We examine resolved spectroscopic data obtained with the Keck II telescope
for 44 spheroidal galaxies in the fields of two rich clusters, Cl0024+16
(z=0.40) and MS0451-03 (z=0.54), and contrast this with similar data for 23
galaxies within the redshift interval 0.3<z<0.65 in the GOODS northern field.
For each galaxy we examine the case for systemic rotation, derive central
stellar velocity dispersions sigma and photometric ellipticities, epsilon.
Using morphological classifications obtained via Hubble Space Telescope imaging
as the basis, we explore the utility of our kinematic quantities in
distinguishing between pressure-supported ellipticals and
rotationally-supported lenticulars (S0s). We demonstrate the reliability of
using the v/(1-epsilon) vs sigma and v/sigma vs epsilon distributions as
discriminators, finding that the two criteria correctly identify 63%+-3% and
80%+-2% of S0s at z~0.5, respectively, along with 76%+8-3% and 79%+-2% of
ellipticals. We test these diagnostics using equivalent local data in the Coma
cluster, and find that the diagnostics are similarly accurate at z=0. Our
measured accuracies are comparable to the accuracy of visual classification of
morphologies, but avoid the band-shifting and surface brightness effects that
hinder visual classification at high redshifts. As an example application of
our kinematic discriminators, we then examine the morphology-density relation
for elliptical and S0 galaxies separately at z~0.5. We confirm, from kinematic
data alone, the recent growth of rotationally-supported spheroidals. We discuss
the feasibility of extending the method to a more comprehensive study of
cluster and field galaxies to z~1, in order to verify in detail the recent
density-dependent growth of S0 galaxies.Comment: 7 pages, 4 figures, updated with version accepted to Ap