Low-resolution spectroscopy of the Sunyaev-Zel'dovich effect and
  estimates of cluster parameters
  The Sunyaev-Zel'dovich (SZ) effect is a powerful tool for studying clusters
of galaxies and cosmology. Large mm-wave telescopes are now routinely detecting
and mapping the SZ effect in a number of clusters, measure their comptonisation
parameter and use them as probes of the large-scale structure and evolution of
the universe. We show that estimates of the physical parameters of clusters
(optical depth, plasma temperature, peculiar velocity, non-thermal components
etc.) obtained from ground-based multi-band SZ photometry can be significantly
biased, owing to the reduced frequency coverage, to the degeneracy between the
parameters and to the presence of a number of independent components larger
than the number of frequencies measured. We demonstrate that low-resolution
spectroscopic measurements of the SZ effect that also cover frequencies $> 270$
GHz are effective in removing the degeneracy. We used accurate simulations of
observations with lines-of-sight through clusters of galaxies with different
experimental configurations (4-band photometers, 6-band photometer, multi-range
differential spectrometer, full coverage spectrometers) and different
intracluster plasma stratifications. We find that measurements carried out with
ground-based few-band photometers are biased towards high electron temperatures
and low optical depths, and require coverage of high frequency and/or
independent complementary observations to produce unbiased information; a
differential spectrometer that covers 4 bands with a resolution of $\sim 6 \
GHz$ eliminates most if not all bias; full-range differential spectrometers are
the ultimate resource that allows a full recovery of all parameters.
