  In our previous works (Kataoka et al. 2013, Tahara et al. 2015), we found
absorbed thermal X-ray plasma with kT ~ 0.3 keV observed ubiquitously near the
edges of the Fermi bubbles and interpreted this emission as weakly shock-heated
Galactic halo (GH) gas. Here we present a systematic and uniform analysis of
archival Suzaku (29 pointings; 6 newly presented) and Swift (68 pointings; 49
newly presented) data within Galactic longitudes |l| < 20 deg and latitude 5
deg < |b| < 60 deg, covering the whole extent of the Fermi bubbles. We show
that the plasma temperature is constant at kT = 0.30+-0.07 keV, while the
emission measure (EM) varies by an order of magnitude, increasing toward the
Galactic center (i.e., low |b|) with enhancements at the north polar spur
(NPS), SE-claw and NW-clump features. Moreover, the EM distribution of kT ~
0.30 keV plasma is highly asymmetric in the northern and southern bubbles.
Although the association of the X-ray emission with the bubbles is not
conclusive, we compare the observed EM properties with simple models assuming
(i) a filled halo without bubbles, whose gas density follows a hydrostatic
isothermal model (King profile) and (ii) a bubble-in-halo in which two
identical bubbles expand into the halo forming thick shells of swept halo gas.
We argue that the EM profile in the north (b > 0 deg) favors (ii), whereas that
of the south (b < 0 deg) is rather close to (i), but weak excess signature is
clearly detected also in the south like NPS (South Polar Spur; SPS). Such an
asymmetry, if due to the bubbles, cannot be fully understood only by the
inclination of bubbles' axis against the Galactic disk normal, thus suggesting
asymmetric outflow due to different environmental/initial condition.

High Energy Astrophysical Phenomena