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A unified accretion-ejection paradigm for Black Hole X-ray Binaries

Astronomy & Astrophysics manuscript no. ms (DOI: will be inserted by hand later)

February 5, 2008

A uni?ed accretion-ejection paradigm for Black Hole X-ray Binaries
I- The dynamical constituents
Jonathan Ferreira1 , Pierre-Olivier Petrucci1 , Gilles Henri1 , Ludovic Saug?1,2 and Guy Pelletier1 e
1 2

arXiv:astro-ph/0511123v1 4 Nov 2005

Laboratoire d’Astrophysique, Observatoire de Grenoble BP53, F-38041 Grenoble cedex 9, France Institut de Physique Nucleaire de Lyon, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex, France

the date of receipt and acceptance should be inserted later Abstract. We present a new picture for the central regions of Black Hole X-ray Binaries. In our view, these central regions have a multi-?ow con?guration which consists in (1) an outer standard accretion disc down to a transition radius rJ , (2) an inner magnetized accretion disc below rJ driving (3) a non relativistic self-collimated electronproton jet surrounding, when adequate conditions for pair creation are met, (4) a ultra relativistic electron-positron beam. This accretion-ejection paradigm provides a simple explanation to the canonical spectral states, from radio to X/γrays, by varying the transition radius rJ and disc accretion rate m independently. Large values of rJ correspond ˙ to the Quiescent state for low m and the Hard state for larger m. These states are characterized by the presence ˙ ˙ of a steady electron-proton MHD jet emitted by the disc below rJ . The hard X-ray component is expected to form at the jet basis. When rj becomes smaller than the marginally stable orbit ri , the whole disc resembles a standard accretion disc with no jet, characteristic of the Soft state. Intermediate states correspond to situations ˙ where rJ > ri . At large m, an unsteady pair cascade process is triggered within the jet axis, giving birth to ? ?ares and ejection of relativistic pair blobs. This would correspond to the luminous intermediate state, sometimes referred to as the Very High state, with its associated superluminal motions. The variation of rJ independently of m is a necessary ingredient in this picture. It arises from the presence of ˙ a large scale vertical magnetic ?eld threading the disc. Features such as possible hysteresis and the presence of quasi-periodic oscillations would naturally ?t within this new framework. Key words. Black hole physics – Accretion, accretion discs – Magnetohydrodynamics (MHD) – ISM: jets and out?ows – X-rays: binaries

1. Introduction
Galactic Black Hole X-ray Binaries (hereafter BH XrBs) are binary systems that were ?rst detected as X-ray sources. They harbor a massive compact object as a primary star, being therefore a black hole candidate, accreting matter from the companion. The X-ray emission probes the inner regions around the compact object and is interpreted as a signature of accretion (Tanaka & Lewin 1995; McClintock & Remillard 2003, hereafter McCR03, and references therein). There is now growing evidence that these objects also display ejection signatures: radio emission is commonly interpreted as the presence of compact steady jets or the sporadic ejection events also seen in infrared and X-ray bands (Fender & Belloni, 2004; Buxton & Bailyn, 2004). In fact, the correlation between
Send o?print requests to: J. Ferreira e-mail: Jonathan.Ferreira@obs.ujf-grenoble.fr

radio luminosity (ejection) and X-ray luminosity (accretion) found in Active Galactic Nuclei (AGN) seems to be also consistent with XrBs (Robertson & Leiter, 2004; Falcke et al., 2004; Gallo et al., 2003; Choudhury et al., 2003; Corbel et al., 2003). The similarity of the ?rst detected galactic jet in 1E1740 with extragalactic jets gave birth to the name ”microquasar” (Mirabel & Rodriguez, 1998). What is so dramatic about microquasars is their multiple manifestations through very di?erent spectral states. They spend most of their time in the Quiescent state which is characterized by a very low accretion rate ˙ (m = Ma c2 /LEdd as low as ? 10?9 ). The multiwavelength ˙ spectral energy distributions are thus very scarse but generally show a hard X-ray (2-10 keV) spectrum with a power law photon index Γ = 1.5 ? 2.1 and an optical/UV continuum reminiscent of a ? 104 K disc blackbody with


Ferreira et al.: An accretion-ejection paradigm for BH XrBs

strong emission lines (McCR03). Occasionnaly, microquasars enter in outburst, resulting from a dramatic increase of their accretion rate. During these outbursts, microquasars show di?erent canonical states, like the well known Hard and Soft states. The hard state is characterized by a spectrum dominated above 2 keV by a hard power-law component (Γ ? 1.5) with a cut-o? around 100 keV (e.g. Grove et al. 1998; Zdziarski & Gierlinski 2003 and references therein), and with a soft X-ray excess below 2 keV interpreted as the presence of a cool (? 0.01-0.2 keV) accretion disc. Strong radio emission is observed during this state and some VLBI images directly revealed spatially resolved structures. These are interpreted as non or only mildly relativistic (bulk Lorentz factor Γb < 2) steady jets (e.g. Stirling et al. 2001; Dhawan et al. 2000). On the contrary, the soft state is dominated by a thermal blackbody-like component, typical of a standard accretion disc of temperature ranging from 0.7 to 1.5 keV (consistent with an inner disc radius rin ? 10 rg = GM/c2 ). A faint power-law component may still be present but with a steep photon index Γ = 2.1 ? 4.8 (McCR03). This state is also devoid of any radio emission which is interpreted as the absence of jet (e.g. Fender et al. 1999; Corbel et al. 2000). Hard and soft state span a relatively large range in luminosity, i.e. from 10?2 to 1 LEdd. Microquasars can also be observed in Intermediate states, generally during transitions between the hard and soft states. Intermediate states present relatively complex spectral and timing behaviors. Detailed studies have been done in the recent literature (see e.g. Fender et al. 2004; Belloni et al. 2005) and reveal a clear evolution with time between hard, variable (in X-ray) and radio-loud systems to softer, less variable and more radio-quiet ones. The transitions between the hard and soft ”?avors”, which seems to correspond also to a transition between jet-producing and jet-free states, can be relatively abrupt especially at high luminosity level where they are apparently coincident with strong radio outbursts (Fender & Belloni, 2004). These non steady ejection events display apparent superluminal velocities, indicative of a highly relativistic plasma (Mirabel & Rodr? ?guez, 1999; Dhawan et al., 2000). These di?erent observational characteristics lead to the de?nition of the so-called ”jet line” by Fender & Belloni (2004), that separates hard/jet dominated states to soft/jet-free ones in hardness-intensity diagrams. These various spectral states obviously carry a huge amount of information about the physical processes behind accretion and ejection. Moreover, since it is believed that microquasars are a scaled down version of AGN, understanding the various states (along with their transitions) in XrBs will certainly provide insights on the observed di?erences between AGN (radio loud/radio quiet, FRI/FRII, blazars...).

The puzzle of the existence of these di?erent spectral states is enhanced by the fact that each state must correspond to a dynamically steady state. Indeed, each state lasts a much longer time than the inferred dynamical time scale. Let us consider the case of GRS1915+105, which is the BH XrB with the most rapid time scales. It shows states lasting ? 103 sec with rising and decay times of the order of one second, whereas the keplerian orbit time scale is several milliseconds at the inner radius (Belloni et al., 1997). One must therefore explain why a system switches from one stationary state to another one. But before that, one must ?rst identify the relevant underlying dynamics describing each state. Up to now, these canonical spectral states are still not fully understood, let alone the transitions between them. The most common paradigm used to interpret observations is based on the low radiative e?ciency of the ADAF model (Esin et al. 1997 and references therein). Within this framework, the highest energy component is due to the inner thick, low radiative disc whereas an outer standard disc is responsible for the UV-soft X ray emission. By varying the transition radius rtr between these two discs (as a function of m) one gets reasonable ˙ ?ts to the spectral energy distributions (hereafter SEDs, e.g. Narayan et al. 1996; Hameury et al. 1997; Esin et al. 1998, 2001). In the ADAF paradigm, the accretion power below the transition radius is essentially stored as thermal energy of protons and eventually advected below the black hole event horizon. Remarkably, energetic ejection events appear to be always associated with hard and intermediate states and are quenched during the soft phase (McCR03 and references therein). This has led several authors to propose that ADAFs could indeed drive out?ows or its ADIOS extension (Blandford & Begelman, 1999, 2004). However, it must be realized that there is only one source of energy, namely the release of gravitational energy through accretion. Hence, whenever a disc is capable of driving jets, these will carry away a fraction of the released accretion energy. As a consequence, the disc luminosity will be quenched. Observations tell us something consistent with this very simple and unavoidable argument: whenever a steady jet is formed the disc may observationally disappear. This does not mean that the disc is really disappearing (i.e., inner region being depleted of its mass), only that we do not see it anymore. Discs that drive jets are indeed radiating only a small fraction of the accretion power released as shown in another class of accretion solution, namely Magnetised Accretion-Ejection Structures (hereafter MAES, see e.g. Ferreira & Pelletier 1993, 1995 and Ferreira 2002 for a review). In this ?ow, a large scale magnetic ?eld is threading the disc, exerts a torque leading to accretion and allows the production of self-con?ned jets. A logical consequence is that whenever a jet is formed, the ADAF hypothesis is no more useful to explain the low radiative e?ciency of the accretion ?ow.

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


The goal of this paper is to provide an alternative view explaining the canonical spectral states observed in BH XrBs based on MAES. We do not intend to address the crucial issue of the transitions between these states, neither time scales involved nor possible hysteresis e?ects. This is delayed for future work. In this paper, we only expose the global physical picture and show that this framework is rich enough to explain all known spectral components. In a forthcoming paper, we will provide calculations of SEDs and compare them to observations. The paper is then organized as follows. Section 2 describes in some detail the four physical components present within our paradigm, their dynamical properties as well as radiative processes governing their emission. The canonical spectral states of BH XrBs are then interpreted within this framework in Section 3. Section 4 is devoted to a discussion of some time scales and timing properties of our model that could be related to some observed features. Section 5 highlights questions opened by our framework as well as future developments.

corresponding vertical ?ux of angular momentum and en+ ergy. This torque writes ?Jr Bz ? Bφ Bz /?o h < 0 where + Bφ is the toroidal ?eld at the disc surface. This shows that the product Jr Bz must remain positive over the whole region driving jets. Such a condition is unlikely to be met with a vertical ?eld changing its polarity from one zone to another because the currents (both radial and azimuthal) induced inside the disc will tend to cancel each other. The most e?cient way to launch jets from an accretion disc is probably from a radial extension (the JED) with a large scale Bz of the same polarity. This vertical ?eld is therefore an unavoidable ingredient to produce self-collimated jets. So, where does this ?eld come from? A ?rst possible origin is in-situ generation of magnetic ?elds by dynamo. The huge di?culty is to provide an ordered large scale vertical ?eld out of turbulent small scale seed ?elds. Opening of magnetic loops by the disc di?erential rotation might provide a mechanism (Romanova et al., 1998). The second origin is advection of magnetic ?eld by the accreting material1 . We therefore assume that the whole accretion disc is pervaded by a large scale magnetic ?eld Bz . The presence of a large scale vertical ?eld threading the disc is however not su?cient to drive super-Alfv?nic e jets. This ?eld must be close to equipartition as shown by Ferreira & Pelletier (1995) and Ferreira (1997). The reason is twofold. On one hand, the magnetic ?eld is vertically pinching the accretion disc so that a (quasi) vertical equilibrium is obtained only thanks to the gas and radiation pressure support. As a consequence, the ?eld cannot be too strong. But on the other hand, the ?eld must be strong enough to accelerate e?ciently the plasma right at the disc surface (so that the slow-magnetosonic point is crossed smoothly). These two constraints can only be met with ?elds close to equipartition. An important local parameter is therefore the disc 2 magnetization ? = Bz /(?o Ptot ) where Ptot includes the plasma and radiation pressures. In our picture, a SAD is established down to a radius rJ where ? becomes of order unity. Inside this radius, a JED with ? ? 1 is settled. At any given time, the exact value of rJ depends on highly non-linear processes such as the interplay between the amount of new large scale magnetic ?eld carried in by the accreting plasma (eg. coming from the secondary) and turbulent magnetic di?usivity redistributing the magnetic ?ux already present. These processes are far to be understood. For the sake of simplicity, we will treat in the following rJ as a free parameter that may vary with time (see Section 3).

2. A novel framework for BH XrBs 2.1. General picture
We assume that the central regions of BH XrB are composed of four distinct ?ows: two discs, one outer ”standard” accretion disc (hereafter SAD) and one inner jet emitting disc (hereafter JED), and two jets, a nonrelativistic, self-con?ned electron-proton MHD jet and, when adequate conditions for pair creation are ful?lled, a ultra-relativistic electron-positron beam. A sketch of our model is shown in Fig. 1 while the four dynamical components are discussed separately below. This is an extended version of the ”two-?ow” model early proposed for AGN and quasars (Pelletier et al., 1988; Sol et al., 1989; Pelletier & Roland, 1989; Henri & Pelletier, 1991; Pelletier & Sol, 1992) to explain the highly relativistic phenomena such as superluminal motions observed in these sources. This model provides a promising framework to explain the canonical spectral states of BH XrBs mainly by varying the transition radius rJ between the SAD and the JED. This statement is not new and has already been proposed in the past by di?erent authors (e.g. Esin et al. 1997; Belloni et al. 1997; Livio et al. 2003; King et al. 2004) but our model distinguish itself from the others by the consistency of its disc–jet structure and by the introduction of a new physical component, the ultrarelativistic electron-positron beam, that appears during strong outbursts. We believe that jets from BH XrBs are self-collimated because they follow the same accretion-ejection correlation as in AGN (Corbel et al., 2003; Fender et al., 2003; Merloni et al., 2003). This therefore implies the presence of a large scale vertical ?eld anchored somewhere in the accretion disc. We think it is unlikely that such a ?eld has a patchy distribution on the disc. Indeed, once a jet is launched, it exerts a torque on the underlying disc with a

Note also that a fraction of the open poloidal ?ux initially tied to the primary’s progenitor could remain trapped by the accretion ?ow.



Ferreira et al.: An accretion-ejection paradigm for BH XrBs

Fig. 1. A Standard Accretion Disc (SAD) is established down to a radius rJ which marks the transition towards a low radiative Jet Emitting Disc (JED), settled down to the last stable orbit. The JED is driving a mildly relativistic, self-collimated electron-proton jet which, when suitable conditions are met, is con?ning an inner ultra-relativistic electron-positron beam. The MHD power PMHD ?owing from the JED acts as a reservoir for (1) heating the jet basis (radiating as a moving thermal corona with power Pc ), (2) heating the inner pair beam (Pe+ e? ) and (3) driving the compact jet (Pjet ). Field lines are drawn in solid lines and the number density is shown in greyscale (log10 n/m?3 ). The MAES solution (JED and MHD jet) was computed with ξ = 0.01, ε = 0.01 and with m = 10 and m(rJ ) = 0.01 ˙ (see text).

2.2. The outer SAD
Accretion requires the presence of a negative torque extracting angular momentum. In a SAD this torque is assumed to be of turbulent origin and provides an outward transport of angular momentum in the radial direction. It has been modeled as an ”anomalous” viscous torque of amplitude ? ?αv Ptot /r, where αv is a small parameter (Shakura & Sunyaev, 1973). The origin of this turbulence is now commonly believed to arise from the magnetorotational instability or MRI (Balbus & Hawley, 1991). The MRI requires the presence of a weak magnetic ?eld (? < 1) and is quenched when the ?eld is close to equipartition. We make the conjecture that a SAD no longer exists once ? reaches unity. We show below that this is very likely to occur in the innermost regions.

The radial distribution Bz (r) is provided by the induction equation which describes the interplay between advection and di?usion. If we assume that, in steady state, the poloidal ?eld is mostly vertical (no signi?cant bending within the SAD) then this equation writes νm ?Bz ? ur Bz ?r (1)

where νm is the turbulent magnetic di?usivity. This equation has the obvious exact solution Bz ∝ r?Rm (2)

where Rm = ?rur /νm is the (e?ective) magnetic Reynolds number. In a turbulent disc one usually assumes that all anomalous transport coe?cients are of

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


the same order so that νm ? νv , νv being the turbulent viscosity. Since the (e?ective) Reynolds number Re = ?rur /νv = 3/2 in a SAD, one gets that any vertical magnetic ?eld is naturally increasing towards the center. Now in a SAD of vertical scale height h(r) ∝ rδ , the total pressure Ptot = ρ?2 h2 (?k is the Keplerian rotation rate) k scales as Ptot = ˙ M a ?2 h k 6πνv ∝ r?3/2?δ (3)

properties and refer the interested reader to speci?c papers. In this dynamical structure accretion and ejection are interdependent: jets carry away the exact amount of angular momentum allowing the disc material to accrete. The ratio at the disc midplane of the jet torque to the turbulent ”viscous” torque is Λ?
+ Bφ Bz /?o h

αv Ptot /r


+ Bφ Bz r ?o Ptot αv h


˙ where Ma is the (constant) disc accretion rate. Using Eq. (2) we get ? ∝ r?? with ? = 2Rm ? δ ? 3/2 (4)

In a SAD Rm ? 3/2 and δ is always close to unity (apart from the unstable radiation pressure dominated zone where δ = 0). Of course, the real value of ? critically depends on the magnetic Prandtl number (Pm = νv /νm ) but this result suggests that one may reasonably expect ? to increase towards the center. Whenever a BH XrB reaches ? ? 1 at a radius rJ > ri , ri being the last marginally stable orbit, the accretion ?ow changes its nature to a JED. To summarize, the accretion ?ow at r > rJ is a SAD with ? ? 1 fueled by the companion’s mass ?ux and driv˙ ing no out?ow (constant accretion rate Ma ). The global energy budget is Pacc,SAD = 2Prad,SAD where Pacc,SAD ? ˙ GM Ma 2rJ (5)

It is straightforward to see that the necessary condition to drive jets (?elds close to equipartition) from Keplerian discs leads to a dominant jet torque. In fact, it has been shown that steady-state ejection requires Λ ? r/h ? 1 (Ferreira, 1997; Casse & Ferreira, 2000a). This dynamical property has a tremendous implication on the JED emissivity. The JED luminosity comes from the accretion power dissipated within the disc by turbulence and transported away by photons, so 2Prad,JED = Pdiss . This dissipated power is very di?cult to estimate with precision because it requires a thorough description of the turbulence itself. Thus, one usually uses crude estimates based on ”anomalous” turbulent magnetic resistivity ηm (Joule heating) and viscosity ηv (viscous heating). This translates into Pdiss = PJoule + Pvisc = ηm J 2 dV + ηv (r??/?r)2 dV where integration is made over the whole volume occupied by the JED. The importance of local ”viscous” dissipation with respect to the MHD Poynting ?ux leaving the disc is approximately given by 1 Pvisc ? 2PMHD Λ (9)

and Prad,SAD is the disc luminosity (from one surface only). Its emission has the characteristic multi-blackbody shape produced by a radial temperature distribution Tef f (r) ∝ r?3/4 . The spectrum is therefore dominated by the hottest inner parts at rJ .

2.3. The inner JED
This inner region with ? ? 1 is fueled by the SAD at a ˙ ˙ rate Ma,J = Ma (rJ ). Since it undergoes mass loss, the JED accretion rate is written as ˙ ˙ Ma (r) = Ma,J r rJ

which is much larger than unity: turbulent ”viscosity” provides negligible dissipation in a JED. Joule heating arises from the dissipation of toroidal and radial currents which are comparable2 . One therefore gets ηm J 2 ? 2 νm Bz /?o h2 ? νv ρ?2 ? ηv (r??/?r)2 , for equipartition ?elds, isotropic magnetic resistivity ηm = ?o νm and a turbulent magnetic Prandtl number of order unity. This leads to 1 PJoule ? (10) 2PMHD Λ namely a negligible e?ective Joule heating. Thus, the total luminosity 2Prad,JED of the JED is only a fraction 1/(1 + Λ) of the accretion disc liberated power Pacc,JED . To summarize, under quite general conditions on the turbulence within magnetized discs, most of the available accretion energy is powering the out?owing plasma (Ferreira & Pelletier, 1993, 1995). This is in strong contrast with ADAFs where the accretion power is stored as heat advected by the accreting plasma. In this case, low luminosity discs can be obtained as long as the central object possesses an event horizon. However, the power
Full computations of MAES show that the three magnetic ?eld components are comparable at the disc surface, namely + + Bφ ? Br ? Bz (Ferreira & Pelletier, 1995; Ferreira, 1997).


where ξ measures the local ejection e?ciency (Ferreira & Pelletier, 1993). The global energy budget in the JED is Pacc,JED = 2Prad,JED + 2PMHD where PMHD is the MHD Poynting ?ux feeding a jet, whereas the liberated accretion power writes Pacc,JED ? ˙ GM Ma,J 2ri ri rJ


ri rJ


The dynamical properties of a JED have been extensively studied in a series of papers (see Ferreira 2002 and references therein). We will here only brie?y recall the main


Ferreira et al.: An accretion-ejection paradigm for BH XrBs

to magnetically drive jets is also missing. In the case of MAES, the JED is weakly dissipative while powerful jets are being produced regardless of the nature of the central object. Complete calculations of MAES showed that isothermal or adiabatic super-Alfv?nic jets from Keplerian e accretion discs were possible only when a tiny fraction of the accreted mass is locally ejected. This translates into a small ejection e?ciency, typically ξ ? 0.01 (Ferreira, 1997; Casse & Ferreira, 2000a). When some heat deposition occurs at the JED upper layers a typical value of ξ ? 0.1 becomes possible, even up to 0.5 but never reaching unity, in agreement with Eq. (7) (Casse & Ferreira, 2000b). This is a much lower mass loss than that assumed in ADIOS models (Blandford & Begelman, 1999). The fact that the jet torque largely dominates the turbulent torque provides another striking di?erence between the internal structures of SADs and JEDs. Indeed, the angular momentum conservation provides a sonic Mach number measured at the disc midplane ms = ? ur = αv ε(1 + Λ) Cs (11)

which allows to precisely specify the above quantities. Moreover, the ratio of radiation to gas pressure, Thomson opacity, e?ective and central temperatures are Prad = 0.3 mRξ?1 ˙ Pgas τT ? nσT h = 3.8 102 m3/4 m1/8 R 4 ? 16 ˙ Tef f ? 876 m ˙
3ξ 9

(15) (16) (17) (18)




5ξ 47 16 ? 64


To = 3.2 m1/2 m?1/4 R ˙

ξ 7 2?8


where Cs = ?k h is the sound speed. Thus, a SAD displays ms = αv ε ? 1 whereas a JED has a much higher accretion velocity, namely ms ? 1 (Ferreira & Pelletier, 1995; Ferreira, 1997). This has two major consequences. First, a JED is much less dense than a SAD3 . Second, there is a stronger bending of the poloidal ?eld lines. Indeed, in spite of the same turbulent magnetic di?usivity (νm ? νv ), the larger accretion velocity ur leads to an e?ective magnetic Reynolds number Rm ? ε?1 where ε = h/r is the disc aspect ratio (Ferreira & Pelletier, 1995). This translates into + a ?eld at the disc surface verifying Br /Bz ? Rm ε > 1, as ? required to magnetically launch cold jets. Mass conservation in the JED writes n = ˙ Ma (r) m?1 ε?2 4πmp ?k r3 s

The spectrum emitted by an optically thick JED is a multi-blackbody but with a temperature drastically reduced from that of a SAD. As a consequence, the ?ux emitted by the JED is expected to be unobservable with respect to that of the outer SAD. In practice, this mostly depends on the radial extension of the JED. Indeed, the 4 ?ux emitted by the surrounding SAD scales as Tef f,SAD r2 measured at rJ whereas the ?ux emitted by the JED is 4 dominated by Tef f,JED r2 measured at ri . One therefore gets that the ratio of the JED to the SAD ?ux scales as (rJ /ri )/(1+Λ) ? εrJ /ri which is much smaller than unity for reasonable values of rJ . Thus, the values of the ”disc inner radius” (rin ) and ”disc accretion rate” observationally determined from spectral ?ts must be understood here as values at the transition radius, namely rin ≡ rJ and m ≡ m(rJ ): the optically thick JED is spectrally hardly ˙ ˙ visible.

2.4. Non-relativistic electron-proton jets from JEDs
The ejection to accretion rate ratio in a JED writes ˙ ˙ 2Mjet /Ma,J ? ξ ln(rJ /ri ). In principle, the ejection e?ciency ξ can be observationally deduced from the terminal jet speed. Indeed, the maximum velocity reachable along a magnetic surface anchored on a radius ro (between ri and rJ ) is u∞ ? ξ ?1/2 GM/ro in the non-relativistic limit (see Ferreira 1997 for relativistic estimates). Although a large power is provided to the ejected mass (mainly electrons and protons), the mass loss (ξ) is never low enough to allow for speeds significantly relativistic required by superluminal motions: MHD jets from accretion discs are basically non or only mildly relativistic with u∞ ? 0.1 ? 0.8 c (Ferreira, 1997). This is basically the reason why they can be e?ciently self-con?ned by the magnetic hoop stress. Indeed, in relativistic ?ows the electric ?eld grows so much that it counteracts the con?ning e?ect due to the toroidal ?eld. This dramatically reduces the self-collimation property of jets (Bogovalov & Tsinganos, 2001; Bogovalov, 2001; Pelletier, 2004). Calculations of jets crossing the MHD critical points have been undergone under the self-similar ansazt (Casse & Ferreira, 2000b; Ferreira & Casse, 2004). In these calculations, the emission of the MHD jet has been neglected and all the available power is converted into ordered jet kinetic energy. However, a fraction of this power

? 1025 ε?2 mm?1 Rξ? 2 m?3 ˙


where m = M/M⊙ , R = r/rg (rg = GM/c2 ) and m = ˙ ˙ Ma,J c2 /LEdd. This density requires a magnetic ?eld Bz = ? ms

˙ ?o Ma (r)?k 4πr
ξ 5


? 4.4 108 m1/2 m?1/2 R 2 ? 4 G ˙


For illustration, we provide below the case of an optically thick, Thomson dominated and gas pressure supported JED. In this region, the disc aspect ratio is ε = h/r = 2.6 10?3 m1/4 m?1/8 R ˙
ξ 1 4 + 16


It has been recently showed that a previously claimed instability of accretion-ejection structures does not apply to this type of solution (see K¨nigl (2004) and references therein). o

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


is always converted into heat and particle acceleration, leading to emission. In our case, jets from MAES have two distinct spectral components and the resultant SED may therefore be quite intricate. Producing a global SED is out of the scope of the present paper. It requires to ?x several parameters, which is legitimate only by object ?tting. This is postponed for future work.

questionable. However, our framework naturally provides another contribution to the high energy emission as long as a JED is present.

2.4.2. A thermal jet basis
Jet production relies on a large scale magnetic ?eld anchored on the disc as much as on MHD turbulence triggered (and sustained) within it. This implies that small scale magnetic ?elds are sheared by the disc di?erential rotation, leading to violent release of magnetic energy at the disc surface and related turbulent heat ?uxes (e.g. Galeev et al. 1979; Heyvaerts & Priest 1989; Stone et al. 1996; Merloni & Fabian 2002). The energy released is actually tapping the MHD Poynting ?ux ?owing from the disc surface. We can safely assume that a fraction f of it would be deposited at the jet basis, with a total power Pc = f PMHD . The dominant cooling term in this optically thin medium is probably comptonization of soft photons emitted by the outer SAD (with a small contribution from the underlying JED). These are circumstances allowing a thermal plasma to reach a temperature as high as ? 100 keV, (Pietrini & Krolik, 1995; Mahadevan, 1997; Esin et al., 1997). The computation of the exact spectral shape produced by this ”corona” through thermal comptonization requires sophisticated computations (e.g. Haardt 1993; Poutanen & Svensson 1996) which are out of the scope of this paper. Instead, a cut-o? power law shape is generally used as zero-order approximation. In this case, the high energy cut-o? is rougly equal to twice the plasma temperature (see e.g. Petrucci et al. 2000 for more discussion). The power law photon index can also be approximated by a simple fonction of the Compton ampli?cation factor A, which is equal to the ratio of the total luminosity outgoing from the jet basis to the soft luminosity Psof t entering in it (see e.g. Beloborodov 1999; Malzac et al. 2001): Γ ? C(A ? 1)?η with A = 1 + Pc /Psof t (19)

2.4.1. A non-thermal extended jet emission
We expect a small fraction of the jet power Pjet to be converted into particles, through ?rst and/or second order Fermi acceleration, populating the MHD jet with supra-thermal particles. These particles are responsible for the bulk emission of the MHD jet. This is similar to models of jet emission already proposed in the literature (Falcke & Biermann, 1995; Vadawale et al., 2001; Marko? et al., 2001, 2003; Marko?, 2004; Falcke et al., 2004). In these models, the jet is assumed to be radiating self-absorbed synchrotron emission in the radio band becoming then optically thin in the IR-Optical bands and providing a contribution up to the X/γ-rays. A ?at or even inverted spectrum index in the radio band is quite easily achieved by self-collimated jets for reasonable values of the parameters (e.g. the exponent p of the power law particle distribution). Note that the MHD jet due to the MAES yields B ∝ m?1/2 m1/2 . In the framework of Heinz & Sunyaev ˙ (2003), this implies that such a jet would provide correlated radio and X-ray emissions close to the observed 0.7 law, namely FR ∝ FX Gallo et al. (2003); Corbel et al. (2003). However, the spectrum index in the X-ray band would not be steep enough, even taking into account the cooling of the particles. Moreover, the fundamental plane of BH activity of Merloni et al. (2003), namely the correlation between mass, radio and X-ray ?uxes, cannot be explained by such synchrotron jets (Heinz, 2004). Following these authors, we conclude that there must be another signi?cant contribution to the X-ray emission in the Low/hard state. The same conclusion was independently reached by Rodriguez et al. (2004) who suggested that, to explain the energy dependence of the quasiperiodic oscillation (QPO) amplitude in GRS 1915+105, the high energy spectrum of the source must be the sum of di?erent emission processes. Another argument comes from the study of the overall spectral energy distributions. At least in some objects, the extrapolation of the Xray power-law spectrum towards the optical and infrared bands is above the observed ?uxes, which shows that hard X-rays cannot be direct synchrotron radiation from the jet (Kalemci et al., 2005). Moreover, BH XrBs in the hard state generally exhibit a spectrum with a high energy cut-o? around 100 keV (e.g. Grove et al. 1998; Zdziarski & Gierlinski 2003 and references therein). While naturally obtained if the emission is thermal (i.e. a comptonized corona), non-thermal emission requires a ?ne tuning of the parameters that we found

where C and η depend on the geometry of the disc-corona con?guration. In the most general case, Psof t should include the SAD and JED emissions but also the reprocessed radiation from the discs (both JED and SAD) that are partly intercepted by the corona. In consequence, the photon index depends implicitly on parameters like f , Λ, rJ but also on the bulk motion of the corona in a complex manner. This will be precisely discussed in a forthcoming paper where calculations of SEDs will be provided. Simple estimates can be given, however, in the case of large rJ and Λ, since in these conditions the SAD and JED emissions become negligible compared to the reprocessed one. This situation has been precisely studied by Malzac et al. (2001). The parameters C and η of Eq. 19 obtained by these authors are equal to 2.19 and 2/15 respectively. Hard X-rays photon indexes in


Ferreira et al.: An accretion-ejection paradigm for BH XrBs

the range 1.4-2 are easily obtained for di?erent corona velocities and corona aspect ratios (i.e. height/width). These values are in good agreement with what is generally observed in the hard states where we expect large rJ (cf. Sect. 3 for a more detailed discussion). We can note also that a decrease of rJ will result in a larger Psof t , due to the increase of the SAD emission, and thus in a softening of the X-ray spectrum.

is strongly anisotropic. The pair plasma will then experience a strong bulk acceleration due to the recoil term of EIC, an e?ect also known as the ”Compton Rocket” e?ect (O’Dell, 1981; Renaud & Henri, 1998). As was shown in previous works, this ”rocket” e?ect is the key process to explain relativistic motions (Marcowith et al., 1995; Renaud & Henri, 1998). At a given distance of the disc, the bulk acceleration saturates at a characteristic Lorentz factor, depending only on the radiation angular distribution. It is de?ned by the condition that the net radiation ?ux in the comoving frame (after Lorentz transform) vanishes. It can be shown easily that this characteristic Lorentz factor is approximately Γb,eq ? (z/ri )1/4 on the axis of a standard accretion disc (Renaud & Henri, 1998), as long as the distance z veri?es rJ ? z: here the relevant disc inner radius is in fact the transition radius rJ . Noticeably this value does not depend on the disc luminosity (or accretion rate): it is only dependent on the angular distribution of the intensity, i.e. the radial dependency of the temperature T ∝ r?3/4 . The photon ?eld is in fact dominated by photons emitted at r ? z. The modi?cation introduced by the JED in the central region is likely to be immaterial for two reasons. First although the luminosity decreases, the radial dependency remains almost unchanged. Second, as we argue below, the ?nal bulk Lorentz factor depends only on the distance where the plasma decouples from the radiation, and not on the motion close to the core. A pure pair plasma will thus experience a continuous bulk acceleration, the bulk velocity increasing slowly with the distance. At some point, the radiation ?eld becomes too weak to act e?ciently: this happens when the relaxation time towards the equilibrium Lorentz factor becomes larger than the dynamical time z/c. At this distance, the acceleration process stops and the plasma decouples from the external radiation ?eld, moving on at a ballistic constant Lorentz factor Γb,∞ . The asymptotic Lorentz factor depends essentially on the location of this critical distance. In the original O’Dell’s version of this process, the pair plasma was not supposed to be reheated and this e?ect has been shown to be rather ine?cient, because cooling is always much faster than acceleration (Phinney, 1987). In fact, for a cold plasma, the mechanism reduces to the ordinary radiation pressure. Under these condi4/7 tions, the critical distance is approximately ?s ,where ?s = σT Prad,SAD /4πme c3 rJ is the soft photon compactness. For a near Eddington accreting disc, ?s ? 103 and 1/7 Γb,∞ ? ?s ? 2 ? 3 (Phinney, 1987). Although this is indeed a relativistic motion (an apparent superluminal motion is possible), this may not be high enough to account for high values around 5, as observed in microquasars.

2.5. The inner ultra-relativistic pair beam
Since the large scale magnetic ?eld driving the selfcon?ned jet is anchored onto the accretion disc which has a non zero inner radius, there is a natural hole on the axis above the central object with no baryonic out?ow (this also holds for neutron stars). This hole provides a place for pair production and acceleration with the outer MHD jet acting as a sheath that con?nes and heats the pair plasma. This is the microquasar version of the ”two ?ow” model that has been successfully applied to the high energy emission of relativistic jets in AGNs (Henri & Pelletier, 1991; Marcowith et al., 1995, 1998; Renaud & Henri, 1998). The e+ ? e? plasma is produced by γ ? γ interaction, the γ-ray photons being initially produced by a few relativistic particles by Inverse Compton process, either on synchrotron photons (Synchrotron Self Compton or SSC) or on disc photons (External Inverse Compton or EIC). Detailed models for AGNs have shown that all processes can contribute, depending on the physical parameters of the system (magnetic ?eld, disc luminosity, distance). We do not intend to build an explicit Spectral Energy Distribution of the pair plasma here, but we will just discuss the general mechanism of pair beam formation and the relevance of each process in explaining the various non thermal components. It is well known that above 0.5 MeV photons can annihilate with themselves to produce an electron-positron pair. Usually, pairs are assume to cool once they are formed, producing at turn non thermal radiation. Some of this radiation can be absorbed to produce new pairs, but the overall pair yield never exceeds 10 %. A key point of the two-?ow model however is that the MHD jet launched from the disc can carry a fair amount of turbulent energy, most probably through its MHD turbulent waves spectrum. A fraction of this power can be transferred to the pairs (Pe+ e? << PMHD ). Thus the freshly created pairs can be continuously reheated, triggering an e?cient pair runaway process leading to a dense pair plasma (Henri & Pelletier, 1991). As we said, reacceleration is balanced by cooling through the combination of synchrotron, SSC and EIC processes. Synchrotron and SSC emission are quasi isotropic in the pair frame, but the external photon ?eld

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


In the two ?ow model however, continuous reheating of the pairs makes the bulk acceleration more e?cient, acting thus over a much larger distance : the radiation force is multiplied by < γ 2 >, where γ is the random ? ? (or relativistic temperature) of the pair plasma, (not to be confused with the bulk Lorentz factor Γb ). Although the equilibrium Lorentz factor at a given distance is unchanged, the critical decoupling distance is much larger. The asymptotic bulk Lorentz factor becomes (?s < γ 2 > / < γ >)1/7 and values of 5 to 10 can be ? ? easily reached in near-Eddington accretion regime around stellar black holes (Renaud & Henri, 1998). Producing this pair plasma requires thus altogether a strong MHD jet, a radiative non-thermal component extending above the MeV range and a minimal γ ? γ optical depth, namely τγγ ? 1. The non thermal component can indeed be associated with the steep power law observed during the intermediate states, given the fact that it seems to extend to MeV range without any break (McCR03). It is most probably due to Inverse Compton process on the disc photons. Indeed, the optical depth τγγ for absorbing photons with energy Eγ = εme c2 is approximately for a spherical source of radius R ?lled by soft photons with density n(ε) by unit reduced energy: σT ε 1 1 (νLν )me c2 /hε (20) τγγ = n( )σT R = ε ε 4πme c3 R We take a typical soft power-law spectrum νLν = ELE = L0 (E/E0 )?Γ+2 where Γ is the soft photon index, typically around 2.5 for luminous intermediate states. Adopting this nominal value, the γ ? γ optical depth becomes a fonction of the energy Eγ : τγγ (Eγ ) = 0.7 × 262(2.5?Γ) × E0 1keV

jet, explaining the disappearance of the compact jet after a strong ejection event.

3. Canonical spectral states of X-ray binaries 3.1. The crucial roles of rJ and m ˙
From Section 2, it is clear that the spectral appearance of a BH XrB critically depends on the size of the JED relative to the SAD, namely rJ . As stated before, rJ is 2 the radius where the disc magnetization ? = Bz /(?o Ptot ) becomes of order unity. Thus, rJ depends on two quantities Ptot (r, t) and Bz (r, t). The total pressure is directly proportional to m since Ptot = ρ?2 h2 ∝ mm?1 r?5/2 . ˙ ˙ k As a consequence, any variation of the accretion rate in the outer SAD implies also a change in the amplitude of the total pressure. But we have to assume something about the time evolution of the large scale magnetic ?eld threading the disc. Within our framework, m and Bz are ˙ two quantities that may vary independently with time. Let us assume that Bz does not depend on the disc accretion rate. If, for instance, m undergoes a sudden in˙ crease (triggered by, e.g. some disc instability at the outer radii Lasota et al. 1996), then there is a corresponding increase of Ptot which is propagating inwards, eventually reaching the inner JED. Since no magnetic ?ux is being simultaneously added, the region where the vertical magnetic ?eld is close to equipartition shrinks, namely rJ decreases. If, on the contrary, the disc accretion rate decreases (without a corresponding decrease of the magnetic ?ux threading the disc), then the decrease of Ptot requires some di?usion of the vertical magnetic ?eld in the inner regions in order to maintain equipartition, hence the JED expands and rJ increases. According to this simplistic argument, one would expect an anti-correlation between rJ and m, namely a larger m implies a smaller rJ (and vice˙ ˙ versa). Alternatively, one could also argue that a larger m ˙ implies more plasma within the disc and that a larger Bz would then be locally generated by dynamo. If such a process provides Bz ∝ m1/2 , then rJ would always remain ˙ unchanged, whatever m. Another alternative could be ˙ advection of the companion’s magnetic ?eld along with the ?ow. Now, because of the stellar dynamo, such a ?eld could also change with a time scale very di?erent from that related to changes in m. In any case, the amount and ˙ polarity advected along strong accretion phases would be an unknown function Bz (m). ˙ The processes governing the amplitude and time scales of these adjustments of rJ to a change in m are far too ˙ complex to be addressed here. They depend on the nature of the magnetic di?usivity within the disc but also on the radial distribution of the vertical magnetic ?eld. We will simply assume in the following that rJ and m are ˙ two independent parameters. In that respect, our view is very di?erent from that of Esin et al. (1997); Mahadevan

L0 0.1LEdd Eγ 1MeV

R 30rg



Thus, assumptions that appear quite reasonable for the luminous intermediate state provide good conditions for pair creation. It is noteworthy that the pair beam is intrinsically highly variable and subject to an intermittent behavior. Indeed, once the pair creation is triggered, a regulation mechanism must occur to avoid in?nite power of the pair plasma and limit the pair run-away. This is probably accomplished by the quenching of the turbulence (Pe+ e? vanishes) when most of its energy is suddenly tapped by the catastrophic number of newly created pairs. These pairs will therefore simply expand freely, con?ned by the heavier MHD jet. One would then expect a ?are in the compact region, followed by the ejection of a superluminal radio component, analoguous to those observed in AGNs (Saug? & Henri 2005, A&A submitted). Such a situation e can repeat itself as long as the required physical conditions are met. Alternatively, it may also that the formation of a dense pair beam destroys the surrounding MHD


Ferreira et al.: An accretion-ejection paradigm for BH XrBs

Fig. 2. The canonical spectral states of BH X-ray binaries. (a) Quiescent state obtained with a low m and a large ˙ rJ : the Jet Emitting Disc (JED) occupies a large zone in the accretion disc. (b) Hard state with much larger m and ˙ smaller rJ : the pair creation threshold is still not reached. (c) Soft state when m is such that there is no zone anymore ˙ within the disc where an equipartition ?eld is present: no JED, hence neither MHD jet nor pair beam. (d) Luminous Intermediate state between the Hard and the Soft states: the high disc luminosity (SAD) combined with the presence of a MHD jet allows pair creation and acceleration along the axis, giving birth to ?ares and superluminal ejection events. (1997) who considered only the dependency of m to ex˙ plain the di?erent spectral states of BH XrBs. SED probably very similar to that of an ADAF. We thus expect rJ ? rtr . The weak MHD Poynting ?ux prevents the ignition of the pair cascade process and no pair beam is produced. It must be noted that slightly more complicated situations can arise depending on the actual value of m. For ˙ instance, the innermost denser regions of the JED could become optically thick for larger values of m, i.e closer to ˙ the Hard state level.

3.2. The Quiescent state
This state is characterized by a very low accretion rate (m as low as ? 10?9 ) with a hard X-ray component. The ˙ ADAF model has been successfully applied to some systems with a large transition radius between the ADAF and the outer standard disc, namely rtr ? 103 ? 104 rg (e.g. Narayan et al. 1996; Hameury et al. 1997). However, such a model does not account for jets and their radio emission, even though XrBs in quiescence seem also to follow the radio/X-ray correlation (e.g. Fender et al. 2003; Gallo et al. 2004, 2005). Within our framework, a BH XrB in quiescence has a large rJ , so that a large zone in the whole disc is driving jets (Fig. 2a). The low m provides a low synchrotron jet ˙ luminosity, while the JED is optically thin, producing a

3.3. The Hard state
Within our framework, the JED is now more limited radially than in the Quiescent state, namely rJ ? 40 ? 100 rg (Fig. 2b). This transition radius corresponds to the inner disc radius rin as obtained within the SAD framework (Zdziarski et al., 2004). Due to the higher m, the JED may become optically thick, ˙ which is required to explain the broad iron lines ob-

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


served in some binary systems (Nowak et al., 2002; Sidoli & Mereghetti, 2002; Frontera et al., 2001). The low velocity of the plasma expected at the jet basis is in good agreement with recent studies of XrBs in Hard state (Maccarone, 2003; Gallo et al., 2003). It can also explain the apparent weakness of the Compton re?ection (Zdziarski et al., 1999; Gilfanov et al., 1999) as already suggested by Marko? et al. (2003, see also Beloborodov 1999; Malzac et al. 2001) and tested by Marko? & Nowak (2004). In any case, the JED intrinsic emission is weak with respect to that of the outer standard disc: most of the accretion power ?ows out of the JED as an MHD Poynting ?ux. Nevertheless, the threshold for pair creation is still not reached and there is no pair beam, hence no superluminal motion. The MHD power is therefore shared between the jet basis, whose temperature increases (the thermal ”corona”) producing X-rays, and the large-scale jet seen as the persistent (synchrotron) radio emission.

elsewhere. The crucial point however is that, in our framework, luminous intermediate states (the so-called Very High State or VHS) with high m provide the best conditions ˙ for the formation of the ultra-relativistic pair beam, as described in details in Sect. 2.5: (1) a high luminosity, (2) a high energy steep power law spectrum extended up to the γ-ray bands and (3) the presence of the MHD jet . The two ?rst characteristics enable a γ ? γ opacity larger than unity (cf. Eq. 22 of Sect. 2.5), while the MHD jet allows to con?ne the pair beam and maintain the pair warm, a necessary condition to trigger a pair runaway process. The total emission would be then dominated by the explosive behavior of the pairs, with the sudden release of blobs. Each blob produced in the beam ?rst radiates in X and γ-ray, explaining the hard tail present in this state, and then, after a rapid expansion, produces the optically thin radio emission. This pair beam would also explain the superluminal ejections observed during this state in di?erent objects (e.g. Sobczak et al. 2000; Hannikainen et al. 2001). We conjecture that the exact moment where this occurs corresponds to the crossing of the ”jet line” recently proposed by Fender et al. (2004) (see also Corbel et al. 2004). This corresponds to a transition from the ”hard” intermediate state to the ”soft” one. The rapid increase of the pair beam pressure in the inner region of the MHD jet, during a strong outburst, may dramatically perturb the MHD jet production. Indeed, a huge pair pressure at the axis may enforce the magnetic surfaces to open dramatically, thereby creating a magnetic compression on the JED so that no more ejection is feasible. Alternatively, it is also possible that the racing of the pair process completely wears out the MHD Poynting ?ux released by the JED, suppressing the jet emission or even the jet itself. Whatever occurs (i.e. jet destruction or jet fading), we expect a suppression of the steady jet emission when a large outburst sets in. Interestingly, the detailed spectral and timing study of the radio/X-ray emission of four di?erent black hole binaries during a major radio outburst (Fender et al., 2004) shows a weakening and softening of the X-ray emission as well as a the quenching of the radio emission after the burst. This is in good agreement with our expectations since the cooling of the pair beam should indeed results in a ?ux decrease and a softening of its spectrum.

3.4. The Soft state
Our interpretation of the Soft state relies on the disappearance of the JED, i.e. when rJ becomes smaller or equal to ri (Fig. 2c). Depending on the importance of the magnetic ?ux in the disc, this may occur at di?erent accretion rates. Thus, the threshold in m where there is no ˙ region anymore in the disc with equipartition ?elds may vary. The whole disc adopts therefore a radial structure akin to the standard disc model. Since no MHD jet is produced, all associated spectral signatures disappear. Even if pair production may take place (when m is large), the ˙ absence of the con?ning MHD jet forbids the pairs to get warm enough and be accelerated: no superluminal motion should be detected. Note however that the presence of magnetic ?elds may be the cause of particle acceleration responsible for the weak hard-energy tail (McCR03, Zdziarski & Gierlinski 2003 and references therein).

3.5. Intermediate states
This state has been ?rst identi?ed at large luminosities (L > 0.2 LEdd ) and was initially called Very High state. However, high luminosity appeared to not be a generic feature since it has be observed at luminosities as low as 0.02 LEdd (McCR03, Zdziarski & Gierlinski 2003). Therefore, the most prominent feature is that these states are generally observed during transitions between Hard and Soft states. Within our framework, they correspond to geometrical situations where rJ is small but remains larger than ri (Fig. 2d). The ?ux of the outer standard disc is thus important while the JED is occupying a smaller volume. The consequences on the spectral shape are not straightforward since the importance of the di?erent spectral components relative to each other depends on the precise values of rJ and m. Such study is ˙ out of the scope of the present paper and will be detailed

4. Temporal properties
Since both SAD and JED are quasi keplerian, the ?rst obvious time scale is the keplerian orbit time, namely τD (rJ ) = m 2π = 0.1 ?k 10 rJ 50rg



measured here at the transition radius rJ . Since gravity is the dominant force, this time is also the dynamical time


Ferreira et al.: An accretion-ejection paradigm for BH XrBs

involved whenever physical conditions are locally modi?ed within the disc. This time scale is much smaller than the duration of a spectral state or even the transition between two states (but comparable to some timing features, see below). In fact, the time evolution of BH XrBs requires large variations of the disc accretion rate m. The time ˙ scales involved, namely rising and decay times but also periodicity, if any, depend therefore on conditions at the outer accretion disc. The inner disc region will thus respond to these variations with its own time scales, which introduces a delay but more importantly a temporal convolution (it acts as a ?lter). We do dot intend to address the issue of the timing behavior of BH XrBs. As discussed earlier, this requires, within our framework, to take into account the evolution of the large scale magnetic ?eld. Here, we just remark that the presence of these four dynamical components (SAD, JED, MHD jet and pair beam) introduces interesting temporal properties that may be relevant to observations. Let us assume an increase in m triggered at some ˙ outer radius rout ? rJ . This information propagates towards the center with the accretion ?ow, as a front of increased total pressure. The time scale involved is therefore τacc,SAD (rout ) ? rout /ur . If we assume that rJ decreases (because of a decrease in ?), then the JED (and its associated MHD jets) will progressively disappear. This evolution from a Hard state to an Intermediate or Soft state will be controlled by the advance of this front, namely τacc,SAD ? 170 α?1 v ε 0.01

m 10

rJ 50rg




If, due to a change in m, the radial distribution of the ˙ vertical magnetic ?eld needs to be readjusted, then this is done quite fast. Indeed, within the SAD, the time scale for ?eld di?usion is the accretion time scale, since τdif f = r2 /νm ? τacc Rm with Rm ? 1. Inside the JED, the di?usion time scale is much longer than the accretion time scale because Rm ? ε?1 (Ferreira & Pelletier, 1995). However, the accretion time scale inside the JED is itself much shorter than in the SAD (see Eq. 11), so that τdif f,JED ? αv τacc,SAD (24)

ξ) display τjet (r) ? τD (r) but undergo a recollimation shock right after that. Jet solutions with smaller ξ propagate much farther away and have τjet (r) ? 102 τD (r). It is not clear yet if these time scales provide an explanation to some observed timing properties. But the fact that jets are indeed observed is a strong indication that one should take into account their dynamics. In our description of the canonical spectral states of XrBs we did not mention the important issue of quasiperiodic oscillations or QPOs. Low-frequency (0.1-30 Hz) QPOs in the X-ray bands (2-30 keV) are indeed observed in the Hard and luminous Intermediate (VHS) states. In the latter state, higher frequencies (up to 300 Hz) are also present (e.g. Remillard et al. 2002, McCR03). We do not o?er yet any precise explanation to these phenomena. However, we note that QPOs are stronger in the hard Xray bands (? 20-30 keV, e.g. Rodriguez et al. 2004) and are correlated with the radio ?ux (Migliari et al., 2005). Their emission must then be related to the dynamics involved in the ejection events (both steady and eruptive). Interestingly, our framework provides a promising environment for the onset of instabilities leading to QPOs. The inner pair beam is an intermittent ?ow from the inner regions (several ri ) and could therefore be responsible for some of the high frequency QPOs. On the other hand, the MHD jet may provide low frequency QPOs. For instance, if some disc material, continuously ejected just outside rJ , is failing to become super-Alfv?nic, then one would expect e waves going back and forth between the disc surface and the Alfv?n surface (located at rA and zA in cylindrical e coordinates) where a shock is occurring. A crude estimate of the frequency gives ν ? VA /zA ? ?? rA /zA ? ?k (rJ ) since ?? rA ? VA and zA ? rA in magnetically driven jets (Ferreira, 1997) and ?? = ?k (rJ ) is the rotation rate of the magnetic surface. For a radius rJ ? 50 rg , this gives a ? 10 Hz QPO. This clearly deserves further investigation.

5. Summary and concluding remarks
We present in this paper a new paradigm for the accretionejection properties of Galactic Black Hole X-ray binaries. We assume the existence of a large scale magnetic ?eld of bipolar topology in the innermost disc regions. Such a ?eld allows for several dynamical phenomena to occur whose relative importance determine the observed spectral state of the binary. The dynamical constituents are: (1) an outer standard accretion disc (SAD) for r > rJ , (2) an inner Jet Emitting Disc (JED) for r < rJ driving (3) a selfcollimated non-relativistic electron-proton surrounding, when adequate conditions are met, (4) a ultra-relativistic electron-positron beam . The dynamical properties of each constituent have been thoroughly analyzed in previous works (e.g. Shakura & Sunyaev 1973; Henri & Pelletier 1991; Ferreira & Pelletier 1995; Marcowith et al. 1997; Renaud & Henri 1998; Saug? & Henri 2003, 2004), but it e is the ?rst time where they are invoked altogether as necessary ingredients to reproduce the di?erent spectral states of a same object.

Another interesting timing feature is introduced by the MHD jets launched from the JED. Indeed, any adjustment in the disc leads inevitably to a modi?cation of the jet parameters, e.g. the ejection e?ciency ξ. The time scale for this readjustment can be considered to be of the order of the travel time of the fast MHD waves, namely
sF M

τjet (r) ?

ds VF M


where VF M is the speed of the fast magnetosonic wave and the integration is made along a magnetic surface anchored at a disc radius r (from the disc surface h to the fast point sF M ). We computed this time using the MAES solutions of Ferreira (1997) and illustrated in his Fig. 6. Solutions crossing the fast point right after the Alfv?n point (larger e

Ferreira et al.: An accretion-ejection paradigm for BH XrBs


We showed that the various canonical states can be qualitatively explained by varying independently the transition radius rJ and the disc accretion rate m. In our ˙ view, the Quiescent and Hard states are dominated by non relativistic jet production from the JED, providing henceforth a persistent synchrotron jet emission. The Soft state is obtained when the transition radius rJ becomes smaller than the last marginally stable orbit ri , a SAD is established throughout the whole accretion disc. Intermediate states, between Hard and Soft, are expected to display quite intricate and variable spectral energy distributions. Luminous Intermediate states, obtained during the Hard-to-Soft transitions, are those providing the unique conditions for intermittent pair creation. These pairs give rise to a ultra relativistic beam propagating on the MHD jet axis, explaining both the observed superluminal motions and hard energy tail. The dynamical structure presented here (JED, SAD, MHD jet and, occasionally, a pair beam) seems to be consistent with all available information about the canonical spectral states of BH XrBs. However, a more quantitative analysis is critical. In particular, we need to show that the base of the MHD jet can indeed provide a hot corona with the correct spectral signature. Then, a precise estimate of the radio/X-ray correlation predicted by our model and its comparison to observations will be a test of prime importance for its validity. This is postponed to a future work (Petrucci et al., in preparation). In our view, the magnetic ?ux available at the inner disc regions is a fundamental and unavoidable ingredient that most probably varies from one system to another. Since changing the amount of magnetic ?ux changes the transition radius rJ , the characteristic value of m ˙ (hence luminosity) associated with each spectral state is also modi?ed. Also, if accreting material is carrying magnetic ?ux of opposite direction (Tagger et al., 2004), then this should lead to a major readjustment of the whole magnetic structure. Clearly, taking into account the advection of a large scale magnetic ?eld within the disc introduces a whole new set of variable phenomena. Finally, we note that the typical values of the magnetic ?eld required to steadily launch jets from JEDs, given in Eq. 13, are consistent with observational estimates (Gliozzi et al., 1999; Gnedin & Natsvlishvili, 1997; Gnedin et al., 2003). We expect that BH XrBs should radiate above the MeV range during luminous intermediate states, when pairs are produced. A similar proposal has been developed recently by Bosch-Ramon & Paredes (2004b,a) but it is here a natural outcome of our model. Very interestingly, such a high energy emission has been recently detected by the HESS instrument in the TeV range (Aharonian et al., 2005). Note also that two microquasars were already detected by EGRET, LS 5039 (Paredes et al., 2000) and LS I +61 303 (Massi et al., 2004, for a recent review), and there is possibly other

unidenti?ed galactic EGRET sources (Paredes, 2004). Besides, the γ-ray emission of the pair beam can occur further away along the jet at the γ-ray photosphere, as proposed for AGNs (e.g. Marcowith et al. 1995). Noticeably, γ-ray spectra of the possible EGRET counterparts seem to exhibit a break in the MeV range, very similar to that observed in many AGNs. This break could be explained by the transition from the optically thin X-ray component to the optically thick, photosphere dominated, γ-ray component. This prediction of γ-ray emission of microquasars during very high ?aring states could be tested by future GLAST observations.
Acknowledgements. We thank S. Corbel for a careful reading of the manuscript and T. Belloni for having sent us a draft of its paper before it was completely accepted.

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