Steady Models of Black Hole Accretion Disks including Azimuthal Magnetic Fields

1. Steady Models of Black Hole Accretion Disks including Azimuthal Magnetic Fields (Ref. Oda et al. 2007, PASJ, 59, 457) 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

2. X-ray spectrum Introduction Slim H/S VH(IM) L/H • 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 (e.g., Miyakawa et al. 2007) • observed during the rising phase (up to ~0.2LEdd) • G ~1.77, Ecut~ 40-200keV(L-0.74) • This means that Te 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 LEddor more. • Dark/fast transition • Fast • Occurring at ≤ 0.1 LEdd B/H Energy [ keV ] Miyakawa et al 2007 GX339-4 Gierliński & Newton 2006 0.3LEdd 0.1LEdd

3. Theoretical Models of Accretion Disks Thermal Equilibrium Curves • 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 ~0.4a2LEdd (Esin et al. 1997) • This luminosity can not explain Bright/slow transition unless a ~1 Soft X-Ray Hard X-Ray Slim Advection Advection Mass Accretion Rate Lcrit/LEdd~0.4a2 Soft X-Ray ADAF Standard SLE Surface Density

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

7. Results : Thermal Equilibrium Curves ADAF red: extremely small thin: small thick: large SLE Slim • 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-b branch”. • The low-b 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-b branches extends to above ~0.2 Low -b Slim Low -b Standard SLE ADAF Standard

8. Discussion : Why does the low-b branch appears? • 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. ADAF Q+~Qadv Wtot~Wrad SLE Q+~Qadv Wtot~Wgas Q+~Q-rad Wtot~Wmag Q+~Q-rad Wtot~Wmag Low -b Slim Standard Q+~Q-rad Wtot~Wgas

9. Hard (Low Ecut) Slim Soft Hard Slim Opt. thin Low-b Opt. thick Low-b ADAF Discussion : Hard-to-Soft Transition red: extremely small thin: small thick: large Slim or Standard Gierliński & Newton 2006 Low-b Low-b Slim or Standard BS DF ADAF ADAF Note: In the outer region, the critical mass accretion rate for the existence of the ADAF is lower, and the temperature is cooler. Note: For smaller aB, the critical mass accretion rate for the existence of the ADAF is lower.

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

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

12. Summary • We obtained the thermal equilibrium curves including azimuthal magnetic fields based on results of numerical simulations. • The low-b branch appears in the optically thin and thick region • The low-b disk is radiatively cooled and magnetically supported • 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.

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