We study steady, radial gas outflows from galaxies in an effort to und
erstand the way tenuous and hot gas is transported to large distances
away from galaxies. In particular, we obtain solutions for outflow pro
blems and study the outflow topology, the effects of the galaxy potent
ial (and thus the mass), the size of outflow regions, the efficiency o
f radiative cooling, and the fate of the cooled gas. Under general pow
er-law forms for the cooling function and the gravitational field of g
alaxies, we show that the outflow solutions are determined by the two-
parameter initial conditions. In an analogy with stellar wind or accre
tion problems, we demonstrate that there exist no transonic flows, but
either subsonic or supersonic flows are obtainable. Solutions of the
supersonic outflows are studied in detail as they are most likely to c
arry gas to large distances away from galaxies. We find that, if gravi
ty is weak, the outflow is characterized by the ratio of the radiative
cooling time to the flow time, t(c)/t(f). If initially t(c)/t(f) less
than or similar to 1 the gas cools as soon as it leaves the galaxy, w
hereas if t(c)/t(f) greater than or similar to 1 the gas first cools a
diabatically and then radiatively. However, if initially t(c)/t(f) muc
h greater than 1 radiation cannot become important; in this case, depe
nding on whether the initial gas temperature is above the escape tempe
rature, the outflow results in either a galactic wind or a hot corona.
The importance of the galactic gravitational field is characterized b
y the fractional energy lost radiatively within the flow time in outfl
ows with velocity equal to the circular velocity of the galaxy; if the
fraction is small, gravity is relatively strong, and it stops the out
flow before the gas has a chance to cool radiatively, resulting in a h
ot corona. In case the gas does cool radiatively, the cooled gas is mo
st likely to form clouds via various instabilities. The clouds coast f
arther away from the galaxy because of the finite kinetic energy they
inherit. Depending on the initial energies, the clouds can either leav
e the galaxy or fall back ballistically. We apply the calculations to
galaxies in general. We find that the hot gas in dwarf galaxies can ei
ther flow out as galactic winds, or cool radiatively to form clouds. I
n the latter case, the clouds escape the galaxies. In contrast, massiv
e galaxies like our own tend to confine the gas. The gas released into
the halo can either cool radiatively or result in a galactic corona.
We present the surface brightness in various X-ray energy bands for so
me representative cooling outflows from dwarf and normal galaxies, and
we find that the extent of the resultant X-ray emission is generally
much smaller than the region of the outflows. In particular, the mean
temperature averaged over entire outflow regions is shown to be a fact
or of 2-6 smaller than the base temperature. We also estimate the mean
surface brightness of the O VI emission lines, and the predicted surf
ace brightness is within the reach of current UV experiments. We brief
ly discuss the implications of cold clouds at large distances from dwa
rf galaxies for recent observations of QSO absorption-line systems.