Global Simulations of Time Variabilities in Magnetized Accretion Disks

1. Global Simulations of Time Variabilities in Magnetized Accretion Disks Ryoji Matsumoto (Chiba Univ.) Mami Machida (NAOJ)

2. Rapid Time Variability of Cyg X-1 -0.9 ＰＳＤ f -1.5 f 1Hz 100Hz Power Spectral Density (PSD) of Time Variation in Cyg X-1 X-ray Flux (Negoro 1995)

3. X-ray Spike and Ejection of Relativistically Moving Blobs in Microquasar GRS1915+105 Time variation in X-ray, IR, and Radio（Mirabel and Rodriguez 1998) Radio Map (Mirabel et al.1994)

4. Soft state Hard state State Transitions during Outbursts of Black Hole Candidates Remillard 2005 Luminosity 10 100 10 100 KeV KeV Optically thick cold disk Optically thin hot disk Color

5. Power Density 0.01 0.01 0.1 0.1 1 1 10 10 100 100 Hz Hz GX 339-4 XTE J1550-564 Black Hole Candidates Sometimes Show Quasi Periodic Oscillations LFQPO LFQPO HFQPO McClintock and Remillard 2004

6. Contents of this Talk • Global MHD Simulations of Hot Accretion Disks • Formation of Accretion Disks • 1/f like Time Variabilities • Global MHD Simulations of State Transitions • Global MHD Simulations Including Radiative Cooling • Global MHD Simulations of QPOs in Black Hole Candidates • Application to Sgr A*

7. Basic Equations of Resistive MHD

8. Global Three-dimensional Resistive MHD Simulations of Black Hole Accretion Flows (Machida and Matsumoto 2003 ApJ ) Gravitational potential 　：　 φ= - GM/(r-rg) Angular momentum　：　initially uniform Magnetic Field : purely azimuthal Pgas/Pmag = β＝　１００ at 50r_g Anomalous Resistivity η= (1/Rm) max [(J/ρ) /vc– 1, 0.0] 2 250*64*192mesh250*32*384

9. Formation of an Accretion Disk Initial State t=26350rg/c

10. Time Variabilities and Magnetic Energy Release in Accretion Disks (Machida and Matsumoto 2003) Joule Heating T=30590 Current density Magnetic Energy T=30610 Accretion Rate T=30630 Current Density and Magnetic Field Lines time

11. Comparison of PSD Obtained by Observation and Numerical Simulation -0.9 ＰＳＤ f -1.5 f 1Hz 100Hz frequency Power Spectral Density (PSD) of Time Variation in Cyg X-1 PSD of accretion rate obtained by Numerical Simulation

12. Intermittent Release of Magnetic Energy Time variations of Joule heating rate

13. Advection ADAF Radiation Standard disk Slim Global MHD Simulations of State Transitions Accretion Rate M = 10Msun, r =5, α= 0.1 Hot disk Cold disk Surface Density Optically thin Optically thick Abramowicz et al. 1995

14. 3D MHD Simulation Including Optically Thin Radiative Cooling (Machida et al. 2006) • Cooling term is switched on after the accretion flow becomes quasi-steady • We assume bremsstrahlung cooling Qrad = Qb r T • Cooling is not included in rarefied corona where r < r crit 2 1/2

15. Transition to Cool Disk density temperature Toroidal field

16. Formation of Low-beta Disk Before the transition After the transition

17. Time Evolution

18. Formation of Magnetically Supported Disk during State Transition Radiative Cooling Cool Down β< 1 β～10 Optically Thin Hot Disk Supported by Gas Pressure Optically Thin Cool Disk Supported by Magnetic Pressure

19. Comparison with Theory of Magnetically Supported Disks Surface density Oda et al. 2006 Machida et al. 2006

20. Advection ADAF Radiation Standard disk Slim QPOs Appear When Hot Disk is Cooled Down Accretion Rate M = 10Msun, r =5, α= 0.1 Hot disk QPO Cold disk Surface Density Optically thin Optically thick Abramowicz et al. 1995

21. Time Evolution of Cooler Disk Density distribution Toroidal magnetic field

22. Accumulation and Release of Magnetic Energy Magnetic Energy Joule Heating Rate

23. Sawtooth Oscillation in Nonlinear Systems • Sawtooth oscillation takes place when instability and dissipation coexists (e.g., Tokamak fusion reactors) When dissipation is large When dissipation is small Growth of instability Energy release Approach to a quasi-steady state Sawtooth oscillation

24. Growth and Disruption of m=1 Non-Axisymmetric Mode Isosurface of Density Equatorial Density

25. Accumulation and Release of Magnetic Energy Magnetic Energy Joule Heating Rate

26. Sawtooth-like Oscillations Accompany High Frequency QPOs Sawtooth HFQPO 1Hz 10Hz 100Hz Radial Dependence of PSD PSD of Luminosity

27. Why QPOs Appear in Low Temperature Disks ? Formation ot the Inner Torus is Essential for QPOs High temperature(HT) model Low temperature (LT) model

28. Mass Outflows from Accretion Disks temperature Isosurface of veritical velocity

29. Mass Outflow Rate also Shows QPOs Log(Temperature) Density

30. Application to SgrA*(Machida et al. 2006 in prep) 43GHz 690GHz τ=1 surface (3Dview)

31. Reversal of Mean Azimuthal Magnetic Fields r=10rs 43GHz 230GHz r=20rs 690GHz Time evolution of mean azimuthal magnetic field

32. Summary • Global 3D resistive MHD simulations of black hole accretion flows reproduced 1/f-like time variations, X-ray shots, and outflows • By carrying out global MHD simulations including radiative, cooling, we found that magnetically supported disk is created during the hard-to-soft transition. • Global 3D resistive MHD simulations of cool disks indicate that cool disks show sawtooth-like oscillations • The sawtooth oscillation appears when one-armed density distribution develops in the inner torus • When sawtooth-like oscillation takes place, high frequency QPOs appear • Polarity of magnetic fields changes in time scale of 10rotation period of the inner torus around a black hole