Global MHD Simulations of Sawtooth-like Oscillations in Black Hole Accretion Disks

1. Global MHD Simulations of Sawtooth-like Oscillations in Black Hole Accretion Disks Ryoji Matsumoto (Chiba Univ.) Mami Machida (NAOJ)

2. X-ray Flares in Black Hole Candidates -0.9 ＰＳＤ f -1.5 f X-ray shots 1Hz 100Hz Power Density Spectrum of Time Variation in Cyg X-1 X-ray Flux (Negoro 1995)

3. Yohkoh Observations Confirmed Magnetic Reconnection in Solar Flares SOHO衛星観測 Shibata and Yokoyama 1995

4. X-ray Flares in Protostars Hayashi, Shibata and Matsumoto 1996 Chandra observation

5. Numerical Simulation of the Magnetic Tower Jet Kato, Hayashi, Matsumoto (2004)

6. Magnetorotational Instability in Accretion Disks Angular momentum MRI in accretion disks （Balbus and Hawley 1991)

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-rs) Initially constant angular momentum Magnetic Field : purely azimuthal Pgas/Pmag = β＝100 at 50r_s Anomalous Resistivity η= (1/Rm) max [(J/ρ) /vc– 1, 0.0] 250*64*192mesh250*32*384mesh 2

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

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

12. 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

13. Advection ADAF Radiation Standard disk Slim HFQPOs Appear When a Hot Disk is Cooled Down (Mami’s talk) Accretion Rate M = 10Msun, r =5, α= 0.1 Hot disk QPO Cold disk Surface Density Optically thin Optically thick Abramowicz et al. 1995

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

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

16. 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

17. Similar Behaviors have been Observed in Resistive 3D Local MHD Simulations Sano and Inutsuka 2001

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

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

20. Dependence on the Azimuthal Resolution Accretion rate Joule Heating 64mesh 32mesh

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

22. Another Example: Double Periodic Oscillation Density Distribution 250*64*384mesh

23. Time Evolution of Mass Accretion Rate and Joule Heating Rate Joule heating Mass accretion rate

24. Time Evolution of Mass Accretion Rate and Joule Heating Rate Joule heating Mass accretion rate

25. PDS of Mass Accretion Rate Frequency (Hz)

26. Summary • Global 3D resistive MHD simulations of cool disks indicate that cool disks show sawtooth-like oscillations • During the sawtooth oscillation, the disk repeats the amplification of magnetic energy and subsequent release of the energy by magnetic reconnection • The sawtooth oscillation appears when m=1 one-armed density distribution develops in the inner torus • The frequency of the sawtooth oscillation is typically 10Hz in stellar mass black holes. • When sawtooth-like oscillation takes place, high frequency QPOs appear • We need simulations including cooling.

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