The Role of Accretion

Let us take as our basic ansatz that the growth of a Black Hole (BH) to produce a Quasar, and subsequently, a massive black hole within an Elliptical Galaxy is the result of a merger of a pair of gas-rich systems, such as considered most recently by Barnes and Hernquist (1996). In addition, assume a detailed symbiosis between the properties of the accretion disk and the properties of the radio jet, inspired by the work of Falcke and Biermann (1995). In this model, the nature of the active galactic nucleus (AGN) that is produced depends critically upon the rate of accretion into the nuclear regions. This type of a model would then imply a number of consequences which we summarise in this section, and develop (to greater or lesser degree) in subsequent sections.

In the sub-Eddington accretion domain we may obtain a classic Shakura and Sunyaev (1973) thin disk. Such disks allow the free escape of the relativistic jet (assumed to be light; electrons + positrons) from the nuclear region, and may produce optical continuum by thermal emission, but are expected to be ineffective in producing either a broad-line or a narrow line emission region. However, the radio jets in such systems are characterised by efficient relativistic boosting, and can therefore give rise to Blazar phenomena. The sub-Eddington (and possibly, advective) nature of the accretion will ensure that such sources are of relatively low luminosity, and of low radio power, and such objects might be identifiable with the FR I radio sources as is indeed postulated in the unified models of radio sources (Urry and Padovani 1995).

At very high (super-Eddington) accretion rates into the nuclear regions, the accumulation of dusty matter in the nuclear regions tends to obscure the central engine. This can be identified with the dusty ``thick'' torus of the unified models. Indeed, Dopita et. al (1997) have demonstrated that since this thick dusty accretion torus is optically thick even at 25m, its properties can be investigated through IR colour-colour diagrams, at least for the hidden broad-line region (HBLR) Seyferts. In these objects the flow a few degrees outside the ionisation cone is found to be highly super-Eddington. Dopita et al. (1997) also point out the importance of the radiation pressure acting on the dust, since the opacity of dusty gas is so much higher than that due to free electrons. In this case, at least some of the inflowing material will be driven back out by radiation pressure. Nonetheless, at least some of the flow makes it past the sublimation point of the dust, thanks to the ram pressure of the inflow. If this flow into the broad-line region is also super-Eddington, much of the matter entering these regions has to be lost in the form of a thermal wind. Murray and his collaborators (Murray and Chiang, 1995; Murray et al. 1995; Chiang and Murray, 1996) have shown that this can be analogous to the radiatively-driven winds produced in hot stars, being optically thick to UV resonance line scattering, and therefore accelerated by radiation pressure. For high enough mass-loss rates, such a wind may become optically-thick to electron scattering as well, and a hot electron-scattering photosphere can be produced. Material below this photosphere serves to reprocess the hard radiation (EUV, X- and -rays) from the central BH and the innermost portions of the accretion disk, and this would serve to obscure the central engine from direct view except in the polar directions where the relativistic jets may escape. Such a toriodal reprocessing photosphere would provide enough absorption to explain the weakness of Seyfert 2 galaxies in X-rays (Mushotzky, Done & Pounds 1993, and references therein), and its inner surface could also be used for K- scattering. Since multiple Compton scattering degrades harder photons to softer photons (analagous to the degradation of radioactive - rays in supernova fireballs), such processing can also make the photosphere an efficient source of UV photons (Big Blue Bump ?) which are then available to ionise the surrounding accretion disk and produce the Broad-Line region (BLR). In this model, an AGN seen in an intermediate angle (but outside the ``thick'' dusty torus) would appear as either a QSO or as a Sy I galaxy, depending on the mass of the nuclear BH.

Models which include such a thermal radiation-driven wind allow the possibility of a direct interaction between the thermal and relativistic winds. Clearly, this interaction is favoured when the accretion into the BLR is highly super-Eddington with respect to the nuclear BH. When such interaction occurs below the reprocessing photosphere, it will lead to mass entrainment into the jet, and a slowing of the jet to highly sub-relativistic speeds. This is likely to be the cause of radio-loud: radio-quiet dichotomy. If radio-loud galaxies can only be produced when the accretion rate to the BH is very much below the Eddington value, then radio-loud QSOs will only be produced in the later stages of such mergers, or when the massive BH subsequently swallows more matter such as in an merger of the elliptical with a small gas-rich system, or when a extremely sub-Eddington cooling flow feeds down to the elliptical nucleus.

Nuclear Accretion Rates

There seems little doubt that galactic merger events can dump large amounts of gas ( 10) into the nuclear regions (e.g. Solomon, Downes and Radford 1992). The process of gas dynamics in the case of a galactic merger has been considered by a number of authors, but most notably by Barnes and Hernquist (1991, 1992, 1996). In all of these computations, the effect of torques and dissipation in the gas is dramatic, and strong inflow towards the centre of the gravitational potential is produced. At the point where orbital support of the gas becomes important, a strong accretion shock is formed, which is likely to trigger a major nuclear starburst. In the simulations of Barnes and Hernquist (1991), about 5.10. of gas found its way to the central 200 pc in a timescale of 10 years. This process may continue to still smaller scales. See, for example the simulations of Bekki (1995), where he considered the gas dynamics of the material within 1 kpc.

In the core region, the infalling gas is processed through an accretion shock and joins the already accreted material in a dense, rotating disk. Applying pressure balance across the accretion shock, we can set the ram pressure in the accretion flow to the gas pressure in the hot phase of the ISM; where is the core radius in units of 300 pc, is the rate of mass accretion in units of 200 yr, is the velocity of infall in units of 300 km.s, and is the solid angle covered by the accretion flow. In this core region, assume a two-phase medium is formed with a hot intercloud medium, and with dense self-gravitating molecular clouds limited by their tidal radius in the core potential. Thanks to their self gravity, the molecular gas clouds have a mean internal density, which is greater than their surface density, ; where is their internal sound speed ( 1 km.s). This translates to a H-number density in excess of 10 cm.

Although the gas in the core is in a very compact region, it still needs to decrease its orbital angular momentum by a factor of 10 relative to the BH if it is to be efficiently accreted. However, in post-merger galaxies this may be somewhat easier than at first appears. If a BH typical of those found in Seyfert galaxies ( 10) is present in the gas-rich region, initially its sphere of influence is quite small, and it will be attracted towards the most massive gaseous complex. Dynamical friction, which is high in the case of the dissipative accretion interactions the BH makes with the cloud, should then allow it to settle towards the dense cloud core of the complex. In this way, the BH positions itself within a dynamical timescale ( 10 years) to sit at the densest point in the accretion flow where it can be optimally fed. The accretion rates for moving BHs have been derived both analytically (Petrich, Shapiro & Teukolsky 1988), and through supercomputer simulations (Petrich et al. 1989) to which the interested reader is referred. However the basic physics is easily understood, and was given by Bondi & Hoyle (1944). Inside a molecular cloud the accretion radius, , and the Bondi-Hoyle mass accretion rate onto the BH is given by:

 
where is the relative velocity of the BH through the molecular cloud. This velocity will not be greater than the orbital velocity of the cloud around the core. Substituting numerical values for the time when the BH passes through a molecular cloud, pc, where is the mass of the BH in units of 10 M, and is now the relative velocity in units of 300 km.s. Therefore, given that the relative velocity is an upper limit, and the density, , defined above, is a lower limit,  Myr,where is the H-atom number density in the molecular cloud in units of 10 cm. This accretion rate is well above the Eddington accretion rate for any reasonable value of BH mass, and will increase rapidly as dynamical friction slows the relative velocities of cloud and BH. Although equation(1) suggests that the radius of attraction can become very large for small values of the relative velocity, in practice it is limited by the tidal radius, or radius of influence of the BH. For the case we are considering, this is pc between molecular clouds and pc inside molecular clouds. It would therefore appear that the BH can move towards and ``graze'' efficiently on the most massive molecular clouds in its vicinity. However, outside the molecular clouds, in the hot intercloud medium, the rate of accretion is several orders of magnitude lower. Therefore, super-Eddington accretion is only turned on when the BH enters a molecular cloud.

The feeding process in non-merger systems is likely to be somewhat different from this, and we would probably have to depend on material (stars or gas) which is either on a radial orbit or else has been driven into the nuclear regions as the consequence of the development of a bar-like potential ( Simkin, Su & Schwartz, 1980; Shlosman, Frank & Begelman, 1989). However, the observational evidence in favour of bar feeding not strong. Regardless of the details of the feeding processes, neither of these offer great potential for runaway growth of the BH, and this may be the reason that BHs in spiral galaxy hosts do not achieve the masses (or potential luminosities) of BHs in elliptical hosts. However, should a molecular cloud happen to interact with the BH, the same considerations as developed in the previous paragraphs should apply. In Seyferts therefore, we might speculate that their duty cycle is low (it has to be of order 1% in order that the BH does not grow too seriously fat), but that during `active' periods, it is shining at near-Eddington luminosity (as confirmed by reverberation mapping analyses, Maoz 1994), and attempting to accrete molecular gas at super-Eddington rates.

During the accretion process, the molecular clouds are presumably being converted rapidly to stars in a massive nuclear starburst, so that the growth of the BH is determined by the competition between inflow, accretion, and star formation.

Consider a simple (toy) parametric form for the mass accretion rate into the nuclear core region;

 
This is just about the simplest form that could be adopted, having only one characteristic timescale. It starts starting at zero, reaching a maximum at and then decreases exponentially at large t. If is the total mass accreted, then 2 This accretion timescale is related to the free-fall timescale from the point of origin of the infalling gas to the mass centre by a scaling factor:

 
with 10 kpc and 10 then years.

Now, the accretion rate to the black hole during the period when the accretion rate into the nuclear regions is super-Eddington is given by:

 
where is the growth timescale for the BH accreting at the Eddington limit. This can be calculated from the luminosity:

 
where is the fraction of the rest mass energy radiated by matter falling into the BH. For a Schwartzschild BH Typically . The factor is the fraction of the Eddington Luminosity produced by this accretion, and is assumed . Thus, the growth timescale of the BH is:

 
inserting numerical values, years. Thus, the growth timescale of the BH is of the same order than, or somewhat smaller than , so that appreciable growth of the BH can occur during the merger. We discuss below whether it is possible that the BH grows from that typical of a Seyfert galaxy ( 10) to that typical of a BH in a Giant Elliptical galaxy ( 10) during the merger event.

© Copyright Astronomical Society of Australia 1997