Magnetically Supported Black Hole Accretion Disk and Its Application to State Transition of Black Hole Candidate Hiroshi Oda (CfA/Chiba Univ.) M. Machida (Kyushu Univ.), K. E. Nakamura (Kyushu Sangyo Univ.), R. Matsumoto (Chiba Univ.) and R. Narayan (CfA)

Outline of my talk Background information on BH accretion disks Basic picture and general aspects of BH accretion disks X-ray spectral states and state transitions of galactic BH candidates Introduction Two types of Hard-to-Soft transitions: Bright/Slow transition and Dark/Fast transition ADAF/RIAF cannot explain Bright/Hard state observed in the Bright/Slow transition Resent 3D MHD simulations Quasi-steady state of optically thin, cool, magnetic pressure dominated disks Purpose Can the magnetic pressure dominated disk explain the Bright/Hard state? Our steady-state model of 1D black hole accretion flows Results Local thermal equilibrium solutions Global transonic solutions Discussion How about the VH/SPL state? Are episodic jets associated with the Bright/Slow transition? Summary

RXTE Basic Picture of Accretion Disks (around a stellar mass BH) Companion Star BH Mass Supply Angular momentum transport due to viscosity Heating due to viscosity Soft X-ray (~1-10 keV) Hard X-ray (~100keV) Suzaku Turbulent magnetic fields Dissipation of turbulent magnetic field energy

X-ray Spectral State Transitions of Galactic BHBs: Hard-to-Soft Transition Intensity Jet Lorentz Factor Hardness Hard Soft Schematic Picture of Hardness-Intensity Diagram Fender+ ‘04 Low/Hard State: Energy [ keV ] FLux νF ν [ keV/cm 2 s ] Cutoff Power-Law Soft Excess High/Soft State: Energy [ keV ] Flux νF ν [ keV/cm 2 s ] DBB Hard tail =L hard /L soft Soft X-ray (High/Soft) Std. Disk Opt. Thick Cool (T eff 〜 10 7 K) Hard X-ray (Low/Hard) ADAF/RIAF Opt. Thin Hot (T e ≥ K) L Max 〜 0.4α 2 L Edd

Soft Hard RXTE: GX339-4 Belloni+ ‘ / /2003 Bright Dark Two Types of Hard-to-Soft Transitions =L keV /L keV

Bright/Slow Transition occurs at L keV ~ 0.3 L Edd, takes ~ 30 days. Dark/Fast Transition occurs at L keV ≲ 0.1 L Edd, takes ≲ 15 days. Gierlinski & Newton ‘06 =L 5-12keV /L 3-5keV 2002/ /2005 How about the shape of the X- ray spectrum? RXTE

Miyakawa+ ‘08 Low/Hard Bright/Hard =L 10-20keV /L keV VH/SPL =L keV /L 5-8.6keV Remillard+ `06 ~ 200 keV ~ keV ~ RXTE: GX339-4 ~0.1 L Edd L 2-200keV Bright/Hard state and Very High/Steep Power-Law state in the Bright/Slow transition [ keV ] Flux νF ν [ keV/cm 2 s -1 ] Low/Hard VH/SPL Bright/Hard

Quick digression: Adv. of MAXI Object: XTE J Example of the Bright/Slow transition L/H B/H VH/SPL H/S Quiescent

Problem Bright/Hard state Power-Law component is dominant → Optically thin E cut ~ keV → T e is relatively low. L ~ L Edd ADAF/RIAF model Optically thin T e ≳ K ~ 200 keV Solutions do not exist above L = 0.4 α 2 L Edd ( viscous parameter α = ) The ADAF/RIAF model cannot explain the Bright/Hard state. We need an optically thin, luminous, cool accretion disk model to explain the Bright/Hard state.

Optically Thin, Cool, Low-β Disk Hot (T~10 11 K) ADAF/RIAF Q + ~Q adv β = p gas /p mag 〜 10 β 〜 0.1 Cool (T~10 8 K) low-β disk Q + ~Q - rad (B φ ≫ B ϖ,B z ) Global 3D MHD (Machida+’06) Transition from ADAF/RIAF to low-β disk Turbulent B When M > M c, ADAF,.. Surface density Temperature Local Thermal Equilibria (Oda+’07, ’09) Thin Opt. Thick Mass Accretion Rate RIAF Std. Slim Low-β β>100 β~ β>10 Optically thin, low-β disk: Cooler than the ADAF/RIAF Exist above M c,ADAF Thermally stable. BH

Before transition After transition log ρ log T <Bφ><Bφ> T ~ K T ~ 10 8 K / r s β ~ 5 β ~ 0.1 BH BH low M high M.. Q + ∝ P gas Q + ~ Q adv (» Q rad ) Q + ∝ P mag Q + ~ Q rad (» Q adv ) T ϖ φ ∝ P gas T ϖ φ ∝ P mag Hot (T~10 11 K) ADAF/RIAF Cool (T~10 8 K) low-β disk

Purpose The low-β disk seems to explain the Bright/Hard state, but, In these works, they assumed T i = T e and Q rad = Q brems for simplicity. T i > T e is expected in a high temperature region (e.g., T i ~ K, T e ~ K in the ADAF/RIAF). Synchrotron and Inverse-Compton cooling become efficient rather than Bremsstrahlung cooling. Therefore, the radiative property is incorrect. We cannot compare these results with the observation quantitatively. We extend the steady model of 1D optically thin, single- temperature black hole accretion flow Two-temperature black hole accretion flow Consider the bremsstrahlung, synchrotron and inverse-Compton cooling apply these results to the Bright/Hard state Can the low-β disk explain the high luminosity and the low electron temperature?

Basic eqs. of vertically integrated 1D two-temperature BH accretion flows Continuity Eq. of motion Energy eqs. ϖ -comp. ϕ -comp. z-comp. (hydrostatic) Cylindrical coordinates Electrons Ions Heat advection Heating Radiative cooling Energy transfer via Coulomb collisions Global transonic solution: Integrate the basic eqs. from the outer boundary. Local thermal equilibria: Approximate the derivative terms, solve the eqs. algebraically. Magnetic flux advection rate

Main Difference from the Conventional Model: 1 ‣ α-prescription of the stress In global MHD, the Maxwell’s stress and heating via the dissipation of the turbulent magnetic fields are still large when the gas pressure become low as long as the magnetic pressure is high. Note: For turbulent viscosity, ν ~ v turb × l turb As a result, the heating rate ∝ W gas +W mag BHBH (then, the kinematic viscosity ) (then, ) [ Conventional model ] [ Our model ] W tot ~ W gas W tot ~ W mag Hot (T~10 11 K) ADAF/RIAF Cool (T~10 8 K) low-β disk Turbulence v turb ~ c s v turb ~ v A

[ Conventional model ] [ Our model ] Main Difference from the Conventional Model: 2 ‣ How to determine the magnetic pressure Fixed β ( Therefore, if W gas decreases, then W mag decreases ) Introducing a parameter: the magnetic flux advection rate In global MHD, β drastically changes during the transition from ADAF/RIAF state to low- β state ( β ~ 10 → 0.1 ) while the magnetic flux advection rate is almost conserved. For given, B φ ( or β ) is calculated. If W gas (and T ) becomes high, β becomes high. If W gas (and T ) becomes low, β becomes low. Set the radial distribution of based on the results of 3D MHD is conserved.

We obtained three types of solutions, ADAF/RIAF, SLE, and low-β solutions. The low-β solutions exist above the maximum M of the ADAF/RIAF. As expected, T i >T e, and inverse-Compton cooling is dominant. The T e in the low-β solutions is lower (T e ~ K) than that in the ADAF/RIAF (T e ≥ K). Surface density Temperature Thermal Equilibrium s Mass Accretion Rate. Results: Local Thermal Equilibia. solid: high Φ dashed:mid Φ dotted: low Φ... Oda+ ‘10 M max, ADAF/RIAF.

High Φ: The ADAF/RIAF (T e ≥ K) undergoes transition to the low-β disk (T e ~ K) when M exceeds the maximum M of ADAF/RIAF Low Φ: The ADAF/RIAF undergoes transition to an optically thick disk. (No optically thin solutions above the maximum M of ADAF/RIAF) The Low-β Disk Can Explain the High Luminosity and the Low T e ( or E cut ) in the Bright/Hard State Thermal Equilibrium s.. high Φ. Low/Hard Bright /Hard Miyakawa+ ‘08 Oda+ ‘10 To Opt. Thick Disk? Temperature Mass Accretion Rate. low Φ...

m = m = Results: Global transonic solutions

Discussion: Why are there 2 types of Hard-to-Soft transition? 3D MHD simulations of galactic disks (Nishikori+ ’06) Polarity of magnetic fields inside the disk changes alternately in the timescale of the Parker instability. The net magnetic flux advection rate can be change in the same timescale. BH

Discussion: What is the VH/SPL state? Hot corona Std. disk Soft X-ray Hard X-ray Opt. thick low-β disk (e.g., Oda + ’09) Soft X-ray Hard X-ray Jet Magnetic fluxes can escape form the disk. The VH/SPL state The DBB and SPL components are comparable → the system can consist of an optically thick cool disk and an optically thin hot corona. If the magnetic fluxes can escape from the optically thin low-β disk with a jet, If the magnetic fluxes cannot escape from the optically thin low-β disk, If the jet and corona disappear, the system will undergo transition to the High/Soft state

Quick digression: Test runs of 1D Rad.-MHD code Shock Tube ProblemDiffusion of E rad

Discussion: Are episodic jets associated with the Bright/Slow transition? The ADAF/RIAF does not seem to be able to produce a relativistic jet. The low-β disk may produce a relativistic jet because the magnetic energy stored in the disk is significant. If a relativistic jet is launched from the low-β disk, the jet should be observed after the Bright/Hard state and before the VH/SPL state during the Bright/Slow transition. No jets might be observed during the Dark/Fast transition. L/H B/H VH/SPL H/S L/H H/S Jet? Bright/SlowDark/Fast No Jet?

Summary We obtained the steady solution of the optically thin low-β disk. This solution exists at high M. The electron temperature is low ( T e ~ K ). The low-β disk can explain the Bright/Hard state. When the magnetic flux advection rate is high: The optically thin, low-β solution exist above the maximum M of ADAF/RIAF The Bright/Slow transition will occur. When the magnetic flux advection rate is low: No optically thin solutions exist above the maximum M of ADAF/RIAF. The Dark/Fast transition will occur. If magnetic fluxes can escape from the optically thin, low-β disk with a jet, the system can consist of an optically thick cool disk and an optically thin hot corona. Then, the system may undergo transition to the VH/SPL state.