1. Luminous Hot Accretion Flows ------extending ADAF beyond its critical accretion rate Feng Yuan Shanghai Astronomical Observatory, Chinese Academy of Science

2. Outline  The dynamics of luminous hot accretion flows (LHAFs)  Main features of LHAFs  Stability  Possible Applications (in AGNs & BH X-ray Binaries)  Questions & Speculations

3. ADAF and Its Critical Accretion Rate  The energy equation of ions in ADAFs:  For a typical ADAF (i.e., ), we have:  Since q - increases faster than q + and q adv with increasing accretion rate, there exists a critical accretion rate of ADAFs, determined by (Narayan, Mahadevan & Quataert 1998): Self-similar solution of ADAF  So advection is a cooling term

4. The dynamics of LHAFs  What will happen above the critical rate of ADAF?  Originally people think no hot solution exists; but this is not true  The energy equation of accretion flow: since: So we have:

5. The dynamics of LHAFs  An ADAF is hot because so the flow remains hot if it starts out hot.  When, up to another critical rate determined by We still have: So again the flow will be hot if it starts out hot, i.e., a new hot accretion solution (LHAFs) exists between 

6. Properties of LHAFs  Using the self-similar scaling law:  LHAF is more luminous than ADAFs since it corresponds to higher accretion rates and efficiency.  The entropy decreases with the decreasing radii. It is the converted entropy together with the viscous dissipation that balance the radiation of the accretion flow.  Since the energy advection term is negative, it plays a heating role in the Euler point of view.  The dynamics of LHAFs is similar to the cooling flow and spherical accretion flow.

7. The thermal equilibrium curve of accretion solutions: local analysis  Following the usual approach, we adopt the following two assumptions  we solve the algebraic accretion equations, setting ξto be positive (=1) and negative (=-0.1, -1, -10) to obtain different accretion solutions. Yuan 2003

8. Four Accretion Solutions Yuan 2001

9. LHAFs: Two Types of Accretion Geometry Hot accretion flow Collapse into a thin disk Strong magnetic dissipation? Type-I: Type-II: See also Pringle, Rees & Pacholczyk 1973; Begelman, Sikora & Rees 1987

10. Global Solutions of LHAFs: Dynamics  α=0.3;  Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LHAF) 0.5 (long-dashed; type-II LHAF) Yuan 2001

11. Global Solutions of LHAFs: Energetics  Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LHAF) 0.5 (long-dashed; type-II LHAF) Yuan 2001

12. Stability of LHAFs  From the density profile, we know that LHAFs are viscously stable.  It is possibly convectively stable, since the entropy of the flow decreases with decreasing radius.  Outflow: the Bernoulli parameter is in general negative in LHAF, so outflow may be very weak.  LHAF is thermally unstable against local perturbations. However, at most of the radii, the accretion timescale is found to be shorter than the timescale of the growth of perturbation, except at the ``collapse’’ radius.

13. The thermal stability of LHAFs Yuan 2003 ApJ For type-I solution For type-II solution

14. Application of LHAFs: the origin of X-ray emission of AGNs and black hole binaries  X-ray Luminosity.  The maximum X-ray luminosity an ADAF can produce is (3-4)%L Edd  X-ray luminosities as high as ~20% Eddington have been observed for the hard state (XTE J1550+564; GX 339-4) & AGNs.  An LHAF can produce X-ray luminosities up to ~10%L Edd  Spectral parameters  Assuming that thermal Comptonization is the mechanism for the X-ray emission of the sources, we can obtain the most suitable parameters (Te, τ) to describe the average spectrum of Seyfert galaxies  On the other side, we can solve the global solution for both ADAF and LHAF, to obtain the values of (T, τ)  We find that the most favored model is an LHAF (with parameterized energy equation), while ADAFs predicting too high T.

15. Modeling Luminous X-ray Sources: LHAFs better than ADAFs Yuan & Zdziarski 2004

16. Modeling the 2000 outburst of XTE J1550-564 Yuan, Zdziarski, Xue & Wu 2007 6% L Edd 3%L Edd 1%L Edd

17. Yuan, Zdziarski, Xue, & Wu 2007 LHAF

18. Temperature profiles of the three solutions. The three dots show the E-folding energy of the three X-ray spectra shown in a previous figure. The theoretical predictions are in good agreement with observations.

19. Questions on LHAFs  Questions on theoretical side  Type-II LHAF is strongly thermally unstable at the transition radius, thus is it applicable in nature, or what is the consequence?  Questions on applications  It seems that an LHAF can only produce up to 10%LEdd X-ray luminosity, but many X-ray sources are likely more luminous  How to explain the very high state? (may related with the above item)  In some relatively luminous hard state, iron Ka line seems to be detected (but…)

20. Two phase accretion: Another possible consequence of the strong thermal instability  The accretion flow is thermally unstable at the collapse radius  two-phase accretion flow? (e.g., prominence in solar corona; multi-phase ISM; Field 1965).  The amount of clouds should be controlled by that the hot phase is in a ‘maximal’ LHAF regime  Such configuration may hold for high accretion rates;  when there are many clumps, they may form a thin disk. But photon bubble & clumping instabilities (Gammie 1998; Merloni et al. 2006) may make the disk clumpy again? Cold clumpsHot gas

21. On the possible application of LHAFs: Questions from observations 1. The origin of X-ray emission in quasars & some BHXBs? a) L x >10% L Edd b) The thin disk sandwiched between corona model does not work because the corona is too weak (Hirose, Krolik & Stone 2006) c) One-phase LHAF can only explain L x up to ~8% L 2. The accretion model for the very high state? a) Both thermal & nonthermal (steep; no cut-off) spectral component are strong b) strong QPOs 3. It is claimed that at some relatively luminous hard state, some broad iron Ka lines are detected (Miller et al. 2006; 2007)

22. Speculations on the above questions  X-ray origin of quasars: accretion rate is high  The accretion rate in the hot phase:  is decreasing with decreasing radii  is in “maximal” value at each radius  Some hot gas gradually collapses into clouds by releasing their thermal energy  The very high state  Accretion Geometry: truncated standard thin disk + two phase flow: QPO  The thermal component is due to the blackbody or bremsstrahlung radiation from the clumps  The nonthermal component is due to Comptonization emission by the (thermal and nonthermal) electrons in the hot phase  The presence of iron Ka line  same line profile can be reproduced by two-phase flow and even better (Hartnoll & Blackman 2001)  Puzzling low Inclination preferrance for some Seyfert 2  Reprocessed fraction too low & uncorrelated with line (Merloni et al. 2006)  The accretion flow of luminous hard state may also be two-phase