  We present a simple analysis of X-ray emission and absorption for hot-star
winds, designed to explore the natural scalings of the observed X-ray
luminosity with wind and sstellar properties. We show that an exospheric
approximation, in which all of the emission above the optical depth unity
radius escapes the wind, reproduces very well the detailed expression for
radiation transport through a spherically symmetric wind. Using this
approximation we find that the X-ray luminosity $L_x$ scales naturally with the
wind density parameter $\Mdot/\vinf$, obtaining $L_x \sim (\Mdot/\vinf)^2$ for
optically thin winds, and $L_x \sim (\Mdot/\vinf)^{1+s}$ for optically thick
winds with an X-ray filling factor that varies in radius as $f \sim r^s$. These
scalings with wind density contrast with the commonly inferred empirical
scalings of X-ray luminosity $L_x $ with bolometric luminosity $L_B$. The
empirically derived linear scaling of $L_x \sim L_B$ for thick winds can
however be reproduced, through a delicate cancellation of emission and
absorption, if one assumes modest radial fall-off in the X-ray filling factor
($s \approx -0.25$ or $s \approx -0.4$, depending on details of the secondary
scaling of wind density with luminosity). We also explore the nature of the
X-ray spectral energy distribution in the context of this model, and find that
the spectrum is divided into a soft, optically thick part and a hard, optically
thin part. Finally, we conclude that the energy-dependent emissivity must have
a high-energy cut-off, corresponding to the maximum shock energy, in order to
reproduce the general trends seen in X-ray spectral energy distributions of hot
stars.
