  We investigate whether gradual dilution of the gas in some elliptical
galaxies is the cause of a positive correlation between star formation rate
(SFR) and gas-phase metallicity (Zg) at high stellar mass (M*) in the local
Universe. To do this, two classes of massive (M* >= 10^10.5 Msun) galaxy are
selected from the Sloan Digital Sky Survey (SDSS) and the Munich semi-analytic
model of galaxy formation, L-Galaxies. The first class is selected by high
specific star formation rates (sSFR) and high Zg, and the second class by low
sSFR and low Zg. These criteria roughly distinguish disc-dominant galaxies from
metal-poor, elliptical galaxies. In the semi-analytic model, the second class
of galaxies obtain low sSFR and low Zg due to gradual dilution of the
interstellar medium by accretion of metal-poor gas via infalling clumps and
low-mass satellites. This occurs after a merger-induced starburst and the
associated supernova feedback have quenched most of the original gas reservoir.
A number of signatures of this evolution are present in these model galaxies at
z=0, including low gas fractions, large central black holes, elliptical
morphologies, old ages, and importantly, low (Zg-Z*) indicating dilution after
star formation. Remarkably, all of these properties are also found in low-sSFR,
low-Zg, massive galaxies in the SDSS-DR7. This provides strong, indirect
evidence that some elliptical galaxies are undergoing gradual dilution after a
gas-rich merger in the local Universe. This dilution scenario also explains the
positive correlation between SFR and Zg measured in high-M* galaxies, and
therefore has consequences for the local fundamental metallicity relation
(FMR), which assumes a weak anti-correlation between SFR and Zg above 10^10.5
Msun.
