Slow-then-rapid quenching as traced by tentative evidence for enhanced
  metallicities of cluster galaxies at z~0.2 in the slow quenching phase
  (Abridged) We explore 7 clusters from LoCuSS at z~0.2 with spectra of 1965
cluster members from the ACReS Hectospec survey covering a region which
corresponds to about three virial radii for each cluster. We measure fluxes of
five emission lines of cluster members enabling us to unambiguously derive O/H
gas metallicities, and also SFRs from extinction corrected Halpha fluxes. We
compare our cluster galaxy sample with a field sample of 705 galaxies at
similar redshifts observed with Hectospec. We find that star-forming cluster
and field galaxies show similar median specific SFRs in a given mass bin, but
their O/H values are displaced to higher values at projected radii of R<R200
compared with galaxies at larger radii and in the field. The comparison with
metallicity-SFR-mass model predictions with inflowing gas indicates a
slow-quenching scenario in which strangulation is initiated when galaxies pass
R~R200 by stopping the inflow of gas. The metallicities of cluster members
inside R200 are thereby increasing, but their SFRs are hardly affected for a
period of time, because these galaxies consume available disk gas. We use the
fraction of star-forming cluster galaxies as a function of clustercentric
radius compared to predictions from the Millennium simulation to constrain
quenching timescales to be 1-2Gyrs. This is consistent with a slow-then-rapid
quenching scenario. Slow quenching (strangulation) starts when the gas inflow
is stopped when the galaxy passes R200 with a phase in which cluster galaxies
are still star-forming, but they show elevated metallicities tracing the
ongoing quenching. This phase lasts for 1-2Gyrs, meanwhile the galaxies travel
to denser inner regions of the cluster, and is followed by a "rapid" phase: a
rapid complete quenching of star formation due to the increasing ram-pressure
towards the cluster center which can also strip the cold gas in massive
galaxies.
