3 ADIOS

We next attempt to model SgrA^* with an ADIOS. The modeling approach is exactly the same as with the ADAF, except that the accretion rate is assumed to be described by $\dot{M}=\dot{M}_0(R/R_{\rm out})^p$. We solve the full set of coupled radiation hydrodynamical accretion equations to obtain the spectra and the structures of the accretion flow consistently. Note that this is an improvement compared to Quataert & Narayan (1999) where some dynamical quantities such as radial velocity and sound speed obtained in corresponding ADAFs (with $\dot{M}= \dot{M}_0$) are used in calculating the spectra of the ADIOS. Following Quataert & Narayan (1999), we assume that the wind does not radiate.

We first assume that the fraction of viscous heating of electrons is $\delta =10^{-3}$. We set $\alpha=0.1$ but treat $\dot{M},~ p$ and $\beta$ as free in order to find the best set of parameters to fit the submm bump and the X-ray spectrum. The dashed line in Fig. 2 shows our best model results. The parameters are $\dot{M}_0= 1.66 \times 10^{-5}~M_{\odot}~{\rm yr^{-1}}$, p=0.28, $\alpha=0.1$, but $\beta=0.5$ (not 0.9 since otherwise the predicted radio flux is too low compared to the observation). The outer boundary conditions are $T_{\rm i}\approx T_{\rm e}=8\times 10^6~{\rm K}$, and $\Omega_{\rm out}=0.295~\Omega_{\rm Kepler}$ at $R_{\rm out}=10^5~R_{\rm s}$. Compared to the ADAF model, both the slope of the X-ray spectrum and the submm bump are now fitted better. However, there are two serious problems for this fit. The first one is that the required mass accretion rate is over 5 times higher than the upper limit estimated in Baganoff et al. (2001a) mentioned above. The second problem is that the X-ray spectra are produced by thermal bremsstrahlung emission alone, therefore this model cannot explain the short timescale variability. In fact, the introduction of a wind makes the variability timescale even longer because the decreasing density of accretion flows (e.g. Di Matteo et al. 2000) makes things worse.

The very rapid variability observed by Chandra indicates that the X-ray emission comes from a very small spatial region. This points towards SSC occurring in the inner region of the disk. In the case of the existence of strong winds, the density of the accretion flow in the innermost region is very low. When the flow is tenuous, SSC will show some spectral peaks as a result of different scattering orders. To make SSC dominate over bremsstrahlung in the X-ray band, the first order of SSC is more promising due to the rapid decrease of Compton scattering probability with increasing scattering orders. To make the first order SSC component reach the Chandra band, the electron temperature in the emission region must be very high.

An effective way to increase the electron temperature in the accretion flow is to increase $\delta$. In the ADAF we generally assume that $\delta$ is as as small as $\delta =10^{-3}$ or 10^-2, i.e., the viscous dissipation mainly heats the ions. However, because of the uncertainty in the microphysics of the ADAF, it is possible that for some reasons, such as magnetic reconnection, the viscous dissipation may prefer heating electrons, i.e., $\delta$ may be much larger (Bisnovatyi-Kogan & Lovelace 1997, 2000; Gruzinov 1998; Quataert & Gruzinov 1999; Blackman 1999). In this case, the temperature of the electrons will be greatly increased.

Figure 2: Three ADIOS spectral models for SgrA*. The short-dashed line is for $\delta =10^{-3}$, p=0.28, the long-dashed line for $\delta =10^{-3}$, p=0.6. The solid line is for $\delta =1$, p=0.4, the dotted line is exactly the same model as the solid line, except that Comptonization of synchrotron radiation is neglected. See text for other parameters.

We try to model the spectrum using various values for $\delta$. We find that only when $\delta \approx 1$, i.e., almost all of the viscous dissipation heats only electrons, can we get a high enough electron temperature to make the first order SSC dominate the X-ray emission. The solid line in Fig. 2 shows such an example. Other parameters in this model are $\dot{M}_0=2.8 \times 10^{-6}~M_{\odot}~{\rm yr^{-1}}, \alpha=0.1, \beta=0.9$, and p=0.4. The outer boundary conditions are $T_{\rm i,e}=10^7~{\rm K}$, $\Omega_{\rm out}=0.25~\Omega_{\rm Kepler}$. The temperature of electrons is as high as 10¹¹ K for the accretion flow within $6~R_{\rm s}$ and the highest temperature is $3 \times 10^{11}$ K. This model is then very similar to the model proposed by Melia et al. (2001) for SgrA^* in the sense that a high-temperature inner disk forms, with $T_{\rm e} >10^{11}$ K. Synchrotron emission in this hottest region produces the submm bump, synchrotron self-Compton dominates the X-ray band and gives a very soft spectrum. The thermal bremsstrahlung radiation only contributes a small part as shown by the dotted line, where SSC is neglected. In this case a very short X-ray variability timescale can be expected.

Putting aside the reality of such a high $\delta$, the fit is not satisfactory on the following points: first, it under-predicts the low-frequency radio spectrum. Second, the predicted X-ray slope is much steeper than the best fit of Baganoff et al. (2001b). The third problem is that this model over-predicts the flux above $\sim$100 GHz by a factor of 4-6. We cannot get a better fit no matter how we adjust the parameters. Because of the strong self-absorption of synchrotron emission, the radio spectrum is the result of a super-position of blackbody radiation from the different parts of the ADAF with different temperatures. So, comparing this model with an ADAF (or ADIOS with small $\delta$), we can understand that the main reason for the over-prediction is its too extreme temperature making the flux of the blackbody radiation stronger. Thus we conclude that, if we do not consider the possible radiation of winds, the ADIOS model is not favored for SgrA^*.

However, the approximation that the wind does not radiate may be an over-simplification. For example, the part of the wind originating from the supersonic region of the accretion disk will possibly be shocked when it is ejected out of the disk. Thus it would reach very high temperatures and its radiation could not be neglected. In this sense, the wind within the sonic radius will present itself as radiative, outflowing plasma - i.e., like the plasma jets typically observed in AGN. The model would then possibly become similar to our jet-disk model presented below.