We examine the K shell emission lines produced by isothermal and simple mul
tiphase models of the hot gas in elliptical galaxies and galaxy clusters to
determine the most effective means for constraining the width of the diffe
rential emission measure, xi(T), in these systems which we characterize by
a dimensionless parameter, sigma(xi). Comparison of line ratios of two-temp
erature (sigma(xi) < 1) and cooling flow (sigma(xi) similar to 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 re-analyse the ASCA spectra of three of the brightest galaxy clusters to
assess the evidence for multiphase gas in their cores: M87 (Virgo), the Ce
ntaurus 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. Con
sideration of both the ratios of H-like to He-like K alpha lines and the lo
cal continuum temperatures clearly rules out isothermal gas in each case. T
o 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 multiph
ase models. We discuss the implications of these results and examine the pr
ospects for determining the temperature structure in these systems with upc
oming X-ray missions.