  We examine the K shell emission lines produced by isothermal and simple
multiphase models of the hot gas in elliptical galaxies and galaxy clusters to
determine the most effective means for constraining the width of the
differential emission measure (xi(T)) in these systems which we characterize by
a dimensionless parameter, sigma_xi. Comparison of line ratios of
two-temperature (sigma_xi << 1) and cooling flow (sigma_xi ~1) models is
presented in detail. We find that a two-temperature model can approximate very
accurately a cooling flow spectrum over 0.5-10 keV.
  We have re-analyzed the ASCA spectra of three of the brightest galaxy
clusters to assess the evidence for multiphase gas in their cores: M87 (Virgo),
the Centaurus cluster, and the Perseus cluster. K-alpha emission line blends of
Si, S, Ar, Ca, and Fe are detected in each system as is significant Fe K-beta
emission. The Fe K-beta/K-alpha ratios are consistent with optically thin
plasma models and do not suggest resonance scattering in these systems.
Consideration of both the ratios of H-like to He-like K-alpha lines and the
local continuum temperatures clearly rules out isothermal gas in each case. To
obtain more detailed constraints we fitted plasma models over 1.6-9 keV where
the emission is dominated by these K shell lines and by continuum. In each case
the ASCA spectra cannot determine whether the gas emits at only two
temperatures or over a continuous range of temperatures as expected for a
cooling flow. The metal abundances are near solar for all of the multiphase
models. We discuss the implications of these results and examine the prospects
for determining the temperature structure in these systems with upcoming X-ray
missions.
