  Current theories of galaxy formation predict that spiral galaxies are
embedded in a reservoir of hot gas. This gas is able to cool onto the galaxy
replenishing cold gas that is consumed by star formation. Estimates of the
X-ray luminosity emitted in the cooling region suggest a bolometric luminosity
of order 10 x 10^41 ergs/s in massive systems. We have used ROSAT PSPC data to
search for extended X-ray emission from the haloes of three nearby, massive,
late-type galaxies: NGC 2841, NGC 4594 and NGC 5529. We infer 95 per cent upper
limits on the bolometric X-ray luminosities of the haloes of NGC 2841, NGC 4594
and NGC 5529 of 0.4, 1.2 and 3.8 x 10^41 ergs/s respectively. Thus the true
luminosity lies well below the straightforward theoretical prediction. We
discuss this discrepancy and suggest a number of ways in which the theoretical
model can be brought into agreement with the observational results. A possible
solution is that the gravitational potentials of the dark matter haloes of
these galaxies are weaker than assumed in the current model. Alternatively, the
present day accretion may be substantially less than is required on average to
build the disk over the Hubble time. Our results are, however, based on only
three galaxies, none of which is ideal for this kind of study. A larger data
set is required to explore this important problem further.
