Environmental effects as a key factor in shaping star-forming S0 galaxies

The origins of lenticular galaxies (S0s) can be classified into two main categories: ``minor mergers" in low-density environments (LDEs) and ``faded spirals" in high-density environments (HDEs). The transitional phase in the evolution of S0s, namely, star-forming lenticular galaxies (SFS0s), can serve as an important probe for analyzing the complex processes involved in the transformation between different galaxy types and the quenching of star formation (SF). We attempt to find the impact of different environments on the global properties and spatially resolved quantities of SFS0s. We selected 71 SFS0s from the SDSS-IV MaNGA Survey, comprising 23 SFS0s in HDEs (SFS0s$\_$HE) and 48 SFS0s in LDEs (SFS0s$\_$LE). We examined the effects of the environment, by studying the global properties, concentration index, and radial profiles of the derived quantities. The varied environments of SFS0s do not lead to any significant difference in global properties (e.g., S$\acute{\rm e}$rsic index). By calculating $CI_{\rm H_{\alpha}/cont}$, we observe that different environments may cause varying concentrations of SF. Specifically, SFS0s$\_$LE, affected by external gas mergers or inflow, exhibit a more centrally concentrated SF (i.e., larger $CI_{\rm H_{\alpha}/cont}$). This trend is further supported by $CI_{\rm SFR, H_{\alpha}}$, which only considers the gas disk of the galaxy. This observation is aligned with the observed shrinking of gas disks in galaxies affected by ram-pressure stripping in HDEs. Furthermore, their $\Sigma_{\rm SFR}$ or resolved sSFR are comparable. On average, SFS0s$\_$LE display significantly higher values for both quantities. Finally, the observed D$_{\rm n}4000$ and gas-phase metallicity gradient correspond well to their assumed origins. However, we did not find a significantly lower gas-phase metallicity in SFS0s$\_$LE. Abridged