  Several deep PSPC observations of the Coma cluster reveal a very large-scale
halo of soft X-ray emission, substantially in excess of the well known
radiation from the hot intra-cluster medium. The excess emission, previously
reported in the central region of the cluster using lower-sensitivity EUVE and
ROSAT data, is now evident out to a radius of 2.6 Mpc, demonstrating that the
soft excess radiation from clusters is a phenomenon of cosmological
significance. The X-ray spectrum at these large radii cannot be modeled
non-thermally, but is consistent with the original scenario of thermal emission
from warm gas at ~ 10^6 K. The mass of the warm gas is on par with that of the
hot X-ray emitting plasma, and significantly more massive if the warm gas
resides in low-density filamentary structures. Thus the data lend vital support
to current theories of cosmic evolution, which predict that at low redshift
\~30-40 % of the baryons reside in warm filaments converging at clusters of
galaxies.
