We present our ROSAT observation of the edge-on spiral galaxy NGC 4631
, a nearby Sc/SBd galaxy best known for its extended radio halo. Becau
se of the low foreground Galactic X-ray-absorbing gas column density,
N-HI approximate to 1.4 x 10(20) cm(-2), this observation is sensitive
to gas of temperature greater than or similar to a few x 10(5) K. We
detected soft (similar to 0.25 keV) X-ray radiation out to more than 8
kpc above the midplane of the galaxy. The strongest X-ray emission in
the halo is above the central disk, a region of about 3 kpc radius wh
ich shows high star formation activity. The X-ray emission in the halo
is bordered by two extended filaments of radio continuum emission. We
also found diffuse X-ray emission from hot gas in the galaxy's disk.
The spectrum of the radiation can be characterized by a thermal plasma
with a temperature of 3 x 10(6) K and a radiative cooling rate of sim
ilar to 8 x 10(39) ergs s(-1). This rate is only a few percent of the
estimated supernova energy release in the interstellar medium of the g
alaxy. Analysis of the X-ray spectrum shows evidence for the presence
of a cooler (several times 10(5) K) halo gas component that could cons
ume a much larger fraction of the supernova energy. We found strong ev
idence for disk/halo interaction. Hot gas apparently blows out from su
pershells in the galaxy's disk at a rate of similar to 1 M. yr(-1). Th
is outflow of hot gas drags magnetic field lines up in the halo and fo
rms a magnetized gaseous halo. If the magnetic field lines are still a
nchored to the disk gas at large disk radii, the outflowing gas may be
confined high above the disk by magnetic pressure. We have identified
a strong X-ray source which coincides spatially with an H I supershel
l. However, the source is likely an extremely luminous X-ray binary wi
th L(x)(0.1-2 keV) approximate to 5 x 10(39) ergs s(-1), which makes i
t a stellar mass black hole candidate.