1. Steady Models of Black Hole Accretion Disks including Azimuthal Magnetic Fields Hiroshi Oda (Chiba Univ.) Mami Machida (NAOJ) Kenji Nakamura (Matsue) Ryoji Matsumoto (Chiba Univ.) YITP Workshop on “Quasi-Periodic Oscillations and Time Variabilities of Accretion Flows” @ Kyoto, Nov, 20-22, 2007 (Ref. Oda et al. 2007, PASJ, 59, 457)

2. Introduction  X-ray observational data shows four spectral states   High/Soft State ·Slim Disk State   Low/Hard State   Very High (Intermediate) State   HFQPOs & LFQPOs are prominent  Bright/Hard state  Bright/Hard state (e.g., Miyakawa et al. 2007)   observed during the rising phase (up to ~0.2L Edd )    ~1.77, E cut ~ 40-200keV (  L -0.74 )   This means that T e decreases as L increases   LFQPOs are prominent?   In my presentation, I focus on the Bright/Hard state   Hard-to-Soft transition ( e.g., Gierliński & Newton 2006)   Bright/slow transition   Slow   Occurring at 0.3 L Edd or more.   Dark/fast transition   Fast   Occurring at ≤ 0.1 L Edd Energy [ keV ] Slim VH(IM) L/H H/S B/H Gierliński & Newton 2006 0.1L Edd 0.3L Edd Miyakawa et al 2007 X-ray spectrum GX339-4

3. Theoretical Models of Accretion Disks  These conventional models do not include the magnetic fields  Hard-to-Soft transition occurs at the critical mass accretion rate for the existence of the ADAF, and this corresponds to ~0.4  2 (Esin et al. 1997)  Hard-to-Soft transition occurs at the critical mass accretion rate for the existence of the ADAF, and this corresponds to ~0.4  2 L Edd (Esin et al. 1997)  This luminosity can not explain Bright/slow transition unless  ~1 Surface Density Mass Accretion Rate Thermal Equilibrium Curves L crit /L Edd ~0.4  2 Advection Hard X-Ray Soft X-Ray ADAF Slim Standard SLE

4. Numerical Simulations of Accretion Disks  Local 3D MHD (e.g., Hawley et al. 1995)   MRI excites and maintains magnetic turbulence   The Maxwell stress transports the angular momentum  Global 3D MHD including the radiative cooling (e.g., Machida et al. 2006) (e.g., Machida et al. 2006)   A radiatively inefficient Torus →An optically thin, hot disk is formed →The cooling instability takes place →The disk shrinks in the vertical direction →The magnetic pressure becomes dominant →The 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;

5. Aim & Assumption for One Temperature Model Our aim  To 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.

6. Basic Equations Heating, cooling, and Advection term,, Prescription of the magnetic flux advection rate Parameters  We fixed,,  Now, free parameters are and mass conservation angular momentum conservation energy eq. ( ) entropy gradient parameter

7. 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 “low-  branch”.  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 ~ 0.2 ADAF Slim Standard SLE ADAF Slim Standard SLE Low -  red: extremely small thin: small thick: large

8. ADAF Slim Standard SLE Low -  Discussion : Why does the low-  branch appears? Q + ~Q adv W tot ~W gas Q + ~Q - rad W tot ~W gas Q + ~Q - rad W tot ~W mag Q + ~Q - rad W tot ~W mag Q + ~Q adv W tot ~W rad 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.

9. red: extremely small thin: small thick: large Discussion : Hard-to-Soft Transition Gierliński & Newton 2006 ADAF Low-  Slim or Standard Slim or Standard BS 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 E cut ) Hard ADAF Opt. thin Low-  Slim Soft Opt. thick Low-  Slim Note: For smaller  B, the critical mass accretion rate for the existence of the ADAF is lower.

10. 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 E cut ) ADAF Slim Standard SLE Low -  Discussion: Bright/Hard State The Low-  branch seems to be a good candidate for the Bright/Hard state Miyakawa et al 2007 B/H state of GX339-4 (anti-correlation L-E cut, kT e ) Thermal equilibrium curve on M-T plane

11. The Slim disk evolves to the Low-  disk  If the magnetic flux escapes from the disk due to the buoyancy, Parker instability, jet, etc… The Low-  disk could undergo transition to the standard disk. ADAF Slim Standard SLE Low -  Discussion: Slim → Low-  →Standard Transition Advection Soft X-Ray The limit cycle of GRS 1915+105 Paul et al. 1998 A typical profile of outburstdip Slim Low-  Standard

12. Summary We obtained the thermal equilibrium curves including azimuthal magnetic fields based on results of numerical simulations. We obtained the thermal equilibrium curves including azimuthal magnetic fields based on results of numerical simulations. The low-  branch appears in the optically thin and thick region The low-  branch appears in the optically thin and thick region The low-  disk is radiatively cooled and magnetically supported The low-  disk is radiatively cooled and magnetically supported This thermal equilibrium state can explain both the Bright/Hard state and the Bright/slow transition, This thermal equilibrium state can explain both the Bright/Hard state and the Bright/slow transition, and, suggest that the existence of the optically thick, magnetically supported disk during the slim → standard transition. and, suggest that the existence of the optically thick, magnetically supported disk during the slim → standard transition.

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