1 Introduction

Jets have been observed in many systems including active galaxies, X-ray binaries, black holes X-ray transients, supersoft X-ray sources and young stellar objects (Königl 1997; Livio 1999; Mirabel 2001). Each of these systems is considered to contain an accretion disk, while jet-speeds have been verified to be of the order of the escape velocity at the vicinity of the central object (Mirabel 1999; Livio 1999 and the references therein). Recent observations of the M 87 galaxy reveal a significant jet-collimation already at 100 gravitational radii from the central engine, and that jet-launching should occur close to the last stable orbit (Biretta et al. 2002).

Several scenarios have been suggested to uncover the mechanisms underlying jet-initiations and their connection to accretion disks (Pudritz & Norman 1986). In most of these models magnetic fields (-MFs) are considered to play the major role in powering and collimating jets (e.g., the magneto-centrifugal acceleration model of Blandford & Payne 1982, the ion-torus model of Rees et al. 1982, X-point model of Shu et al. 1994, ADAF and ADIOS models of Narayan & Yi 1995 and Blandford & Begelman 1999).

Previous radiative hydrodynamical studies without magnetic fields have confirmed the formation of a transition layer (-TL) between the disk and the corona, governed by thermally-induced outflows (Hujeirat & Camenzind 2000). The aim of this paper is to show that incorporating large scale magnetic fields (-MFs) manifests such formation and dramatically strengthen the dynamic of the in- and out-flows. Moreover, the TL is shown to be an optimal runaway region where highly energetic ion-jets start off. The back reaction of jet-flows on the structure of the disk and on the corona surrounding the nucleus is investigated also.

The study is based on self-consistent 3D axi-symmetric quasi-stationary MHD calculations, taking into account magnetic and hydro-turbulent diffusion, and adopting the two-temperature description (Shapiro et al. 1976). This adaptation is fundamental as 1) the dynamical time scale around the last stable orbit may become shorter than the Coulomb-coupling time. Therefore turbulent dissipation, adiabatic or shock compression preferentially heat up the ions rather than electrons ( $T_{\rm i} \propto \rho^{2/3}_{\rm i}$, while $T_{\rm e} \propto \rho^{1/3}_{\rm i}$). 2) Taking into account that ions radiate inefficiently, having virial-heated ions in the vicinity of the last stable orbit is essential for the total energy-budget of large scale jets.

Figure 1: The model consists of $10^8~M_{\odot}$ Schwarzschild BH at the center (its gravity is described in terms of the quasi-Newtonian potential of Paczynski & Wiita 1980), and an SS-disk (blue color, extending from r=1 to r=20 in units of the radius of the last stable orbit i.e., in $3\times R_{\rm Schwarzschild}$, thickness $H_{\rm d} = 0.1 r,$ an accretion rate of  ${~\dot{\cal M}}= 0.01\times {~\dot{\cal M}}_{\rm Edd},$ and a central disk temperature of $T=10^{-3}~ T_{\rm virial}$ at the outer radius). The ion-temperature $T_{\rm i}$ is set to be equal to the electron temperature $T_{\rm e}$ initially.) The low-density hot corona ( $T=T_{\rm virial}$, and density $\rho (t=0,r,\theta )=10^{-4}\rho (t=0,r,\theta =0$) is set to envelope the disk. A large scale magnetic field is set to thread the disk and the overlying corona (blue lines, $\beta = P_{\rm mag}/P_{\rm gas} = 1/4$ at the outer radius, where $P_{\rm gas}$is the ion-pressure, $P_{\rm mag} = B\cdot B/8 \pi$ is the magnetic pressure, and B is the magnetic field whose components are $(B_{\rm P}, B_{\rm T})= (B1,B2,B_{\rm T})$.) The low-density hot corona ( $T=T_{\rm virial}$, and density $\rho (t=0,r,\theta )=10^{-4}\rho (t=0,r,\theta =0$) is set to envelope the disk. A large scale magnetic field is set to thread the disk and the overlying corona (blue lines, $\beta = P_{\rm mag}/P_{\rm gas} = 1/4$ at the outer radius, where $P_{\rm gas}$is the ion-pressure, $P_{\rm mag} = B\cdot B/8 \pi$ is the magnetic pressure, and B is the magnetic field whose components are $(B_{\rm P}, B_{\rm T})= (B1,B2,B_{\rm T})$.) The numerical procedure is based on using the implicit solver IRMHD3 to search steady-state solution for the 3D axi-symmetric two-temperature diffusive MHD equations in spherical geometry (for further clarifications about the equations and the numerical method see Hujeirat & Rannacher 2001; Hujeirat & Camenzind 2000). The ion-pressure is used to describe the turbulent viscosity: $\nu _{\rm turb} = \alpha P_{\rm gas}/\Omega$, where $\alpha$ is the usual viscosity coefficient, and $\Omega$ is the angular frequency. The magnetic diffusivity is taken to be equal to $\nu _{\rm turb}.$ $250\times 80$ strongly stretched finite volume cells in the radial and vertical direction have been used. Normal symmetry and anti-symmetry boundary conditions have been imposed along the equator and the rotation axis. Extrapolation has been adopted to fix down-stream values at the inner boundary. Non-dimensional formulation is adopted, using the reference scaling variables: $\rm{\tilde{\rho}}= 2.5 \times 10^{-12}~{\rm g~ cm^{-3}}$, $\tilde{T}= 5 \times 10^7~{\rm K},$ $\tilde{U}=\tilde{V_{\rm S}} = \gamma {\cal R}_{\rm g} \tilde{T}/ \mu_{\rm i},$ $(\mu _{\rm i}=1.23)$. $\tilde{B}=\tilde{V_{\rm S}} \sqrt{4 \pi \tilde{\rho}}.$ The location of the transition layer (-TL), where the ion-dominated plasma is expected to rotate super-Keplerian and being accelerated into jets, is shown for clarity.