Relativistic Jet Model

In the spirit of our parametric analysis, let us adopt the main features of the jet model developed by Falke and Biermann (1995), and as fitted to the observational material by Falke, Malkan and Biermann (1995):

 
It therefore follows immediately that :

 
Thus, the mass flux in the jet is only about 1% of the mass flux into the BH, and more importantly, is only about 0.1% of the mass flux in the radiatively-driven wind, when the BH is attempting to accrete at a super-Eddington rate. This very low mass flux compared to the wind then implies that mixing between the jet and the thermal wind will be critical in determining whether the jet can escape (radio-loud) or is trapped within the radio photosphere of the wind determined by its free-free opacity at radio frequencies.

Radio Loud or Radio Quiet?

The degree of mass-loading of the thermal wind material into the relativistic jet will determine the energy loss rate of the electrons in the jet. Energy losses from the relativistic plasma may either be through Synchrotron radiation or by electron Bremsstrahlung. For electron Bremsstrahlung losses in a medium with ionic density n, the fractional energy loss per unit path length dx is given by:

 
where is the classical electron radius. Thus for a jet with the stopping length, given by is cm. However, the density in the wind is given by eqn. 9. For a BH luminosity (in units of 10ergs.s the radius of the photosphere is Thus, in order to bury the loss region of the jet along with its associated Bremsstrahlung photons below the electron scattering photosphere, the jet must interact with the wind at a radius of 2.10 cm; or about 100 gravitational radii, in this example. Since, to first order, the mass loss in the wind scales as the mass of the BH, this critical distance of about 100 gravitational radii will hold true for different BH luminosities.

The radio frequency photons produced in the jet - wind interaction are blocked by the free-free optical depth in the ionised wind. At frequency the photospheric radius (defined as a free-free opacity of unity) is given by:

 
where is the frequency considered (GHz). For an electron temperature of 30000K, this implies 8x10 cm, which is several times larger than the radius of the electron scattering photosphere. Presumably the radio flux emerging over this photosphere determines the brightness and frequency spectrum of the radio core component of the AGN.

As far as the electrons which escape to emerge into the lobe are concerned, Bicknell, Dopita and O'Dea (1997) have shown that the jet energy flux is related to the synchrotron power at frequency through an efficiency factor:

 
where is the index of the power law in the density distribution of the galactic medium (2) , t is the age of the source, B the magnetic field in the radio lobes, is the lower energy limit of the relativistic electrons, is the spectral index, and is the fraction of the internal energy of the plasma contained in relativistic electrons. In the super-Eddington phase, in which the relativistic jet gas is able to mix with the thermal wind either below, or near, the electron scattering photosphere; On the other hand, highly sub-Eddington accretion allows for the free escape of the relativistic plasma so However, radio-quiet objects have lobe luminosities which are typically weaker by a factor of a thousand than their radio-loud counterparts. Thus, for a given jet energy flux, this difference in the entrainment factor is in itself sufficient to explain the difference between the radio-quiet, and the radio-loud cases, respectively, provided that the entrainment has occurred below a radio photosphere. We may therefore conclude that radio-quiet behaviour is a signature of an AGN which is undergoing rapid accretion.

The transition between the radio-quiet and radio-loud cases presumably comes about at the time that the accretion rate into the BLR decreases to the point that the thermal wind starts to clear in the polar regions( in equation (7)), and entrainment into the radio jet is no longer enough to slow this to transonic speeds. This allows for the possibility that there are transition objects displaying both BLRs and relativistic jets. Examples of such objects may be IC5063, BL Lac itself and 3C120.

The Radio Core

For the quasars in the Bright Quasar Sample (BQS) of Schmidt and Green (1983), Lonsdale, Smith and Lonsdale (1995) have shown that there is a good correlation between the radio core flux and the bolometric luminosity. This correlation exists independently of the assumptions used to calculate the bolometric luminosity. Moreover, the correlation is improved by the exclusion of the radio-loud QSOs (for which relativistic beaming effects enhance the core luminosity). Lonsdale, Smith and Lonsdale (1995) have also shown that this correlation extends to the ultraluminous infrared galaxies as well. This correlation strongly suggests that, since the optical / UV continua are thought to be thermal, the radio core is either produced by thermal processes or through non-thermal emission powered directly by these thermal processes. Of these two possibilities the latter seems more probable in the light of the observations of Barvainis, Lonsdale and Anonucci (1996), which demonstrated that at least some VLBI cores of the radio-quiet AGN show nonthermal brightness temperatures characteristic of synchrotron emission.

In this model, how could this synchrotron emission arise? The most likely solution is through Fermi acceleration of electrons in strong shocks surrounding the nucleus. Such shocks arise when the fast radiatively-driven wind impinges upon either slow, magnetically-driven winds from the accretion disk, or upon the accretion flow itself. Since these shocks carry a nearly constant fraction of the bolometric luminosity, the correlation between radio core luminosity and bolometric luminosity would then find a natural explanation.

Since this shocked region is the region in which mass entrainment into the fast wind will occur, we can speculate that the Broad Absorption Line (BAL) QSOs are those objects in which the shock interface is aligned with the line of sight.

If core radio power can be used in this way to estimate bolometric luminosity and hence (for BHs accreting at their Eddington rate) the mass of the BH, the correlations of Nelson and Whittle (1996) could be used to link the mass of the BH with the mass of the bulge in which it resides. Nelson and Whittle (1996) found that (with large overlap between different classes of object) the radio core luminosity relates directly to either bulge absolute magnitude, or to velocity dispersion in the bulge for Sy 1 and Sy 2 galaxies, and for FR I and FR II radio galaxies, although objects with jets have systematically higher core luminosities as might be expected in the presence of a relativistically beamed component. This correlation is most easily explained if the bulge stars were formed coevally with the main growth phase in the central BH, i.e. during a merger event.

© Copyright Astronomical Society of Australia 1997