          Astron. Astrophys. 329, 845-852 (1998)

## 4. Matter distribution

Here we discuss the matter distribution of both the uniform and cloudy medium through which the jet propagates as well the density and characteristic size of the clouds. The density distribution of extensive halos around giant elliptical galaxies follows a general law of the type where and is the density at the galactic center (Forman et al., 1985). If we put kpc for the characteristic radius and cm-3, then will represent the density distribution around an extended source. This distribution should be appropriate to study the propagation of the jet outside the galactic central regions. It has been used in a simplified form by Fanti et al. (1995) in the case of kiloparsec-sized steep-spectrum sources. However, in the case of compact sources, the distances from the central object are much smaller, of the order of tens of parsec and one expects the density to be higher. Therefore, we add a second, short-scale height component, which enables us to describe the motion of the jet near the galactic center. In this case one would take cm-3 and a characteristic radius pc. Therefore the density distribution has the form, Consider now a cloudy medium surrounding the central object. Not much information exists on the distribution and structure of the clouds. Assuming that the galaxy has suffered an increase in the gas density due to an interaction or merger with a gas-rich companion, we suppose that this gas will form clouds that will be distributed around the central object up to an outer radius . An inner boundary of the cloud distribution must also exist if the individual clouds are to be stable against tidal forces. If, for instance, the mass of the central object is of the order of the lower limit of is pc otherwise the density of the clouds will be much greater than cm-3.

We shall suppose that the clouds' contribution to the mean density is also given by the general law (8) but with a much smaller value of , around pc and cm-3. We shall call this density . It is given by and The outer radius of the cloud region can only be estimated roughly and should not be much larger than the galaxy central region. One constraint to is the total mass present inside the cloudy region. If we take this to be then for the value of above one must have in the range 200-500 pc. We therefore take a characteristic value pc as a lower limit.

The number of clouds per unit length and the internal density of the clouds should be such that the mean density of the ambient medium is achieved. The average number of clouds per unit length is then given by Since the linear density always appears multiplied by we also give the expression where is the particle number density of the cloud. We assume that depends on the distance from the central object. For instance, in the case of dense, self-gravitating clouds, if they were to be stable against tidal disruption, one would have . Since other factors also may come into play, we generalize this and use the following parametrization where is a free parameter in the range 0-3. The value of depends on the mass of the central object and of the radius of the inner boundary of the cloud distribution and it is given by This expression ensure that the cloud will always withstand tidal forces at .

Finally, the radius of the clouds should not be constant so that we allow for a linear increasing with the distance R, that is,     © European Southern Observatory (ESO) 1998

Online publication: December 16, 1997 