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VIS3COS: III. environmental effects on the star formation histories of galaxies at z~0.8 seen in [OII], H$δ$, and Dn4000

[ABRIDGED] We present spectroscopic observations of 466 galaxies in and around a superstructure at $z\sim0.84$ targeted by the VIMOS Spectroscopic Survey of a Supercluster in the COSMOS field (VIS$^{3}$COS). We use [OII]$λ$3727, H$δ$, and $D_n4000$ to trace the recent, mid-, and long-term star formation histories and investigate how stellar mass and the local environment impacts those. By studying trends both in individual and composite galaxy spectra, we find that both stellar mass and environment play a role in the observed galactic properties. We find that the median [OII] equivalent width (|EW$_\mathrm{[OII]}|$) decreases from $27\pm2$ Å to $2.0_{-0.4}^{+0.5}$ Å and $D_n4000$ increases from $1.09\pm0.01$ to $1.56\pm0.03$ with increasing stellar mass (from $\sim10^{9.25}$ to $\sim10^{11.35}\ \mathrm{M_\odot}$). Concerning the dependence on the environment, we find that at fixed stellar mass |EW$_\mathrm{[OII]}|$ is tentatively lower in higher density environments. Regarding $D_n4000$, we find that the increase with stellar mass is sharper in denser environments, hinting that such environments may accelerate galaxy evolution. Moreover, we find larger $D_n4000$ values in denser environments at fixed stellar mass, suggesting that galaxies are on average older and/or more metal-rich in such dense environments. This set of tracers depicts a scenario where the most massive galaxies have, on average, the lowest sSFRs and the oldest stellar populations (age $\gtrsim1$ Gyr, showing a mass-downsizing effect). We also hypothesize that the observed increase in star formation (higher EW$_\mathrm{[OII]|}$, higher sSFR) at intermediate densities may lead to quenching since we find the quenched fraction to increase sharply from the filament to cluster-like regions at similar stellar masses.