5 Summary and discussion

Recent Chandra X-ray observations put new constraints on the theoretical models of SgrA^*. The spectrum is very soft, the flux is rapidly variable and the source is extended. In this paper we consider three different models to explain the observational results of SgrA^*. We find that an ADAF model can give a marginally satisfactory interpretation to the Chandra spectrum and the rapid X-ray variability. But our best fit is still not good for the radio spectrum in the sense that it over-predicts the high-frequency radio by a factor of 2-3 and significantly under-predicts the low-frequency radio. We then consider the possibility of strong winds from ADAFs, i.e., an ADIOS model. If the winds are non-radiative and viscous dissipation in the accretion flow mainly heats ions, as generally assumed in the literature, this model can fit the spectrum ranging from submm bump to X-ray quite well. However, it is hard to explain the rapid X-ray variability since in this model bremsstrahlung is the sole contributor at X-ray band. If we assume that most of the viscous dissipation preferentially heats electrons, a rapidly variable X-ray spectrum is expected since in this case the X-ray emission is dominated by SSC. But in this case the model over-predicts the radio flux above $\sim$100 GHz by a factor of 4-6, and the predicted X-ray spectrum is much steeper than the best fit of the Chandra observations.

An excellent fit to all the data including low-frequency radio can be obtained with a coupled jet-disk model. In this model, the accretion disk is described by an ADAF. In the innermost region of the ADAF, $\sim$ $2~R_{\rm s}$, some fraction $q_{\rm m}$ ($\sim$0.5% if any cold jet component is neglected. See our discussion in Sect. 4 for the possibility of a cold jet component) of the accretion flow is ejected out of the ADAF and transferred into the jet. In this process, a shock occurs because the accretion flow is radially supersonic before the shock. After the shock the temperature of electrons in the nozzle (the base of the jet) reaches about $2 \times 10^{11}~{\rm K}$. In this case, the synchrotron emission in the nozzle largely dominates the submm bump, and its Comptonization dominates the quiescent X-ray spectrum in SgrA^*. The X-ray spectrum is soft and the variability timescale is short. Out of the nozzle, the jet gas expands freely outward under the force of the gas pressure gradient of gas pressure. Furthermore its self-absorbed synchrotron radiation gives a good fit to the low-frequency radio spectrum of SgrA^* which is hard to explain in ADAF models. The model is completely self-consistent.

The jet in our model produces a slightly inverted radio spectrum, as can be understood from the canonical model of Blandford & Königl (1979), with modifications as in Falcke (1996a). In the absence of a shock acceleration region in the highly-supersonic outer region of the jet, the particles retain the highly-peaked relativistic Maxwellian energy distribution which is attained by shock heating occurring when the radial supersonic accretion flow is transferred into the vertical direction. On the other hand, the electrons in AGN jets typically seem to have a power-law high-energy tail after shock acceleration in jets, since the Mach number in jets is very high (Drury 1983). In that case, a corresponding optically thin power-law spectrum at IR/optical frequencies is generally expected, as is seen in many AGN and perhaps even X-ray binary jets (e.g., Markoff et al. 2001a). In the case of SgrA^*, the absence of an optically-thin power-law indicates that, for some unknown reason, such high Mach number shocks do not occur. If they would occur under certain conditions, we should still see an inverted radio spectrum, but we would also expect some kind of hard power-law emission at higher frequencies (mid-IR to X-rays).

In addition to the observations we mention in the present paper, there are also constraints to the model through the frequency-size relationship obtained from VLBI observations (Rogers et al. 1994; Krichbaum et al. 1998; Lo et al. 1998). The jet-disk model can fit this well as shown in Falcke & Markoff (2000).

We therefore conclude that it is possible to present a consistent picture of the emission processes associated with the central black hole in our Galaxy by combining the three basic astrophysical ingredients that have been discussed in recent years: Bondi-Hoyle accretion from the immediate environment, optically thin accretion through an ADAF, and energy extraction and visible emission by a plasma jet. Our jet-ADAF model predicts a closely correlated variability among sub-millimeter, IR, and X-ray. More broad-band observations and monitoring at various wavebands (radio, IR, X-rays) will help to judge whether it will be possible to establish a standard model invoking those elements for SgrA^* in the near future. For example, more precise determination of the IR flux will help to further discriminate between the jet-ADAF model and the pure ADAF model since the former predicts higher IR flux than the latter. This will also be crucial for understanding the activity in low-power black holes in general.

Acknowledgements

We are grateful to Peter Biermann for discussions on shock physics. F.Y. thanks the partial support from China 973 Project under NKBRSF G19990754.