  Early-type galaxies are considered to be the end-products of massive galaxy
formation. Optical spectroscopic studies reveal that massive early-type
galaxies formed the bulk of their stars over short timescales (1<Gyr) and at
high redshift (z>2), followed by passive evolution to the present. However,
their optical spectra are insensitive to constrain small episodes of recent
star formation, since they are dominated by old stars. Fortunately, this
problem can be tackled in the ultraviolet range. While recent studies that make
use of ultraviolet absorption lines have suggested the presence of young stars
in a few early-type galaxies, the age and mass fractions of young stars and
their dependence on galaxy mass, is unknown. Here we report a detailed study of
these young stellar populations, from high-quality stacked spectra of 28,663
galaxies from the BOSS survey, analysing optical and ultraviolet absorption
lines simultaneously. We find that residual star formation is ubiquitous in
massive early-type galaxies, measuring average mass fractions of ~0.5% in young
stars in the last 2 Gyr of their evolution. This fraction shows a decreasing
trend with galaxy stellar mass, consistent with a down-sizing scenario. We also
find that synthetic galaxies from state-of-the-art cosmological numerical
simulations significantly overproduce both intermediate and young stellar
populations. Therefore, our results pose stringent constraints on numerical
simulations of galaxy formation.
