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

Rapid Time Variability of Cyg X-1 X-ray Flux (Negoro 1995) ＰＳＤ Power Spectral Density (PSD) of Time Variation in Cyg X-1 f -0.9 f Hz100Hz

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

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

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

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*

Basic Equations of Resistive MHD

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

Formation of an Accretion Disk Initial State t=26350r g /c

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

Comparison of PSD Obtained by Observation and Numerical Simulation ＰＳＤ Power Spectral Density (PSD) of Time Variation in Cyg X-1 f -0.9 f Hz100Hz frequency PSD of accretion rate obtained by Numerical Simulation

Intermittent Release of Magnetic Energy Time variations of Joule heating rate

Global MHD Simulations of State Transitions SurfaceDensity AccretionRate Slim Optically thick Optically thin ADAF Advection Standard disk Radiation M = 10M sun, r =5, α= 0.1 Abramowicz et al Hot disk Cold disk

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 Q rad = Q b  T Cooling is not included in rarefied corona where  <  crit 21/2

Transition to Cool Disk densitytemperatureToroidal field

Formation of Low-beta Disk Before the transitionAfter the transition

Time Evolution

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

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

QPOs Appear When Hot Disk is Cooled Down SurfaceDensity AccretionRate Slim Optically thick Optically thin ADAF Advection Standard disk Radiation M = 10M sun, r =5, α= 0.1 Abramowicz et al QPO Hot disk Cold disk

Time Evolution of Cooler Disk Density distributionToroidal magnetic field

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

Accumulation and Release of Magnetic Energy Magnetic Energy Joule Heating Rate

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

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

Mass Outflows from Accretion Disks temperatureIsosurface of veritical velocity

Mass Outflow Rate also Shows QPOs Log(Temperature)Density

Application to SgrA* (Machida et al in prep) τ=1 surface (3Dview) 43GHz690GHz

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

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