Some issues on models of black hole X-ray binaries Feng Yuan Shanghai Astronomical Observatory, Chinese Academy of Sciences

Outline  The accretion model for the hard state (XTE J as an example)  Introduction to luminous hot accretion flows (LHAFs) luminous  Explaining the X-ray emission of the luminous hard state of XTE J with LHAFs  On the contribution of jet in the X-ray radiation of the hard state  The model for the quiescent state: jet-dominated?

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

The dynamics of LHAFs: Basic Physics (I)  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:

The dynamics of LHAFs: Basic Physics (II)  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 

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.

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

Four Accretion Solutions Yuan 2001

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

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

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

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.

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

Application of LHAFs: the origin of X-ray emission in 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 J ; GX 339-4) & AGNs.  An LHAF can produce X-ray luminosities up to ~10%L Edd  Spectral parameters  Assuming thermal Comptonization model for the X-ray emission, we can obtain (T e, 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 e, τ)  We find that an LHAF can produce better Te & τ than an ADAF (predicted T e too high compared to observation).

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

An example: the 2000 outburst of XTE J Yuan, Zdziarski, Xue & Wu % L Edd 3%L Edd 1%L Edd

Yuan, Zdziarski, Xue & Wu 2007 LHAF

The three dots show the E-folding energy of the three X-ray spectra shown in the previous figure. Yuan, Zdziarski, Xue & Wu 2007

Questions on LHAFs  Questions on theoretical side  Type-II LHAF is strongly thermally unstable at the transition radius, thus is it applicable in nature?  The range between the critical ADAF and type-I LHAF seems to be rather small  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…)

Speculations on the Above Questions  the accretion flow is thermally unstable at the collapse radius. As a result, a two- phase accretion flow may be formed (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 a two-phase configuration may correspond to a large range of rate; when the rate is higher, more matter will condense out.  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 clumps Hot gas

Speculations on the above questions  A very high X-ray luminosity as observed may be produced due to the high accretion rate (Comptonization in the hot phase + condensation energy).  Due to the existence of cold clumps, strong reflection/reprocessing features are expected (reflection-dominated spectrum: Merloni et al. 2006; relativistic iron Ka line: Blackman).  An example: the very high state (Yuan 2001; Yuan et al. 2006)?  Observations  Both thermal & nonthermal (steep; no cut-off) spectral component are strong  Ejection of matter  The thermal component is due to the blackbody emission from the cold dense clumps  The nonthermal component is due to Comptonization emission by the thermal (steep due to strong cooling) and nonthermal (magnetic dissipation due to B field expanding) electrons in the hot phase  Magnetic expanding  ejection of matter from accretion flow?

Jain et al. 2001, ApJ The optical and X-ray light curves of XTE J during its 2000 outburst. Secondary maxima No maximum in the X-ray!

Yuan, Zdziarski, Xue & Wu 2007 Secondary Maximum: the contribution of the jet Jet emission

Radio/X-ray correlation of GX 339-4; from Corbel et al. 2003, A&A Observed radio---X-ray correlation

Radio-X-ray correlation and the quiescent state  The optically-thin synchrotron emission, while the Comptonization from the hot accretion flow  With the decrease of accretion rate, the X-ray emission of the system will be dominated by the jet  Thus a change of the radio---X-ray correlation is expected, from AB to CD. The critical luminosity is:  The X-ray emission of the quiescent state (below the above critical luminosity) should be dominated by jets

Radio-X-ray correlation in the larger regime of luminosity The change of the radio—X-ray correlation from hard to quiescent states Yuan & Cui 2005, ApJ

Test the prediction Wu, Yuan, & Cao 2007