1. Magnetically Supported Black Hole Accretion Disk and Its Application to State Transition of Black Hole Candidate Hiroshi Oda (CfA/Chiba Univ.) M. Machida (Kyushu Univ.), K. E. Nakamura (Kyushu Sangyo Univ.), R. Matsumoto (Chiba Univ.) and R. Narayan (CfA) Group meeting at ITC lounge, 9th June 2010

2. Table of Contents Background information Basic picture and general aspects of BH accretion disks X-ray spectral states and state transitions of galactic BH candidates Introduction Two types of Hard-to-Soft transitions Bright/Slow transition and Dark/Fast transition Bright/Hard state and Bright/Slow transition ADAF/RIAF cannot explain these Resent 3D MHD simulations Quasi-steady state of magnetic pressure dominated disks Purpose Can the magnetic pressure dominated disk explain the Bright/Hard state? Model Results Local thermal equilibria Global transonic solutions Discussion Summary

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) Suzaku Turbulent magnetic fields Dissipation of turbulent magnetic field energy

4. X-ray Spectral State Transitions of Galactic BHBs: Hard-to-Soft Transition Intensity Jet Lorentz Factor Hardness Hard Soft Schematic Picture of Hardness-Intensity Diagram Fender+ ‘04 Low/Hard State: Energy [ keV ] 1 10 100 FLux νF ν [ keV/cm 2 s ] Cutoff Power-Law Soft Excess High/Soft State: Energy [ keV ] 1 10 100 Flux νF ν [ keV/cm 2 s ] DBB Hard tail =L hard /L soft Soft X-ray (High/Soft) Std. Disk Opt. Thick Cool (T eff 〜 10 7 K) Hard X-ray (Low/Hard) ADAF/RIAF Opt. Thin Hot (T e ≥10 9.5 K) L Max 〜 0.4α 2 L Edd

5. Soft Hard RXTE: GX339-4 Belloni+ ‘06 2004/2005 2002/2003 Bright Dark Two Types of Hard-to-Soft Transitions =L 9.4-18.5keV /L 2.5-6.1keV

6. Bright/Slow Transition occurs at L 1.3-12keV ~ 0.3 L Edd, takes ~ 30 days. Dark/Fast Transition occurs at L 1.3-12keV ≲ 0.1 L Edd, takes ≲ 15 days. Gierlinski & Newton ‘06 =L 5-12keV /L 3-5keV 2002/2003 2004/2005 How about the X-ray spectrum? RXTE

7. Miyakawa+ ‘08 Low/Hard Bright/Hard =L 10-20keV /L 3.5-5.5keV VH/SPL =L 8.6-18keV /L 5-8.6keV Remillard+ `06 ~ 200 keV ~ 50 - 100 keV ~ 1.4 - 1.7 RXTE: GX339-4 ~0.1 L Edd L 2-200keV Bright/Hard state and Very High/Steep Power-Law state in the Bright/Slow transition [ keV ] 1 10 100 Flux νF ν [ keV/cm 2 s -1 ] High/ Soft Low/Hard VH/SPL Bright/Hard

8. Quick digression: Adv. of MAXI Object: XTE J1752- 223 Example of the Bright/Slow transition http://maxi.riken.jp L/H B/H VH/SPL H/S Quiescent

9. Problem Bright/Hard state Power-Law component is dominant → Optically thin E cut ~ 50 - 100 keV → T e is relatively low. L ~ 0.1 - 0.3 L Edd ADAF/RIAF model Optically thin T e ≳ 10 9.5 K ~ 200 keV Solutions do not exist above L = 0.4 α 2 L Edd ( viscous parameter α = 0.01 - 0.1) The ADAF/RIAF model cannot explain the Bright/Hard state. We need an optically thin, luminous, cool accretion disk model to explain the Bright/Hard state.

10. Optically Thin, Cool, Low-β Disk Hot (T~10 11 K) ADAF/RIAF Q + ~Q adv β = p gas /p mag 〜 10 β 〜 0.1 Cool (T~10 8 K) low-β disk Q + ~Q - rad (B φ ≫ B ϖ,B z ) Global 3D MHD (Machida+’06) Transition from ADAF/RIAF to low-β disk Turbulent B When M > M c, ADAF,.. Surface density Temperature Local Thermal Equilibria (Oda+’07, ’09) Thin Opt. Thick Mass Accretion Rate RIAF Std. Slim Low-β β>100 β~0.1-0.01 β>10 Optically thin, low-β disk: Cooler than the ADAF/RIAF Exist above M c,ADAF Thermally stable. BH

11. Before transition After transition log ρ log T <Bφ><Bφ> T ~ 10 11 K T ~ 10 8 K / r s β ~ 5 β ~ 0.1 BH BH low M high M.. Q + ∝ P gas Q + ~ Q adv (» Q rad ) Q + ∝ P mag Q + ~ Q rad (» Q adv ) T ϖ φ ∝ P gas T ϖ φ ∝ P mag Hot (T~10 11 K) ADAF/RIAF Cool (T~10 8 K) low-β disk

12. Purpose The low-β disk seems to explain the Bright/Hard state, but, In these works, they assumed T i = T e and Q rad = Q brems for simplicity. T i > T e is expected in a high temperature region (e.g., T i ~ 10 11.5 K, T e ~ 10 9.5 K in the ADAF/RIAF). Synchrotron and Inverse-Compton cooling become efficient rather than Bremsstrahlung cooling. Therefore, the radiative property is incorrect. We cannot compare these result with the observation quantitatively. We extend the steady model of 1D optically thin, single- temperature black hole accretion flow Two-temperature black hole accretion flow Consider the bremsstrahlung, synchrotron and inverse-Compton cooling apply these results to the Bright/Hard state Can the low-β disk explain the high luminosity and the low electron temperature?

13. Main Differences from the Conventional Model ‣ α-prescription of the stress In global MHD, the Maxwell’s stress and heating via the dissipation of the turbulent magnetic fields are still large when the magnetic pressure is high even though the gas pressure becomes low. Note: For turbulent viscosity, ν ~ v turb × l turb As a result, the heating rate ∝ W gas +W mag BHBH (then, the kinematic viscosity ) (then, ) [ Conventional model ] [ Our model ] W tot ~ W gas W tot ~ W mag Hot (T~10 11 K) ADAF/RIAF Cool (T~10 8 K) low-β disk

14. [ Conventional model ] [ Our model ] Main Differences from the Conventional Model ‣ How to determine the magnetic pressure Fixed β ( Therefore, if W gas decreases, then W mag decreases ) Introducing a parameter: the magnetic flux advection rate In global MHD, β drastically changes during the transition from ADAF/RIAF state to low- β state ( β ~ 10 → 0.1 ) while the magnetic flux advection rate is almost conserved. For given, B φ ( or β ) is calculated. If W gas (and T ) becomes high, β becomes high. If W gas (and T ) becomes low, β becomes low. Set the radial distribution of based on the results of 3D MHD is conserved.

15. Basic eqs. of vertically integrated 1D two-temperature BH accretion flows Continuity Eq. of motion Energy eqs. ϖ -comp. ϕ -comp. z-comp. (hydrostatic) Cylindrical coordinates Electrons Ions Heat advection Heating Radiative cooling Energy transfer via Coulomb collisions Global transonic solution: Integrate the basic eqs. from the outer boundary. Local thermal equilibria: Approximate the derivative terms, solve the eqs. algebraically.

16. We obtained three types of solutions, ADAF/RIAF, SLE, and low-β solutions. The low-β solutions exist above the maximum M of the ADAF/RIAF. As expected, T i >T e, and inverse-Compton cooling is dominant. The T e in the low-β solutions is lower (T e ~ 10 8 - 10 9.5 K) than that in the ADAF/RIAF (T e ≥10 9.5 K). Surface density Temperature Thermal Equilibrium Curves@5r s Mass Accretion Rate. Results: Local Thermal Equilibia. solid: high Φ dashed:mid Φ dotted: low Φ... Oda+ ‘10

17. High Φ: The ADAF/RIAF (T e ≥10 9.5 K) undergoes transition to the low-β disk (T e ~10 8 -10 9.5 K) when M exceeds the maximum M of ADAF/RIAF Low Φ: The ADAF/RIAF undergoes transition to an optically thick disk. (No optically thin solutions above the maximum M of ADAF/RIAF) The Low-β Disk Can Explain the High Luminosity and the Low T e ( or E cut ) in the Bright/Hard State Thermal Equilibrium Curves@5r s.. high Φ. Low/Hard Bright /Hard Miyakawa+ ‘08 Oda+ ‘10 To Opt. Thick Disk? Temperature Mass Accretion Rate. low Φ...

18. m = 10 -4 m = 9.5 × 10 -2.. Results: Global transonic solutions

19. Discussion: Why are there 2 types of Hard-to-Soft transition? 3D MHD simulations of galactic disks (Nishikori+ ’06) Polarity of magnetic fields inside the disk changes alternately in the timescale of the Parker instability. The net magnetic flux advection rate can be change in the same timescale. BH

20. Discussion: What is the VH/SPL state? Hot corona Std. disk Soft X-ray Hard X-ray Opt. thick low-β disk Soft X-ray Hard X-ray Jet Magnetic fluxes can escape form the disk. The VH/SPL state The DBB and SPL components are comparable → the system can consist of an optically thick cool disk and an optically thin hot corona. If the magnetic fluxes can escape from the optically thin low-β disk with a jet, If the magnetic fluxes cannot escape from the optically thin low-β disk, If the jet and corona disappear, the system will undergo transition to the High/Soft state We need a Radiation-MHD code to simulate such transition.

21. Quick digression: Test runs of 1D Rad.-MHD code Shock Tube ProblemDiffusion of E rad

22. Discussion: Are episodic jets associated with the Bright/Slow transition? The ADAF/RIAF does not seem to be able to produce a relativistic jet. The low-β disk may produce a relativistic jet because the magnetic energy stored in the disk is significant. If a relativistic jet is launched from the low-β disk, the jet should be observed after the Bright/Hard state and before the VH/SPL state during the Bright/Slow transition. No jets might be observed during the Dark/Fast transition. L/H B/H VH/SPL H/S L/H H/S Jet? Bright/SlowDark/Fast No Jet?

23. Summary We obtained the steady solution of the optically thin low-β disk. This solution exists at high M. The electron temperature is low ( T e ~ 10 8.5 -10 9.5 K ). The low-β disk can explain the Bright/Hard state. When the magnetic flux advection rate is high: The optically thin, low-β solution exist above the maximum M of ADAF/RIAF The Bright/Slow transition will occur. When the magnetic flux advection rate is low: No optically thin solutions exist above the maximum M of ADAF/RIAF. The Dark/Fast transition will occur. If magnetic fluxes can escape from the optically thin, low-β disk with a jet, the system can consist of an optically thick cool disk and an optically thin hot corona, then, may undergo transition to the VH/SPL state.