Thermal Equilibria of Magnetically Supported Black Hole Accretion Disks Table of Contents Introduction: Bright/Hard state observed in BHBs Purpose: To explain B/H state by magnetically supported (low-β) disks Results: Thermal equilibrium curves for each disk Conclusion: The optically thin, low-β disk can explain the B/H state Hiroshi Oda (CfA) M. Machida (Nagoya Univ., Japan), K. E. Nakamura (Matsue Collage, Japan), R. Matsumoto (Chiba Univ., Japan) and Ramesh Narayan (CfA) 2009 CfA Postdocs Science Symposium

RXTE: GX339-4 (Gierlinski & Newton`06) H-L Diagram Hardness Ratio = L 5-12keV / L 3-5keV Dark/Fast [ keV ] Flux νF ν [ keV/cm 2 s -1 ] High/Soft Low/Hard Very High/ Steep PL E cut ≥ 200keV E cut 〜 keV L/H H/S X-ray Spectrum Bright/Hard Bright/Slow B/H VH/SPL Soft X-ray (High/Soft) Std. Disk Opt. Thick Cool (T 〜 10 7 K) Hard X-ray (Low/Hard) ADAF/RIAF Opt. Thin Hot (T e ≥ K) L Max 〜 0.4 α 2 L Edd X-ray Spectral State Transition of Galactic BHBs Optically thin, moderately cool disk?

Surface density Temperature Accretion Rate Time evolution Transition from ADAF/RIAF to Low-β Disk Hot ADAF/RIAF Q + ~Q adv β 〜 10 β 〜 0.1 Moderately cool low-β disk Q + ~Q - rad (B φ ≫ B ϖ,B z ) Thermal Equilibrium s Global 3D MHD (Machida+ 06) Turbulent B New Thermal Equilibrium Solution? When M > M c, ADAF,..

Purpose: To explain the bright/hard state Construct the vertically integrated 1D steady model incorporating magnetic fields. The low-β disk is thermally stable? How does T depend on M? Can explain the bright/hard state during the bright/slow transition? Global transonic solutions of optically thin 1-temperature plasma (Oda et al. 2007, PASJ) Thermal equilibria of 1-temperature plasma (Oda et al. 2009, ApJ) Thermal equilibria of optically thin 2-temperature plasma (Oda et al in prep.) But, it is difficult to carry out the global 3D MHD/Rad.-MHD simulations of the whole transition... (but in progress).

Main Difference from the Conventional Model ‣ α-prescription of the stress ‣ How to determine β Fixed β Introducing a parameter: the magnetic flux advection rate In global MHD, the Maxwell’s stress is still large when the magnetic pressure is large even though the thermal pressure become low. If we rewrite this relation in term of the kinematic viscosity In global MHD, although β drastically changes during the transition, this quantity is almost conserved. (c.f. This concept is similar to that of the mass accretion rate )

Results We obtained the sequence of low-β solutions in the middle range of Σ and M. Low-β solutions are thermally stable. Cooler than the ADAF/RIAF. Surface density Temperature Thermal Equilibrium s Thin Opt. Thick Mass Accretion Rate RIAF Std. Slim Low-β thin solid: conventional model dotted: small Φ dashed: mid thick solid: large β>100 β~ β>10.

The Opt. Thin Low-β Disk: Can Explain the Bright/Hard State and Bright/Slow Transition RIAF Std. Slim SLE Low-β 〜 0.1L Edd Bright/Slow Thermal Equilibrium s Mass Accretion Rate Temperature According to Pessah & Psaltis (2005), the MRI is stabilized for v A > [c s 2 +v K 2 ] 1/2. In such region, Q + → 0, therefore the low-β solution may disappear and the disk undergoes transition to the standard disk. v A > [c s 2 +v K 2 ] 1/2 RXTE: GX339-4 (Gierlinski & Newton`06) H-L Diagram Hardness Ratio = L 5-12keV / L 3-5keV Low/Hard Bright/Hard High/Soft VH/SPL

Bright/Slow transition Dark/Fast transition Mass Accretion Rate the MRI is stabilized if v A > [c s 2 +v K 2 ] 1/2. High/soft Magnetic flux advection rate

Summary We construct 1D steady models incorporating magnetic fields on the basis of the results of 3D MHD simulations. ‣ We assume that the stress (therefore the heating rate) is proportional the total pressure. ‣ We prescribe the magnetic flux advection rate (instead of fixing β). RIAF Std. Slim SLE Low-β Opt. thin low-β disks ✓ exist at high mass accretion rate. Temperature is lower than that of the ADAF/RIAF. ➡ explain the Bright/Hard state during the Bright/Slow transition. ‣ Opt. thick low-β disks ✓ The radial distribution of the effective temperature is the same as that for the standard disk. ➡ observed as the thermal disk state? ➡ Limit-cycle between Slim disk ⇔ Opt. thick disk? Thin Opacith Thick

The Opt. Thick Low-β Disk: Maybe Observed as a Thermal Disk State Radiation mechanism: Black body radiation Radial distribution of the effective temperature: T eff ϖ -3/4 Same as that for the standard disk! RIAF Std. Slim SLE Low-β Limit cycle observed in GRS : Slim ⇔ Opt. thick low-β? (Smaller variation in luminosity compared to that expected from Slim ⇔ Std.) Surface density Thermal Equilibrium s Mass Accretion Rate ∝ But, in order to form the low-β disk, the disk should shrink in a thermal timescale (< t escape B )... One candidate

RIAF Slim SLE Low-β RIAF Std. Slim Low-β RIAF Std. Slim Low-β

Φ increase inward (ζ=0.6) RIAF Low-β RIAF Low-β Result: Radial Structure of the Disks Φ remain constant (ζ=0) RIAF Low-β Low M: The disk is in the RIAF at every radius. High M: The disk undergoes a transition from RIAF to Low-β from the outer radii. [Φ increase inward( ζ=0.6 )] Opt. thin low-β [Φ remain const.(ζ=0)] Opt. thick low-β (T eff ∝ ϖ -3/4 ) Higher M: The disk undergoes a transition to Slim from the inner radii. Slim Temperature Optical depth Radius.....

Why does the magnetic pressure become dominant? ⇒ Because of the flux freezing. The disk shrinks in a thermal timescale which is shorter than the escape timescale of B t th < t escape B What is the heating source in 3D MHD? ⇒ Dissipation of turbulent B energy correlates with p gas In α-prescription, In ADAF (ν turb ~ c s × H), In low-β (ν turb ~ v A × H), correlates with p mag In quasi-equilibrium state, generation rate of B turb ~ dissipation rate of B turb B fields are still turbulent even in low-β disks (β~0.1) gas In ADAF region, in which ν turb ~ c s × H, In low-β region, in which ν turb ~ v A × H, mag gas ∝ αp gas In conventional model, the stress ∝ αW gas As a result, Q + < Q - rad in such low temperature region. gas Therefore, the heating rate According to the conventional model, no thermal equilibrium solution in such low temperature region (Q + < Q - rad ) Why does the disk stay in the quasi-steady state? Dynamics: The strong magnetic tension force suppresses the Parker instability. Energetics: Since the MRI is not yet stabilized, the heating via the dissipation of turbulent B is effective. This heating balances the radiative cooling even in such low temperature region.

‣ Conventional model: ➡ No Q + balances Q rad ‣ This model: ➡ Q + balances Q rad when the magnetic pressure is high. Why Can We Obtain the Low-β Solutions? Energy density, low temperature 0 ~ 0 ~ Surface density Temperature Thermal Equilibrium s Mass Accretion Rate BH Heat Rad. p mag RIAF Std. Slim Low-β

Bright/Slo w Transition occurs at ~0.3 L Edd, takes ≲ 30 days Dark /Fast Transition occurs at ≳ 0.1 L Edd, takes ≳ 15 days Gierlinski & Newton `06 How about other sources? =L 5-12keV /L 3-5keV