  The Fermi bubbles are large gamma-ray-emitting structures. They are symmetric
about the Galactic Centre (GC), and their creation is therefore attributed to
intensive energy injection at the GC. In this study, we focus on the
non-equilibrium X-ray gas structures associated with the bubbles. We show that
a combination of the density, temperature, and shock age profiles of the X-ray
gas can be used to distinguish the energy injection mechanisms. By comparing
the results of numerical simulations with observations, we indicate that the
bubbles were created by a fast wind from the GC because it generates a strong
reverse shock and reproduces the observed temperature peak there. On the other
hand, instantaneous energy injection at the GC cannot reproduce the temperature
profile. The wind had a speed of ~1000 km/s, and blew for ~10^7 yr. Because the
mass flux of the wind is large, the entrainment of interstellar gas by
wide-angle outflows from the black hole is required. Thus, the wind may be the
same as active galactic nuclei outflows often observed in other galaxies and
thought to regulate the growth of galaxies and their central black holes.
