It is now widely accepted that accretion of matter onto a central object plays a major role in astrophysics: in active galactic nuclei (AGN), young stellar objects (YSOs), but also in evolved binary systems like cataclysmic variables or low-mass X-ray binaries.
The standard theory of accretion discs (Shakura & Sunyaev 1973, Novikov & Thorne 1973, Lynden-Bell & Pringle 1974) assumes the presence of a turbulent viscosity that allows the matter to loose its angular momentum and mechanical energy. This energy is then radiated away at the disc surfaces, providing the observed luminosity (e.g., Bregman 1990, Bertout et al. 1988). However, such a theory is unable to explain the origin, acceleration and collimation of bipolar jets, that are emanating from radio loud AGN and quasars (Bridle & Perley 1984), all YSOs (Lada 1985) and some galactic objects like SS 433, Sco X-1 (Padman et al. 1991) and "microquasars" (Mirabel et al. 1992).
In the vicinity of a black hole, the jet plasma has to come from a surrounding accretion disc. Lynden-Bell (1978) suggested that in the framework of a thick accretion disc, jets could be produced in the inner funnel around the axis of the torus, and accelerated like in a De Laval nozzle. Such a thick torus could be either radiation-supported (with a super-Eddington accretion rate, e.g. Abramowicz et al. 1980), or ion-supported (with a sub-critical accretion rate, Rees et al. 1982). Jets would then be accelerated by radiation pressure (Abramowicz & Piran 1980) or by the rotational energy of the central black hole (Blandford & Znajek 1977). This latter process, unique possibility within the second scenario, invokes a large scale magnetic field dragged in by the disc, braking the fastly rotating hole and transferring its energy to matter (see also Phinney 1983). However, it has been shown that such thick tori are violently unstable (Papaloizou & Pringle 1984, Zurek & Benz 1986, Begelman et al. 1987), casting therefore strong doubts upon their viability to produce jets.
The remaining scenario invokes a large scale magnetic field, anchored on a geometrically thin (Keplerian) accretion disc (Blandford & Payne 1982, hereafter BP82). These authors showed that this magnetic field could brake the disc and carry away its angular momentum. If jets carry a current, then the toroidal component of the magnetic field would provide a tension that naturally confines the jet (previously recognized by Chan & Henriksen 1980).
For protostars, the situation is more complex, since the observed jets could be either stellar winds (Canto 1980, Hartmann et al. 1982, Lago 1984) or disc winds (Pudritz & Norman 1983, Uchida & Shibata 1985). However, both mass and momentum fluxes of the observed outflows are much higher than the ones provided by the protostar luminosity, hence forbidding both thermally and radiation pressure driven stellar winds (DeCampli 1981, Königl 1986). The possibility remains that stellar magnetic fields play a major role in producing a wind (Mestel 1968, Hartmann & MacGregor 1982, Sakurai 1985, Tsinganos & Trussoni 1991, Sauty & Tsinganos 1994). But the strongest argument in favour of disc-driven jets is certainly the observed correlation between signatures of accretion and ejection (Cabrit et al. 1990, Hartigan et al. 1995).
To summary, one can conclude that both observational and theoretical investigations tend to show that, in order to produce powerful self-collimated jets, one has to rely on an accretion disc and a large scale magnetic field. Of course, the possibility that jets arise from the interaction between the central object magnetosphere and the disc has still to be worked out (Camenzind 1990, Shu et al. 1994). Nevertheless, the study of such an interaction requires first the deep understanding of the interplay between accretion and ejection processes. Hereafter, we call Magnetized Accretion-Ejection Structures (MAES), objects where these two processes are interdependent.
There have been a number of studies of magnetized jets in the past (BP82, Camenzind 1986, Lovelace et al. 1987, Heyvaerts & Norman 1989, Chiueh et al. 1991, Pelletier & Pudritz 1992, Li et al. 1992, Appl & Camenzind 1993a, Rosso & Pelletier 1994, Contopoulos 1995, to cite only a few), but all these works were focused on jet dynamics. Thus, it was not yet proved that the underlying disc could indeed provide the required boundary conditions.
Despite serious advances in the theory of magnetized accretion discs driving jets (Königl 1989, Ferreira & Pelletier 1993a, 1993b, 1995, Wardle & Königl 1993, Li 1995), this question has not yet been fully addressed. Indeed, in both Wardle & Königl and Li approaches, the disc solutions were obtained by not properly treating the disc vertical equilibrium and were directly matched to BP82's jet solutions (see Sect. 4.2.1). Moreover, by doing so, they were not able to specify the physical process leading plasma to change its radial motion (accretion) into a vertical one (ejection). Ferreira & Pelletier (1995, hereafter FP95) constructed disc solutions by taking into account all the dynamical terms, thus being able to answer this question, as well as derive the physical conditions required to magnetically launch jets. However, it remained to be proved that their solutions could indeed produce super-Alfvénic jets.
The goal of this paper is therefore to construct global, non-relativistic solutions for magnetically-driven jets from Keplerian discs. Our treatment allows a smooth transition between the resistive disc and the ideal MHD jet. This paper is organized as follows. We start by briefly recalling the MHD equations of MAES and their main features. In particular, we expose some general results on the physical processes that govern the disc. Sect. 3 is devoted to the properties of magnetically-driven jets and the constraints arising from their interplay with the underlying disc. Self-similar, non-relativistic solutions that smoothly cross both slow-magnetosonic and Alfvén critical points are displayed in Sect. 4. In the following section, we show the asymptotic behaviour of self-similar jets and investigate analytically the reason for their systematic behaviour. We conclude by summarizing our results in Sect. 6.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998