  We have calculated the emergent X-ray properties for models of cluster
cooling flows including the effects of accumulated cooled material. The opacity
of this cooled gas can reduce the overall X-ray luminosity of the cooling flow,
and values of Mdot based on these luminosities can underestimate the true value
by factors of ~2. We find that accumulated cooled material can produce emergent
surface brightness profiles much like those observed even for nearly
homogeneous gas distributions. Consequently, much more of the gas may be
cooling below X-ray emitting temperatures in the central regions of cooling
flows (r < 10 kpc) than one would infer from observed X-ray surface brightness
profiles assuming the gas was optically thin. Similarly, the central densities
and pressures in cooling flows may have been underestimated. We show that
distributed absorption in cooling flows produces a number of observable effects
in the spectrum which may allow it to be differentiated from absorption due to
gas in our Galaxy. These include a characteristic suppression of the continuum
below ~2 keV, absorption features such as a redshifted O K-edge, and diminished
intensity of resonance emission lines. Spectra including the effects of
intrinsic absorption are not well fit by foreground absorbing models.
Attempting to fit such models to the spatially resolved spectra can lead to
underestimates of the true absorbing column by factors of 3-20. Fits to
integrated spectra of the entire cooling flow region can either underestimate
or overestimate the mass of the absorbing gas depending on the specifics of the
model. We discuss the potential detection of these effects with AXAF, XMM, and
Astro-E.
