After calculating the radio spectrum, we can now make a rough estimate of the expected X-ray spectrum from Sgr A^*. For AGN, there are typically four processes discussed to explain the observed X-ray emission in various objects:

(1) synchrotron emission,

(2) Bremsstrahlung,

(3) thermal Comptonization by a hot corona, and

(4) inverse Compton scattering of photons off the relativistic electrons in the jet plasma.

Possibility (1) can be excluded here since the radio synchrotron spectrum cuts off already in the mid-infrared; (2) and (3) have been discussed in chapter 10. Thus, we will here concentrate on the fourth possibility.

Since the only photons we see from Sgr A^* outside the X-ray regime are radio photons, here we will consider solely the synchrotron self-Compton (SSC) process, which is absolutely unavoidable. The relativistic electrons that produce synchrotron radiation also have a finite probability to Compton up-scatter the very photons they have produced in the first place. The frequency of the upscattered photons will be increased by a factor  γ² with respect to the target photons. Inverse Compton is a scattering process where the probability of an interaction of an electron from a population with particle density ne with a photon of a population with photon density n_γ depends on n_e × n_γ . Since in SSC the electrons are also responsible for the target photons, the efficiency of SSC will go as n²_e . For the case of a jet, where the density increases inwards with R⁻², while the volume decreases inwards with R³, the dominant contribution to the up-scattered spectrum will be at the smallest scale in the system, where n_e is maximal. Following the previous discussion, this will be at a few Schwarzschild radii where the sub-mm bump in the spectrum is produced.

One can show (Rybicki and Lightman 1979) that the luminosity L_SSC of the inverse-Compton process is proportional to the luminosity of the synchrotron emission L_sync, with the proportionality factor given by the ratio of the energy densities of synchrotron photons:

 (1.1)

and magnetic field

 (1.2)

such that

 (1.3)

We find that the maximum of emission in Sgr A^* is about 3 Jy at 10¹² Hz. Hence the synchrotron luminosity of Sgr A^* is

 (1.4)

and from equations (1.3) we get, independent of the radius,

 (1.5)

As can be seen the SSC emission is sensitive to the ratio between synchrotron emission and magnetic field. If a different parametrization is used we have a dependence on the equipartition factor k. In general one can also state that the SSC emission should be more variable than the synchrotron emission since it depends with a high power on flux density and peak synchrotron frequency. The peak of the SSC emission itself will roughly occur at γ² × ν_max. For γ_e  100 and ν_max 10¹² Hz, the peak will be above 10¹⁶ eV, hence in the far ultraviolet and soft X-rays.

All of this is quite consistent with the X-ray observations by Baganoff et al (2001) who find a quiescent, soft X-ray emission of a few times 10³³ erg s⁻¹ in Sgr A^* which can vary rapidly at times.