  It is suspected that the ultraviolet (UV) upturn phenomenon in elliptical
galaxies and extended horizontal-branch stars in globular clusters have a
common origin. An extremely high abundance of helium (Y~0.4) allows for a
working hypothesis, but its origin is unclear. Peng & Nagai (2009) proposed
that primordial helium sedimentation in dark haloes over cosmic timescales may
lead to extreme helium abundances in galaxy cluster centers. In this scenario
UV upturn should be restricted to brightest cluster galaxies (BCGs) only. This
is a clear and testable prediction. We present tests of this hypothesis using
galaxy clusters from Yoon et al. (2008) that were detected by both the Sloan
Digital Sky Survey and the Galaxy Evolution Explorer Medium Imaging Survey.
Using a new UV classification scheme based on far-UV, near-UV, and optical
photometry we found only 5% of cluster elliptical galaxies show a UV upturn,
while 27% and 68% are classified as "recent star-formation" and "UV-weak"
ellipticals, respectively. The data reveal a modest positive dependence of the
UV upturn fraction on galaxy velocity dispersion, which is in agreement with
the earlier findings of Burstein et al. (1988) and possibly with the helium
sedimentation theory. However, we do not see any dependency on rank or
luminosity of galaxies. Besides, BCGs do not show any marked difference in UV
upturn fraction or strength, which is inconsistent with the prediction. We
conclude that the aforementioned helium sedimentation theory and its inferred
environmental effects are not supported by the available data.
