‣ Model & Assumption ‣ Results ✓ Low-β(≡(p pas +p rad )/p mag ) solutions ➡ explain the Bright/Hard state & the Bright/Slow transition.

2. Background Information Basic Picture of Accretion Disks General Aspects of X-ray Spectrul States and State Transitions of Galactic BH Binaries Conventional Theory of Accretion DIsks Basic equations Model for optically thick disks Model for optically thin disks

3. RXTE Basic Picture of Accretion Disks (around a stellar mass BH) Companion Star BH Mass Supply Angular momentum transport due to viscosity Heating due to viscosity Soft X-ray (~1-10 keV) Hard X-ray (~100keV) Gravitational E. → Kinetic(Rotation) E. → Thermal E. →Radiation or Accretion onto BH Suzaku magnetic stress dissipation of magnetic energy → Magnetic E.

4. The Origin of the α-viscosity Turbulent magnetic fields generated by MRI The Maxwell stress transports the angular momentum. Disk heating via the dissipation of magnetic energy. In quasi-steady state ~10, ~0.01-0.1, ~10, ~0.01-0.1, Shearing-box 32×64×256 (Hirose+ ’06) (Machida+ ’00) 200×64×240 Global 3DMHD of opt. thin disks (RIAF) Local 3D Rad-MHD of opt. thick disks (Standard disk) Density (initial) BφBφ Turburent B Isosurface of |B|

5. General Aspects of X-ray Spectral States and State Transitions of Galactic BHBs Low/Hard State: High/Soft State: Intensity Jet Lorentz Factor Hardness Hard Soft Jet line Hard-to-Soft Transition: Relativistic. jet Energy [ keV ] 1 10 100 Flux νF ν [ keV/cm 2 s ] Energy [ keV ] 1 10 100 FLux νF ν [ keV/cm 2 s ] Schematic Picture of Hardness-Intensity Diagram Fender+ `04 DBB Hard tail Cutoff Power-Law Soft Excess Emission from optically thick disks. Emission from optically thin disks. =L hard /L soft

6. Basic eqs. of conventional viscous accretion disks Continuity Eq. of motion Energy eq. ϖ -comp. ϕ -comp. z-comp. Viscous force Surface density Vertically integrated total pressure Viscous heating Assumption:Steady, axisymmetric, Kepler rotation., hydrostatic balance Integrate in vertical direction. α-viscosity(Shakura & Sunyaev ’73) Gravity Pressure gradient Cylindrical coordinates

7. Standard Disk (High/Soft state) low M, high Σ Geometrically thin ( H ≪ϖ ) Q + vis ~Q - rad (black body; T eff ∝ϖ -3/4 ) p gas dominant, cool (T 〜 10 7 K) (p rad dominant Std. Disk) Thermally unstable Slim Disk (Slim Disk state) High M, high Σ photon trapping Geometrically moderately thick (slim) Q + vis ~Q - adv ( T eff ∝ϖ -1/2 ) p rad dominant, moderately hot(T 〜 10 7-8 K) Theoretical Models: Optically Thick DIsks Soft X-ray (Slim Disk) Advection Heat moderately hot(T 〜 10 7-8 K) p rad dominant Soft X-ray (High/Soft) Heat Radiation cool (T 〜 10 7 K ) p gas dominant Surface density Thermal Equilibrium Curves@5r s Mass Accretion Rate.. Energy [ keV ] 1 10 100 FLux νF ν [ keV/cm 2 s ] X -ray spectrum form disks

8. (SLE solution) Q + vis ~Q - rad (e.g., brems., Inv.-Comp.) p gas dominant, hot (T e 〜 10 ９ K) Thermally unstable Advection Dominated Accretion Flow(ADAF)/Radiatively Inefficient Accretion FLow(RIAF) (Low/Hard state) Low M, low Σ The viscously dissipated energy is stored in the gas as entropy and advected inward. Geometrically thick. Q + vis ~Q - adv p gas dominant, hot (T e 〜 10 9 K) Advection Heat Hard X-ray (Low/Hard) RIAF hot (T e 〜 10 9 K) p gas dominant Theoretical Models: Optically Thin DIsks Surface density Thermal Equilibrium Curves@5r s Mass Accretion Rate. Energy [ keV ] 1 10 100 FLux νF ν [ keV/cm 2 s ] X -ray spectrum form disks

9. Surface density Temperature Slim Std. Hard-to-Soft Thermal Equilibrium Curves@5r s Thin Opacith Thick Adv. Heat Hard X-ray (Low/Hard) RIAF hot (T e 〜 10 9 K) p gas Soft X-ray (Slim Disk) Adv. Heat Slim Disk moderately hot(T 〜 10 7-8 K) p rad Soft X-ray (High/Soft) Heat Rad. Std. Disk cool(T 〜 10 7 K) p gas Thermal Equilibrium Curves of Accretion Disks Mass Accretion Rate

10. Motivation Two hard-to-soft transition: Bright/Slow & Dard/Fast Bright/Hard state durging the Bright/Slow transition Importance of the magnetic fields in such transition: Suggestion form 3D MHD

11. Soft Hard RXTE: GX339-4 Belloni+ `06 2004/2005 2002/2003 Bright Dark Two Distinct Hard-to-Soft Transitions Energy [ keV ] 1 10 100 FLux νF ν [ keV/cm 2 s ] Energy [ keV ] 1 10 100 Flux νF ν [ keV/cm 2 s ] =L 9.4-18.5keV /L 2.5-6.1keV

12. Bright/Slo w Transition occurs at ~0.3 L Edd, takes ≲ 30 days Dark /Fast Transition occurs at ≳ 0.1 L Edd, takes ≳ 15 days Gierlinski & Newton `06 Hard-to-Soft Transition of Other Objects =L 5-12keV /L 3-5keV

13. Bright/Slow Transition & Bright/Hard State [ keV ] 1 10 100 Flux νF ν [ keV/cm 2 s ] High/Soft Low/Hard Very High/ Steep PL Slim Disk Cutoff PL (E cut 〜 200keV) Cutoff PL (E cut 〜 50-200keV) HR = L 5-12keV / L 3-5keV Soft Hard L/H B/H VH/SPL Slim H/S (Gierlinski & Newton`06) X-ray Spectral States H-L Diagram GX 339-4 Bright/Slow (2002/2003) Jet line Bright/Hard E cut Low/Hard E cut 〜 200keV Bright /Hard 〜 〜 0.2L Edd E cut vs. L E cut anti- correlates with L GX 339-4 (Miyakawa+ `08) ‣ Bright/Slow Transition: occurs at ~0.3L Edd ‣ Bright/Hard State: E cut anti-correlates with L (>0.07L Edd ). Conventional models (RIAF, Std., Slim) can not reproduce these features. Dark/Fast (2004/2005) Luminosity

14. Surface density Temperature Slim Std. Hard-to-Soft Thermal Equilibrium Curves@5r s Thin Opacith Thick Adv. Heat Hard X-ray (Low/Hard) RIAF hot (T e 〜 10 9 K) p gas Soft X-ray (Slim Disk) Adv. Heat Slim Disk moderately hot(T 〜 10 7-8 K) p rad Soft X-ray (High/Soft) Heat Rad. Std. Disk cool(T 〜 10 7 K) p gas 〜 0.4 α 2 L Edd 〜 0.001 L Edd Bright/Slow Transition [ FAILED ] Bright Hard State [ FAILED ] T e ≥ 10 9 K in RIAF Thermal Equilibrium Curves of Accretion Disks Mass Accretion Rate Dark/Fast Transition [ OK ] Low/Hard State [ OK ] Dark/Fast Transition [ OK ] Low/Hard State [ OK ]

15. Magnetic Pressure Dominated (Low-β) Disks: Candidates for the Bright/Hard State? “Magnetic Accretion Disks Fall into Two Type” (Shibata+ ’90) High β disk: B escapes due to the buoyancy (or Parker). Low β disk: B cannot escapes due to the strong magnetic tension. Such low-β disks emit hard X-rays (e.g., Mineshige+ ’95) “Formation of Magnetically Supported Disks during Hard-to- Soft Transitions in Black Hole Accretion Flows” (Machida+ ’06) Global 3D MHD of optically thin accretion disks with cooling Hot RIAF → Cool Low-β Surface density Low-β Low-β Temperature Accretion Rate RIAF cool shrink Turbulent B φ dominant β 〜 10 t cool ≪ t escape B ➡ B φ is almost conserved β 〜 0.1 ✦ Early phase ✦ Final phase ‣ As M increase ➡ Σ > Σ crit ➡ cooling instability ➡ shrink in z Time evolution.

16. Aims Construct 1D steady models incorporating magnetic fields. Aim 2: Transonic solutions (one-temperature; T i =T e : Oda+ ’07, PASJ) How does the radial structure of disks change due to the magnetic field? Aim 3: Thermal equilibria & transonic solutions (two- temperature; T i ≠T e ) No longer valid T i =T e in high temperature, low density region. Although we consider the bremsstrahlung emission in the 3DMHD and above- mention models, how about the synchrotron emission and the inverse-Compton effect? Spectrum form the low-β disks? Reproduce the spectrum observed in Bright/Hard state? Aim 1: Local thermal equilibria for opt. thin ~ thick disks. (Oda+ ’09, ApJ) Exist thermal equilibrium solutions of low-β disks? Low-β solutions explain Bright/Hard state and Bright/Slow transition? Low-β solutions explain Bright/Hard state and Bright/Slow transition?

17. Basic Eqs. Grav.Lorentz forceP grad Steady, azimuthal average p tot = p gas +p rad +p mag HeatingCooling Continuity Eq. of motion Energy eq. ϖ -comp. ϕ -comp. z-comp. Cylindrical coordinates Induction eq.

18. Magnetic Field & Velocity Field We assumed that magnetic fields are turbulent and dominated by the azimuthal component. [mean field][fluctuating field] Azimuthal averages of the fluctuating component are zero ‣ Decompose into the mean field and the fluctuating field Note: is not zero. Evolution of the turbulent B inside the disk (face on view) cvcv cvcv differential rotation turbulence

19. Kepler rotation instead of the radial component fo the eq. of motion. hydrostatic in z, polytropic,,, are constant in z, integrate in z direction Maxwell Stress Angular momentum swallowed by BH: Mass accretion rate: Disk thickness: 2H Entropy gradient: ξ Surface density: Dynamo term Magnetic diffusion term Basic Eqs. Steady, azimuthal average Continuity Eq. of motion Energy eq. ϖ -comp. ϕ -comp. z-comp. Induction eq. p tot = p gas +p rad +p mag Cylindrical coordinates Magnetic flux advection rate

20. proportional to total pressure (gas+radiation+magnetic ) ∵ Following the results of 3DMHD(Machida et al. 2006) When the disk shrink due to the cooling instability, t cool ≪ t escape B →conserving the azimuthal component of magnetic fields →The gas pressure decreases, while the magnetic pressure increases Then, the ϖ φ-component of the Maxwell stress is proportional to the total pressure Note: In the conventional theory, this term is proportional to ( gas+radiation ) pressure Decrease in T→Decrease in p gas, p rad →Decrease in the Maxwell stress Maxwell Stress BH Key point If we rewrite this relation in term of the kinematic viscosity

21. Note: If we fix Decrease in T and p gas +p rad ➡ Decrease in p mag Inconsistent with the results of 3DMHD At least, when the disk shrinks in the vertical direction due to the cooling instability, the magnetic pressure decreases. Magnetic Flux Advection Rate Following the results of the 3DMHD (Machida+ ’06) Dynamo termMagnetic diffusion term If we ignore the dynamo term and the magnetic diffusion term, Φ is constant. However, Φ is not always conserved in the radial direction due to the presence of the dynamo term and the magnetic diffusion term. ( ) Note: ς~1 in the 3DMHD We parametrize the radial dependence Φ introducing a parameter ς...

22. Heating rate If the magnetic pressure is high, the heating rate can also be large even when the gas pressure and the radiation pressure are low. Cooling rate In the opt. thick limit: Black body In the opt. thin limit: Brems. Advection term Following the result of 3DMHD(Machida+ ’04), entropy gradient ξ=1 ξ> 0: heat advection act as cooling at certain radius. ξ< 0: heat advection act as heating at certain radisu. Energy Eq. Key point ( e.g., Hubeny 1990; Narayan & Yi 1995; Abramowicz et al. 1996)

23. Result: New Thermal Equilibrium Solution Connecting an Opt. Thin Region and an Opt. Thick Region Hard X-ray (Bright/Hard) Opt. thin low-β disk ソフト X 線 (High/Soft?) Opt. thick low-β disk hotter than Std. disk (T 〜 10 7-8 K) BH cooler than RIAF (T 〜 10 7-11 K) Surface density Temperature Thermal Equilibrium Curves@5r s Thin Opacith Thick Adv. Heat Hard X-ray (Low/Hard) RIAF hot (T e 〜 10 9 K) p gas Soft X-ray (Slim Disk) Adv. Heat Slim Disk moderately hot(T 〜 10 7-8 K) p rad Soft X-ray (High/Soft) Heat Rad. Std. Disk cool(T 〜 10 7 K) p gas Mass Accretion Rate Heat Rad. p mag BH Heat Rad. p mag RIAF Std. Slim Low-β ζ= 0(dotted) 0.3(dashed) 0.6(thick solid) Conventional(thin solid)

24. ‣ Conventional model: ➡ No Q + balances Q rad ‣ This model: ➡ Q + balances Q rad when the magnetic pressure is high. Why Can We Obtain the Low-β Solutions? Energy eq. @high density, low temperature 0 ~ 0 ~ Surface density Temperature Thermal Equilibrium Curves@5r s Thin Opacith Thick Mass Accretion Rate BH Heat Rad. p mag RIAF Std. Slim Low-β ζ= 0(dotted) 0.3(dashed) 0.6(thick solid) Conventional(thin solid)

25. The Opt. Thin Low-β Disk: Bright/Hard State & Bright/Slow Transition =L 5-12keV /L 3-5keV Luminosity Hardness-Luminosity Diagram RIAF Std. Slim SLE Low-β 〜 0.1L Edd Low/Hard Bright /Hard High /Soft Slim VH/SPL GX 339-4 〜 0.1L Edd 50 100 200 [ keV ] Low/Hard XTE J1550-564 Jet line Bright/Slow Hardness Ratio Gierlinski & Newton (‘06) 20 10 5 2 1 0.5 [10 37 erg s -1 ] E cut vs. L Large ς: Bright/Slow transition ‣ RIAF→Opt. thin low-β→Opt. thick disk ‣ T anti-correlates with M in opt. thin low-β ➡ explain Bright/Hard state Small ς ( ≒ conventional model ): Dark/Fast ‣ RIAF→Opt. thick low-β If the magnetic flux escape with the jet around the jet line, the disk undergoes a transition to equilibrium state withsmaller ς. Bright /Hard Electron Temperature Thermal Equilibrium Curves@5r s Mass Accretion Rate Luminosity ζ= 0(dotted) 0.3(dashed) 0.6(thick solid) Conventional(thin solid) Miyakawa+ (‘08) Temperature

26. Method: Radial Structure of the Disks 5rs5rs 10r s 100r s 5rs5rs 10r s 100r s solutions for fixed M and various ϖ Local thermal equilibrium curve: solutions for fixed ϖ and various M Radial dependence When 3 solutions are found for the same M: Since we focus on the Hard-to-Soft transition, ➡ we choose the RIAF solution. Surface density Mass Accretion Rate Surface density Radius..

27. Φ increase inward (ζ=0.6) RIAF Low-β RIAF Low-β Result: Radial Structure of the Disks Φ remain constant (ζ=0) RIAF Low-β Low M: The disk is in the RIAF at every radius. High M: The disk undergoes a transition from RIAF to Low-β from the outer radii. [Φ increase inward( ζ=0.6 )] Opt. thin low-β [Φ remain const.(ζ=0)] Opt. thick low-β (T eff ∝ ϖ -3/4 ) Higher M: The disk undergoes a transition to Slim from the inner radii. Slim Temperature Optical depth Radius.....

28. Bright/Slow transition Dark/Fast transition Mass Accretion Rate

29. The Opt. Thick Low-β Disk: Thermal Disk Radiation mechanism: Black body radiation Radial distribution of the effective temperature: T eff ∝ϖ -3/4 Same as that for the Standard disk! X-ray spectrum in Low/Hard state of Cyg X-1 (Makishima et al. (2008) ? RIAF Std. Slim SLE Low-β Limit cycle observed in GRS 1915+105: Slim ⇔ Opt. thick low-β? (Smaller variation in luminosity compared to that expected from Slim ⇔ Std.) Surface density Thermal Equilibrium Curves@5r s Mass Accretion Rate ζ= 0(dotted) 0.3(dashed) 0.6(thick solid) Conventional(thin solid)

30. Summary We construct 1D steady models incorporating magnetic fields on the basis of the results of 3D MD simulations. ‣ We assume that the Maxwell stress (therefore the heating rate) is proportional the total pressure. ‣ We prescribe the magnetic flux advection rate (instead of β) to determine the azimuthal magnetic flux. RIAF Std. Slim SLE Low-β Opt. thin low-β disks ✓ exist at high mass accretion rate. Temperature anti-correlates with mass accretion rate. ➡ explain the Bright/Slow transition and the Bright/Hard state ‣ Opt. thick low-β disks ✓ The radial distribution of the effective temperature is same as that for the standard disk. ➡ origin of the DBB component? ➡ Limit-cycle between Slim disk ⇔ Opt. thick disk? Thin Opacith Thick