  An X-ray study was made to examine whether some part of the soft X-ray
background is coming from hot gas in the Local Group. For this purpose, four
consecutive pointings were made with ASCA toward a sky region between M 31 and
M 33, which is close to the direction of the center of the Local Group. By
comparing the X-ray surface brightness in this sky direction with that in
another blank sky region near the north equatorial pole, an upper limit on any
soft excess X-ray background was determined to be 2.8$\times10^{-9}$ erg
cm$^{-2}$ s$^{-1}$ sr$^{-1}$ with a 90% confidence level statistical error.
Assuming an optically thin thermal bremsstrahlung energy spectrum
(Raymond-Smith model) for a temperature of 1 keV and a $\beta$-model electron
density distribution for a core radius of 100 kpc for the X-ray halo, the upper
limit of the central plasma density was obtained to be 1.3$\times10^{-4}$
cm$^{-3}$. The plasma column density is too low to contribute significantly to
the observed quadrupole anisotropy in the cosmic microwave background.
