A huge amount of data at all wavelengths has been collected during the last 10-20 years on black hole X-ray binaries (hereafter BHB). A glaring example is the satellite RXTE that revolutionized their study by revealing the richness of their timing and spectral properties. A rough picture of their evolution has then begun to emerge (see Corbel at al. 2004; Fender et al. 2006; Remillard & McClintock 2006 or Done et al. 2007 for recent reviews). X-ray binaries spend most of their time in quiescence at very low mass accretion rates. They occasionally produce outbursts that last from a few months to a year, during which their flux rises by several orders of magnitude across the whole electromagnetic spectrum. An example of light curve is shown in the right panel of Fig. 1 for the 2002-2003 outburst of the famous BHB GX 339-4. The origin of these outbursts is commonly explained by the release of gravitational power of the accreting material coming from the secondary star and forming an accretion disc around the central compact object. The gas drifts slowly in the accretion disc and, as it approaches the black hole, it is heated up to very high temperatures. Through relatively complex mechanisms, X-ray binaries are also able to eject (similarly to Active Galactic Nuclei) a fraction of the accreting material at relativistic speed in the form of collimated jets, usually observed in the radio band but that can, at least in extreme cases, contribute significantly to the X-ray emission (Corbel et al. 2002; Rodriguez et al. 2008). Jetted X-ray binaries are also called microquasars due to their global similarities, but on a much smaller scale, to quasars (Mirabel et al. 1992; Mirabel & Rodriguez, 1998, 1999).

Figure 1: Left: Count rate and hardness light curves of the BHB GX 339-4 during its 2002-2003 outburst observed by RXTE (from Belloni et al. 2005). The letters (A, B, C, D) indicate different time of the outburst and are also reported on the right plot. Right: Corresponding Hardness-Intensity diagram with a typical hysteresis behavior (see text for the meaning of the A-B-C-D steps).

During the outburst, a BHB shows very different spectral and temporal states than can be easily distinguished in the so-called hardness-Intensity Diagram (HID) where the X-ray luminosity is plotted versus the hardness ratio (HR) of the X-ray spectrum, producing an hysteresis with a typical Q-shaped track. The corresponding HID of the 2002-2003 outburst of GX 339-4 is shown in the right panel of Fig. 1. At the beginning of the outburst (A-B segment in the HID), the system is in the so-called hard state during which the X-ray spectrum has a hard power law shape up to a few tens of keV, signature of non-thermal processes in a very hot, optically thin, plasma (usually called the 'corona'). The radio emission observed in this state, that extends up to the IR, is believed to be entirely produced by a steady jet, usually called the “compact jet”, based on its very small size (few tens of a.u.). Their flat/inverted radio/IR spectrum fit very well with that expected from a stratified self-absorbed compact synchrotron jet (Blandford & Koenigl 1979).

Then, when the system reaches high luminosities (B-C segment in the HID), it transits in a few days, through the bright intermediate state, into the so-called soft state. Discrete optically thin super-luminal ejections occur at the transition. It is still not clear yet whether these discrete ejections differ fundamentally from the flat-spectrum steady jets observed in the hard states or if they are different manifestations of the same phenomenon. In the soft state (C-D segment in the HID), the spectrum is dominated by a bump in the soft X-rays (< 2 keV) commonly interpreted by the thermal emission from an optically thick accretion disc. In this state, the radio/IR emission is strongly reduced (e.g. Coriat et al, 2009) and even undetectable in most cases. This suggests the disappearance (or strong fading) of the jet component. At the end of the outburst (D-A segment in the HID), the accreting system turns back to the hard state, transiting through the faint intermediate state with the reappearance of the radio/IR emission (but without super-luminal ejection), and usually falls back to the quiescent state at the end of the outburst. Examples of typical X-ray spectra in the soft and hard states are plotted in the left panel of Fig. 2.

The Q-shaped loop followed by BHB in the HID is characteristic of an hysteresis behavior i.e. the luminosities at which the systems transit from hard to soft states differ by a factor of a few to the luminosities of the reverse transition (e.g. Dunn et al. 2010). Above a luminosity of the order of 0.1-1% of the Eddington one, the systems can be either in a hard or a soft state depending if it is in the rising of fading phase of the outburst. The mass accretion rate is therefore not the unique parameter governing the transition.

BHB also exhibit noticeably different X-ray timing properties between the hard and soft states. In the hard state, the Power Density Spectrum (PDS) Pν can be described as a band limited noise with a ‘flat top’ hat, in the ν Pν space. A good fit requires however the addition of a series of generally broad peaked noise components (Lorentzians). One can also find thin features, especially in the bright hard states and intermediate states, referred to as Quasi- Periodic Oscillations (QPO) with frequencies in the range 0.1-50 Hz. During the transition to the soft state, and close to the super-luminal ejection events, most of the variability suddenly disappears. In the soft state, the power density spectrum is featureless and its integrated amplitude (also called the rms) has a much lower level than in the hard state. Examples of X- ray PDS in the hard and soft states are plotted in the right panel of Fig. 2. Fast variability is also observed in Optical and IR with very complex interconnections with the X-rays (e.g. Kanbach et al. 2001; Hynes et al. 2003; Malzac et al. 2003).

Figure 2: Typical X-ray spectra (left) and PDS (right) in the hard/soft (blue/red) states of the BHB Cygnus X-1.

Multi-wavelength campaigns, like those done in X-ray and Radio in the last 10 years, were crucial to bring to light the importance of the ejection phenomena during the outburst. In this respect, the strikingly tight correlation observed, on several order of magnitudes, between the radio emission, coming from the compact jet, and the X-ray emission from the inner accretion flow (Corbel et al. 2000, 2003, 2011; Gallo et al. 2003) revolutionized the field for several reasons (see Fig. 3). First, it demonstrated that two wave bands and their associated components (jet and inner accretion flow, respectively) were intimately related whereas before they had been treated as separate objects. Secondly, it opened the door for new progress in the understanding of the physics close to the BH which, prior to this discovery, had been thought to lie in the X-ray regime alone. The X-ray/radio correlation still brings very constraining information and, very recently, it was noticed that some BHB (the so-called “outliers”) followed a radio-X-ray luminosity correlation different from, and steeper than, the “historical” one (e.g. Coriat et al. 2011). Up to now, there is no clear reason why these “outliers” differ from the others. The correlation was also extended to AGNs if one includes an additional term to take into account the mass of the central black hole (Merloni et al. 2003; Falcke et al. 2004).

Figure 3: The radio/X-ray correlation observed for different X-ray binaries (from Coriat et al. 2011). We can distinguish two branches: the “historical” one, followed by e.g. GX 339-4, and the recently discovered steeper one followed by the so-called “outliers” (e.g. H1743- 322).

The recent years also demonstrated that relativistic jets may be the most significant output channels of the accretion power for X-ray binary systems, either in the weakly accreting regime, i.e. in quiescence and hard states (Corbel et al. 2000, 2003; Fender et al. 2003; Malzac et al. 2004; Corbel et al. 2006, 2008) or in the most luminous states, associated with the major superluminal jets during transition states (Rodriguez et al. 2008). Jets also appear as powerful multi-wavelength emitters: from radio (e.g. Corbel et al. 2003), near infrared and optical (Corbel & Fender 2002) and even up to X-rays (Corbel et al. 2002, 2005) or gamma- rays (Abdo et al. 2009). Jets, and more generally ejection phenomena, appear then as crucial ingredients in the physical processes governing BHB.

Following the Blandford & Payne pioneering work, it has been realized that jets could extract a significant fraction of the underlying disc angular momentum and accretion power. The whole structure of the disc, the so-called Jet Emitting Discs (JED hereafter, see Fig. 4), should then be revisited by taking the disc-jet interrelation into account. This was done more than 10 years ago, in the IPAG sherpas team, by solving the full set of dynamical MHD equations describing a resistive, viscous accretion disc thread by a large scale magnetic field without neglecting any term (Ferreira & Pelletier 1995; Ferreira 1997; Casse & Ferreira 2000a, 2000b; Ferreira & Casse 2004; Ferreira 2002, 2008 and references therein). This set of MHD equations have been solved within a self-similar Ansatz, from the disc mid-plane to the jet termination point, subjected to the constraint of smoothly crossing the critical points of the flow (mainly slow-magnetosonic and Alfvén). These two regularity conditions severely constrain the parameter space of the JEDs solutions. Indeed, defining the disc magnetization μ as the ratio of the magnetic pressure to the total pressure, we have shown that powerful jets can only be obtained with 0.1 < μ < 1, namely a large-scale field close to equipartition. This result was in severe contrast with previous works (e.g. Ogilvie & Livio 1998, 2001) and explains why the latter could not obtain super-Alfvénic steady-state jets from thin discs. Our JED framework differs drastically from other accretion-ejection studies where the disc was only treated as a boundary condition. To date, it is the only steady-state disc model capable of relating disc properties to jet properties.

Figure 4: A schematic view of the accretion-ejection model developed in the IPAG Sherpas team. The accretion disc evolves from a Standard Accretion Disc solution (Shakura-Sunyaev 1973) in its outer region (R>Rtr) to a Jet Emitting Disc solution in its inner region (R < Rtr) where the conditions are fulfilled to the production of a powerful, self-collimated jet

The CHAOS project was a collaboration of leading competences with state- of-the-art skills on accretion-ejection processes, radiative transfer numerical simulations and multi-wavelength observations, in order to lead a decisive advance in our understanding of accretion-ejection processes in compact objects. Building on the rich expertise we developed in our past ANR project Astro2flow (2006-2009), we proposed to carry on developing our global holistic theoretical framework with the additional ambition of a direct comparison with the most up-to- date multi-wavelength observations.

Our aim was to develop new numerical tools able to produce, within the dynamically consistent accretion-ejection framework proposed by the IPAG group, broadband SEDs directly comparable to real data. New tools, developed with the IRAP group, were used to produce realistic SEDs and constrain the required changes in the model parameter to reproduce the observed HID. We were able to investigate the predictions of different coronal geometry (like ADAF or JED) and parameters. We were also able to make robust predictions regarding the polarization of the X-ray emission of BHBs.

Most of the developments proposed in this project required essential inputs that was provided from observations: spectral shapes, timing properties, multi-wavelength behavior etc... The AIM group aimed at constructing the most generic diagram of black holes properties along the course of their outbursts in order to characterize the evolution of the accretion-ejection coupling with time to provide the most important set of constraints for models to date. These were informations of crucial importance as they allowed falsifying the theoretical framework and were unaccessible for non-observer experts.