1. Introduction 
Active galactic nuclei (AGN) and Quasars (QSOs) were discovered and extensively investigated in the second half of 20-th century.They are the bright objects with luminosity about 10⁴⁶ ergs/s (and up to 10⁴⁷ ergs/s, that is hundreds times more than our Galaxy total luminosity), located in the centers of large galaxies. The observed power of the radiation is generated by the process of disk accretion of matter to the super massive black hole (MBH). Now, AGNs are observed in a wide range of spectral bands, but still there are major open questions about the physical properties of the AGN’s engine, the dynamics and structure of matter flow around the MBH and the generation of spectra of AGNs. One of the “hot problems” attracting the attention of investigators during the last decade is the nature of matter outflows from AGNs. In fact, outflows were detected in the early 1970s as broad absorption lines (BALs) in several quasars (BALQSOs).Subsequen tly, they were observed in the UV and X-ray spectral bands of ~ 13% of QSOs and ~ 50% of Seyfert galaxies (Weymann et al., 1991; Crenshaw et al., 1999). 

There is no commonly accepted or worked-out theory of the AGN outflows. The most developed theory and model calculations were performed by Weymann et al.(1982), Arav and Begelman (1994), Murray and Chang (1997), and by Vilkoviskij et al.(1999). In the last work both wide absorption troughs and line-locking effect were obtained with numerical simulations of UV spectra. 

Creation of the general theory of matter outflows from AGN as well as detailed numerical models of the corresponding absorption spectra in the UV and X-ray bands are the main goals of the proposed Project. The scientific value of the theory is very high, because it will give (together with the disk-accretion theory, e.g., Park and Ostriker 2001) a relatively complete picture of the matter dynamics in the vicinity of the AGN engine. 

2. Approaches and Specific Problems 

2.1. The Interacting Subsystems (IS) Approach: The interacting subsystems approach means that we consider the AGN engine as a complicated physical system, consisting of three main subsystems: the central massive black hole (MBH), the surrounding compact stellar cluster (CSC), and the gas subsystem.The last consists of several components, (i) hot plasma with temperatures from 10⁷ K to 10⁹ K, (ii) imbedded “cold” gas clouds with T ~ 10⁴−10⁵ K, and colder clouds of the so-called obscuring torus (OT). Figure 1 indicates the supposed geometry of the matter distribution around the black hole. 

2.2. Structure of the Outflows: We suppose that the outflow of hot gas is generated in the hot corona above the accretion disk. It creates a hot gas wind, which fills the internal hole of the OT. A t the internal surface of the OT the hot-gas wind interacts with the cold clouds of the OT and partly entrains these clouds into the wind. The large clouds fragment into the smaller ones. As a result, a two-phase outflow is produced along a “conical surface” with middle solid angle of the outflow corresponding to the BALQSO part of QSOs. We suppose that the low-ionization BALQSOs are those with line of sights deeply intersecting the OT at the outer part of the conical outflow. On the other hand, the BALs in Seyfert galaxies are produced by wider solid-angle conical outflows with lower velocities. Thus the BAL-AGNs are included into the standard “geometrical unification scheme” (Antonucci 1993) as objects intermediate between AGN-1 and AGN-2. But other geometries of the outflows will be tested as well. 

2.3. Gas Dynamics and Radiation Transfer:  The gas-dynamic task have to be solved both for the hot gas outflow and the two-phase outflow in the cone. A velocity gradient or shear exists at the outer conical boundary of the flow (the velocity decreases in the transition layer from pure hot gas to the OT interior). In the transition layer, the problem of two-phase gas dynamics demands consideration of the drag forces between the cold clouds and the hot gas, and the radiation pressure forces acting on the cold clouds. For the last force calculations, as well as the absorption coefficients calculations, the problem of the photo-ionization balance in the clouds has to be solved. The radiation transfer calculations must take into consideration the two-phase “cloudy” structure of the moving cold gas. The shortcoming of this approach was the semi-empirical treating of the hot gas heating (Vilkoviskij et al. 1999). So the important problem which have to be solved is relation of the gas outflows and jets, especially as this problem is connected with the well-known puzzle of the radio quiet/loud dichotomy of AGNs. For this purpose the magnetohydrodynamic theory will be involved.

3. Magnetohydrodynamic Outflows and Jets from AGN Disks 
Stationary magnetohydrodynamic outflows from a rotating accretion disk have been obtained by the group of Prof. Lovelace by time-dependent axisymmetric simulations (Ustyugova et al. 1999). The initial magnetic field was taken to be a split monopole poloidal field configuration (Sakurai 1987) frozen into the disk. The disk is treated as a perfectly conducting, time-independent density boundary [ρ(r)] in Keplerian rotation which is different from our earlier specification of a small velocity outflow (Ustyugova et al. 1995). The outflow velocity from the disk is determined self-consistently from the MHD equations. We have found a large class of stationary MHD winds. Within the simulation region, the outflow accelerates from thermal velocity (~ c_s) to a muchlarger asymptotic poloidal flow velocity of the order of 0.5(GM/r_i)^1/2, where M is the mass of the central object and r_i is the inner radius of the disk. This asymptotic velocity is much larger than the local escape speed and is larger than fast magnetosonic speed by a factor of ~ 1.75. The acceleration distance for the outflow, over which the flow accelerates from ~ 0 to, say, 90% of the asymptotic speed, occurs at a flow distance of about 80r_i. The flows are approximately spherical outflows, with only small collimation within the simulation region. The collimation distance over which the flow becomes collimated (with divergence less than, say, 10^o) is much larger than the size of our simulation region. Close to the disk the outflow is driven by the centrifugal force while at all larger distances the flow is driven by the magnetic force which is proportional to −Ñ (rBφ)², where Bφ is the toroidal field (see Blandford & Payne 1982; and Lovelace et al. 1991). 

In the proposed work we plan to study: (1) The collimating effect of having the outflow propagate into a pre-existing hot gas distribution above the disk. This mechanism of collimation was investigated theoretically by Lovelace et al. (1991). (2) The entrainment and acceleration of the hot gas in the direction perpendicular to the disk. And, (3) The modification of our Godonov-type axisymmetric MHD code to include special relativistic effects.