Toward Understanding the Evolutionary Role of Star-forming Lenticular Galaxies: New HI Detections and Comparison with Quiescent S0s and Red Spirals

As one type of blue early-type galaxies, the evolutionary history and fate of star-forming lenticular galaxies (S0s) remain elusive. We selected 134 star-forming S0s from the SDSS-IV MaNGA survey and found that they have steep and warped size-mass relations, similar to quiescent S0s and red spirals, indicating that they may have similar gas dissipation scenarios. These galaxies have a higher central stellar mass surface density than normal blue spirals. The radial profiles of $D_{\mathrm{n}}4000$ and [Mgb/Fe] show that red spirals and quiescent S0s have similar old central populations and high [Mgb/Fe] values, suggesting rapid bulge formation, though red spirals exhibit a steeper gradient possibly due to residual star formation (SF) in outer regions. In contrast, star-forming S0s exhibit profiles between quiescent S0s/red spirals and normal blue spirals, with relatively flat $D_{\mathrm{n}}4000$ and [Mgb/Fe] gradients. More long-term SF history causes normal blue spirals to have very flat $D_{\mathrm{n}}4000$ and [Mgb/Fe] profiles, and the majority of them (79 $\pm$ 5 $\mathrm{\%}$) have S$\acute{\mathrm{e}}$rsic index $<$ 2. We also found that the halo mass of star-forming S0s resembles that of quiescent S0s/red spirals, with 82 $\pm$ 5 $\mathrm{\%}$ exceeding the critical mass ($M_{\mathrm{h}\mathrm{a}\mathrm{l}\mathrm{o}}={10}^{12}$$M_{\odot }$h${}^{-1}$). To supplement previous H,{\sc i} detection of star-forming S0s covered by H,{\sc i}MaNGA, we obtained new observation for H,{\sc i} emission from 41 star-forming S0s in our sample using the Five-hundred-meter Aperture Spherical Radio Telescope. We found that the H,{\sc i} mass distribution of star-forming S0s matches that of normal blue spirals, although both star-forming S0s and red spirals are relatively gas-poor, resulting in varying atomic gas depletion times due to different SF levels. Based on these observational results, we discuss the possible evolutionary scenarios of star-forming S0s.