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Astron. Astrophys. 342, 49-56 (1999)

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4. Discussion and conclusion

4.1. Model fitting

The results of the model fitting in the previous section has a number of interesting consequences and caveats. The fact that all radio cores can be fitted with one simple model is already important, since the sources discussed here are so well constrained that by far not all combinations of size and flux could be fitted by the model. What is, however, more striking is the fact that the parameters required to explain sizes and fluxes are very similar. Firstly, in all sources the typical Lorentz factor of the electrons is of the order of a few hundred. Given the extreme simplicity of the model and the extensive use of equipartition assumptions (departing from which would be reflected in a change of [FORMULA] as well) this similarity points to a relatively similar internal structure of the radio cores. Secondly, all sources have jet-powers very close to or larger than the luminosity of their thermal radiation, i.e. the suspected accretion disk luminosity. Since the model was constructed such that the radiative efficiency is maximal, applying more realistic models-for example by using different equipartition factors, velocity fields, or electron distributions-will therefore in almost all cases only lead to an increased demand for jet power in these sources.

The model fits perhaps most convincingly the jet in GRS 1915+105, where it not only reproduces core size and flux very well, but apparently also predicts radio time delay and jet velocity reasonably well. The latter indicates that perhaps the pressure gradient in the jet of GRS 1915+105 is mainly responsible for reaching its asymptotical velocity-unless higher velocities are found in future observations.

4.2. Limitations

We note that for determining [FORMULA] from the jet model, the flux and to some degree the inclination angle (especially for small i) are most important, while [FORMULA] is mainly determined by the size of the core. Consequently, the latter seems to be the most uncertain part since it is often ambiguous how to define the core and its characteristic size, especially when the resolution is of the order of the core size. Moreover, we have introduced [FORMULA] mainly to easily reflect the possibility of a low-energy cut-off or break in the spectrum. This has the positive effect that cores can be larger than their size purely given by the [FORMULA] surface (which is particularly useful in GRS 1915+105 and NGC 4258), however, it also means that the core size may depend sensitively on the evolution of the electron distribution which we have ignored almost completely. Hence, the predictive power of this model for radio core sizes is very limited and only good to an order of magnitude, so that we will not base our interpretation heavily on the sizes. It should also be noted that the jet model used here has been trimmed towards LLAGN to achieve the greatest possible degree of simplification with the assumption that their velocity field can be described by Eq. 1. We know that this does not apply to quasars where the bulk Lorentz factor of the jets seems to be larger and the fully parametrized equations (e.g. as in Falcke & Biermann 1995) have to be used.

However, taking all this into consideration we can give yet a more simplified formula where we have fixed [FORMULA] at an intermediate value of 300 and which can be used to very roughly estimate the jet power of a LLAGN from its flux and presumed inclination angle alone:


4.3. Jet/disk-symbiosis

The main result of this work, however, is that in three very different sources, with very different sizes and fluxes, we can explain the central core with a single model by just scaling the jet power with the accretion rate. This works because the three selected sources, GRS 1915+105, NGC 4258, and M 81*, all have some very important ingredients in common. All three have clear evidence for a massive black hole, signs of (large or small scale) accretion disks, jet structures in their radio cores, and a good determination of the inclination angle (important for the fitting of individual sources). In GRS 1915+105 there is even direct evidence for a coupling between jet and disk from the X-ray and radio light curves. The high jet power we derive for the radio core in a relatively quiescent phase is quite consistent with but lower than the power derived for the major outbursts (e.g. Mirabel et al. 1998).

In hindsight this high power in the radio cores justifies the assumptions we have made in earlier papers that jet and disk can be considered as symbiotic systems and that-at least in a few systems-the assumption of [FORMULA] (or even larger) seems appropriate. This also strengthens the picture that jets are produced in the inner region of an accretion disk, where a major fraction of the dissipated energy is channeled into the jet (Falcke & Biermann 1995; Donea & Biermann 1996). As a consequence, modelling of accretion disks and X-ray light curves in jet systems like GRS 1915+105 clearly requires taking the jet into account.

4.4. Accretion disks and ADAFs

Another consequence from those radio cores is their amazing scale invariance. It seems that we can use the very same model for a stellar mass black hole which is accreting near its Eddington limit (GRS 1915+105) as well as for a super-massive black hole which is presumably accreting at an extreme sub-Eddington rate (M 81, NGC 4258). Moreover, a very similar model was successfully applied to a quasar sample earlier (Falcke et al. 1995), i.e. super-massive black holes near the Eddington limit. That would suggest that certain properties of an accretion disk/flow, namely jet production, is very insensitive towards changes in accretion rate or black hole mass, and that the `common engine' mechanism of black hole accretion and jet formation, suggested by Rawlings & Saunders (1991), may include a much larger range of AGN than only quasars and radio galaxies.

If this is so, it has to be asked whether indeed every accretion flow necessarily has to make a transition from a thin [FORMULA]-disk to an ADAF when turning sub-Eddington. In order to maintain this proposition one then needs to explain how the accretion disk structure can change so drastically without affecting its innermost region, where jets presumably are being produced. If one asks what the arguments for ADAFs in low-power AGN really are, the evidence remains thin. For NGC 4258 it is quite obvious now that the radio core cannot serve to support an ADAF emission model. Quite contrary the derived jet power is consistent with a low accretion rate, which in turn is consistent with the low luminosity of the nucleus and, of course, a thin disk is directly seen at least at larger radii. With the radio emission gone the ADAF spectral energy distribution, extending over many orders of magnitude, merely serves to explain a single X-ray data point. Hence, it is currently not obvious that an ADAF is really needed to explain this source at all.

The same seems to be true for M 81, which is equally sub-Eddington as NGC 4258. Here the situation is even worse, since Ishisaki et al (1996) also claim the detection of a broad iron Fe-K line suggesting that probably the inner disk cannot be as hot as required in an ADAF model. As similar broad line has been tentatively claimed also for NGC 4258 by Cannizzo et al. (1997). In any case the two galaxies serve as a general warning to view the existence of a compact radio core in low-luminosity AGN as prima facie evidence for an ADAF-a jet origin may be a more natural explanation here and in other cases. We also want to point out that the argument by Narayan et al. (1995) a pure ADAF interpretation of radio cores were superior because the latter requires an `additional' emission component is not quite true if one considers disks and jets to be symbiotic, i.e. to be essentially one system.

4.5. Sgr A*

So far we have concentrated the discussion mainly on the three sources which fitted the model well and have not mentioned Sgr A*. The jet-power we derive for the latter source now is virtually unchanged with respect to the power used to introduce the Sgr A* jet model in Falcke et al. (1993) and it still explains the radio properties of Sgr A* very well. However, as pointed out in this earlier paper already, the required jet power also provides a lower limit to the accretion rate onto the black hole of [FORMULA]yr (using the current numbers and ignoring unlikely small inclination angles). Yet, even such a low accretion rate seems to be excluded on the basis of very stringent upper limits for the NIR flux of Sgr A* placed by Menten et al. (1996, see also Falcke & Melia 1997 for a discussion of this point). If one ignores the possibility of intrinsic obscuration in the Galactic Center this indeed seems to indicate a very low radiative efficiency of the accretion flow onto the black hole and, ironically, the jet model may provide in this case supporting argument for advection. As an alternative model one could envisage a scenario where the missing energy, instead of being radiated away, is put almost completely into a (magnetically) driven wind throughout the disk-this, however, would need to be worked out in more detail. As a side note we also want to mention that the low [FORMULA] we derive for Sgr A* requires a relativistic electron fraction of [FORMULA]. A value for [FORMULA] significantly larger than unity is only possible if additional pairs were produced and thus could support the suggestions by Falcke (1996b) and Mahadevan (1998) that pair production through proton-proton collisions is at work here. However, as pointed out before, the determination of [FORMULA] and especially its interpretation within our simple model is fairly unreliable and hence should be taken very cautiously.

4.6. Summary

To summarize this section, we believe that the jet model does seem to provide an excellent description of nuclear radio cores also in LLAGN and that considering jets and disks as symbiotic systems can explain the vast range of radio core luminosities and sizes we find in the nuclei of galaxies and in stellar mass black holes. Comparison of jet powers and nuclear luminosities of some radio cores seem to indicate that they are of similar order, thus supporting an under-fed black hole scenario with low accretion rates. Consequently, even though they are not excluded, ADAFs need not be as ubiquitous in low-luminosity AGN as has been claimed while the jet interpretation for compact radio nuclei seems to be a natural interpretation also for low-luminosity AGN. It therefore does not appear as if the presence of a compact radio core and a low optical luminosity alone serve as a good indicator for an ADAF. On the other hand-as the example of Sgr A* shows-a jet interpretation of low-luminosity radio cores could in some cases support the presence of an advection dominated accretion flow or some other kind of radiatively deficient accretion disk. Therefore a combination of ADAF and jet models should also be considered for the fitting of nuclear spectral energy distributions.

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Online publication: December 22, 1998