IMPLICATION OF STELLAR PROPER MOTION OBSERVATIONS ON RADIO EMISSION OF SAGITTARIUS A

It is suggested that a flying-by star in a hot accretion disk may cool the hot accretion disk by the Comptonization of the stellar emission. Such a stellar cooling can be observed in the radio frequency regime since synchrotron luminosity depends strongly on the electron temperature of the accretion flow. If a bright star orbiting around the supermassive black hole cools the hot disk, one should expect a quasi-periodic modulation in radio, or even possible an anti-correlation of luminosities in radio and X-rays. Recently, the unprecedentedly accurate infrared imaging of the Sagittarius A$\ast$ for about ten years enables us to resolve stars around it and thus determine orbital parameters of the currently closest star S2. We explore the possibility of using such kind of observation to distinguish two quite different physical models for the central engine of the Sagittarius A$\ast$, that is, a hot accretion disk model and a jet model. We have attempted to estimate the observables using the observed parameters of the star S2. The relative difference in the electron temperature is a few parts of a thousand at the epoch when the star S2 is near at the pericenter. The relative radio luminosity difference with and without the stellar cooling is also small of order $10^{-4}$, particularly even when the star S2 is near at the pericenter. On the basis of our findings we tentatively conclude that even the currently closest pass of the star S2 is insufficiently close enough to meaningfully constrain the nature of the Sagittarius A$\ast$ and distinguish two competing models. This implies that even though Bower et al. (2002)have found no periodic radio flux variations in their data set from 1981 to 1998, which is naturally expected from the presence of a hot disk, a hot disk model cannot be conclusively ruled out. This is simply because the energy bands they have studied are too high to observe the effect of the star S2 even if it indeed interacts with the hot disk. In other words, even if there is a hot accretion disk the star like S2 has imprints in the frequency range at v $\le$ 100 MHz.