The soft X-ray afterglow of gamma ray bursts, a stringent test for the fireball model

I consider the recent discovery of a soft X-ray source inside the error box of the gamma ray burst GB 960720 by the SAX, ASCA and ROSAT satellites, in terms of the fireball model. I show that the ejecta shell, which, after causing the burst is cold and dense, but still relativistic, keeps plowing through the interstellar medium, heating up the just-shocked matter which then emits X-rays. I compute the radiation emitted by this matter. I show that, up to about two months after the burst, in the cosmological scenario a soft X-ray (0.1-10 keV) flux of at least $\approx 10^{-13} erg s^{-1} cm^{-2}$, well within current observational capabilities, is generated, explaining the observations of the three satellites. Instead, in the Galactic Halo scenario a flux 3 orders of magnitude lower is expected. Detection of this non-thermal, declining flux in a statistically significant number of objects would simultaneously establish the fireball model and the cosmological nature of gamma ray bursts.