Global MHD Simulations of Sawtooth like Oscillations in
Global MHD Simulations of Sawtooth -like Oscillations in Black Hole Accretion Disks Ryoji Matsumoto (Chiba Univ. ) Mami Machida (NAOJ)
X-ray Flares in Black Hole Candidates PSD f -0. 9 f X-ray shots 1 Hz -1. 5 100 Hz Power Density Spectrum of X-ray Flux (Negoro 1995) Time Variation in Cyg X-1
Yohkoh Observations Confirmed Magnetic Reconnection in Solar Flares SOHO衛星観測 Shibata and Yokoyama 1995
X-ray Flares in Protostars Chandra observation Hayashi, Shibata and Matsumoto 1996
Numerical Simulation of the Magnetic Tower Jet Kato, Hayashi, Matsumoto (2004)
Magnetorotational Instability in Accretion Disks Angular momentum MRI in accretion disks (Balbus and Hawley 1991)
Basic Equations of Resistive MHD
Global Three-dimensional Resistive MHD Simulations of Black Hole Accretion Flows (Machida and Matsumoto 2003 Ap. J ) Gravitational potential : φ= - GM/(r-rs) Initially constant angular momentum Magnetic Field : purely azimuthal Pgas/Pmag = β= 100 at 50 r_s Anomalous Resistivity η= (1/Rm) max [(J/ρ) /vc– 1, 0. 0] 2 250*64*192 mesh 250*32*384 mesh
Formation of an Accretion Disk Initial State t=26350 rg/c
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 T=30630 Magnetic Field Lines time
Black Hole Candidates Sometimes Show Quasi Periodic Oscillations Power Density LFQPO HFQPO 0. 01 0. 1 1 10 GX 339 -4 100 Hz 0. 01 0. 1 1 10 XTE J 1550 -564 Mc. Clintock and Remillard 2004 100 Hz
HFQPOs Appear When a Hot Disk is Cooled Down (Mami’s talk) Accretion Rate M = 10 Msun, r =5, α= 0. 1 Hot disk Advection Slim QPO Radiation ADAF Standard disk Cold disk Surface Density Optically thin Abramowicz et al. 1995 Optically thick
Time Evolution of Cooler Disk Density distribution Toroidal magnetic field
Accumulation and Release of Magnetic Energy Joule Heating Rate
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 Approach to a quasi-steady state Energy release Sawtooth oscillation
Similar Behaviors have been Observed in Resistive 3 D Local MHD Simulations Sano and Inutsuka 2001
Growth and Disruption of m=1 Non. Axisymmetric Mode Isosurface of Density Equatorial Density
Sawtooth-like Oscillations Accompany High Frequency QPOs Sawtooth HFQPO Radial Dependence of PSD 1 Hz 100 Hz PSD of Luminosity
Dependence on the Azimuthal Resolution Accretion rate Joule Heating 32 mesh 64 mesh
Mass Outflow Rate also Shows QPOs Log(Temperature) Density
Another Example: Double Periodic Oscillation Density Distribution 250*64*384 mesh
Time Evolution of Mass Accretion Rate and Joule Heating Rate Joule heating Mass accretion rate
Time Evolution of Mass Accretion Rate and Joule Heating Rate Joule heating Mass accretion rate
PDS of Mass Accretion Rate Frequency (Hz)
Summary • Global 3 D 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 10 Hz in stellar mass black holes. • When sawtooth-like oscillation takes place, high frequency QPOs appear • We need simulations including cooling.
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