We investigate the effect of a putative X-ray-emitting halo surroundin
g the Local Group of galaxies, and specifically the possible temperatu
re anisotropies induced in the COBE-DMR four-year sky maps by an assoc
iated Sunyaev-Zel'dovich effect. By fitting the isothermal spherical h
alo model proposed by Suto et al. to the co-added four-year COBE-DMR 5
3- and 90-GHz sky maps in Galactic coordinates, we find no significant
evidence of a contribution. We therefore reject the claim that such a
halo can affect the estimation of the primordial spectral index and a
mplitude of density perturbations as inferred from the DMR data. We fi
nd that correlation with the DMR data imposes constraints on the plaus
ible contribution of such an X-ray-emitting halo to a distortion in th
e cosmic microwave background spectrum (as specified by the Compton y-
parameter), up to a value for R - the ratio of the core radius of the
isothermal halo gas distribution to the distance to the Local Group ce
ntroid - of 0.68. For larger values of R, the recent cosmological uppe
r limit derived by COBE-FIRAS provides stronger constraints on the mod
el parameters. Over the entire parameter space for R, we find an upper
limit to the inferred sky rms anisotropy signal of similar to 14 mu K
(95 per cent confidence), a negligible amount relative to the similar
to 35-mu K signal observed in the COBE-DMR data.