Probing the Halo Gas Distribution in the Inner Galaxy with Fermi Bubble
  Observations
  The hot halo gas distribution in the inner Milky Way (MW) contains key fossil
records of the past energetic feedback processes in the Galactic center. Here
we adopt a variety of spherical and disk-like MW halo gas models as initial
conditions in a series of simulations to investigate the formation of the Fermi
bubbles in the jet-shock scenario. The simulation results are compared directly
with relevant X-ray and gamma-ray observations of the Fermi bubbles to
constrain the halo gas distribution in the inner Galaxy before the Fermi bubble
event. Our best-fit gas density distribution can be described by a power law in
radius $n_{\rm e}(r)=0.01(r/1 \text{~kpc})^{-1.5}$ cm$^{-3}$. Our study can not
determine if there is an inner density core, which if exists, should be very
small with size $r_{c} \lesssim 0.5$ kpc. When extrapolating to large radii
$r\sim 50-90$ kpc, our derived density distribution lies appreciably below the
recently estimated gas densities from ram-pressure stripping calculations,
suggesting that the halo gas density profile either flattens out or has one or
more discontinuities within $10 \lesssim r \lesssim 50$ kpc. Some of these
discontinuities may be related to the eROSITA bubbles, and our derived gas
density profile may correspond to the hot gas distribution in the inner eROSITA
bubbles about $5$ Myr ago.
