**4.1. Current Status of SZE/X-ray Distances**

To date, there are 41 distance determinations to 26 different galaxy
clusters from analysis of SZE and X-ray observations. All of these
SZE/X-ray distances use *ROSAT* X-ray data and model the cluster
gas as a spherical isothermal model
(Cavaliere &
Fusco-Femiano, 1976;
Cavaliere &
Fusco-Femiano, 1978).
The *ROSAT* data do not warrant a more
sophisticated treatment. In Figure 6
we show all SZE-determined
distances from high signal-to-noise ratio SZE experiments. The
uncertainties shown are statistical at 68% confidence. The
theoretical angular-diameter distance relation is shown for three
cosmologies assuming *H*_{0} = 60 km s^{-1}
Mpc^{-1}.

There are currently three homogeneously analyzed samples of clusters
with SZE distances: (1) a sample of seven nearby (*z* < 0.1) galaxy
clusters observed with the OVRO 5 m telescope (green solid triangles)
that finds *H*_{0} = 66^{+14+15}_{-11-15}
(Mason et al., 2001;
Myers et al., 1997),
(2) a sample of five intermediate-redshift (0.14 < *z* < 0.3)
clusters from the RT interferometer that finds
*H*_{0} = 65^{+8+15}_{-7-15}
(cyan solid squares)
(Jones et al.,
2003),
and (3) a sample of 18 clusters with 0.14 < *z* < 0.83 from
interferometric observations by the OVRO and BIMA SZE imaging project,
which infers *H*_{0} = 60^{+4+18}_{-4-13}
(blue solid stars)
(Reese et al.,
2002).
The above Hubble constants assume a
_{m} = 0.3,
_{} =
0.7 cosmology, and the uncertainties are statistical followed by
systematic at 68% confidence. The treatment of uncertainties varies
among the three cluster samples.

A fit to the ensemble of 41 SZE-determined distances yields
*H*_{0}
61 ± 3 ± 18 km s^{-1} Mpc^{-1} for an
_{m} = 0.3,
_{} =
0.7 cosmology, where the uncertainties are statistical
followed by systematic at 68% confidence. Since many of the clusters
are at high redshift, the best-fit Hubble constant will depend on the
cosmology adopted; the best-fit Hubble constant shifts to 57 km
s^{-1} Mpc^{-1} for an open
_{m} = 0.3
universe, and to 54 km s^{-1} Mpc^{-1} for a flat
_{m} = 1
geometry. The systematic
uncertainty, discussed below, clearly dominates. The systematic
uncertainty is approximate because it is complicated by shared
systematics between some distance determinations. For example,
including multiple distance determinations to a single cluster overstresses
any effects of asphericity and orientation from that galaxy cluster.

Statistical uncertainty includes contributions from the ICM shape
parameters, the electron temperature, point sources in the field, and
the cooling functions, which depends on *T*_{e},
metallicity, and the
column density. The largest sources of statistical uncertainty are
the ICM shape parameters (from model fitting) and the X-ray determined
electron temperature (*D*_{A}
*T*_{e}^{-2}). Uncertainty from model
fitting is roughly 20% in the distance and is dominated by the
uncertainty in the central decrement. The contribution from
*T*_{e} on
the distances varies greatly from ~ 5% to ~ 30%, with
10%-20% being typical values. As expected, nearby cluster
temperatures are more precisely determined than those of distant
galaxy clusters.