Sawtooth-like Oscillations of Black Hole Accretion Disks Ryoji Matsumoto (Chiba Univ.) Mami Machida (NAOJ)

Black Hole Candidates Sometimes Show Quasi Periodic Oscillations Power Density Hz GX Hz XTE J McClintock and Remillard 2004 LFQPO HFQPO

Let’s Show How QPOs are Excited by Global 3D MHD Simulations of Black Hole Accretion Flows Gravitational potential ： φ= - GM/(r-r g ) Magnetic Field : purely azimuthal  Pgas/Pmag =100 at r = r 0 Anomalous Resistivity  = (1/Rm) max [(J  /v c – 1, 0.0] 2 250*32*384mesh 250*64*384mesh r g =3.0 x 10 6 (M/10M sun ) cm t 0 =r g /c=10 -4 (M/10M sun ) sec Unit

Basic Equations of Resistive MHD

Numerical Results for Radiatively Inefficient Hot Disk Power Spectral Density of time variation of accretion rate

QPOs Appear When a Hot Disk is Cooled Down SurfaceDensity AccretionRate Slim Optically thick Optically thin ADAF Advection Standard disk Radiation Abramowicz et al QPO Hot disk Cold disk

Time Evolution of Cooler Disk Density distributionAzimuthal magnetic field

Magnetic Reconnection in Accretion Disks Dense blob accretes Current Sheet is Formed Magnetic Reconnection Takes Place Machida and Matsumoto 2003

Accumulation and Release of Magnetic Energy 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 Growth of instability Energy release Sawtooth oscillationApproach to a quasi-steady state When dissipation is small

Growth and Disruption of m=1 Non-Axisymmetric Mode Isosurface of DensityEquatorial Density

Sawtooth-like Oscillations Excite High Frequency QPOs SawtoothHFQPO 1Hz10Hz100Hz Radial Dependence of PSD PSD of Luminosity

Another Example: Double Periodic Oscillation Density Distribution

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

PSD of Mass Accretion Rate Frequency (Hz)

Mass Outflow Rate also Shows QPOs (Machida’s poster) Log(Temperature)Density

Summary Global 3D resistive MHD simulations of cool disks indicate that cool disks show sawtooth-like oscillations During the sawtooth oscillation, amplification of magnetic energy and subsequent release of the magnetic energy repeats The sawtooth oscillation appears when one-armed density distribution develops in the inner torus The frequency of the sawtooth oscillation is several times of the rotation period of the torus, and typically 5-10Hz in stellar mass black holes. This frequency agrees with that of low frequency QPOs in galactic black hole candidates The sawtooth-like oscillation excites high frequency QPOs

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