Lessons on Star-forming Ultra-diffuse Galaxies from the Stacked Spectra of the Sloan Digital Sky Survey

We investigate the on-average properties for 28 star-forming ultra-diffuse galaxies (UDGs) located in low-density environments, by stacking their spectra from the Sloan Digital Sky Survey. These relatively isolated UDGs, with stellar masses of ${\mathrm{log}}_{10}({M}_{* }/{M}_{\odot })\sim 8.57\pm 0.29$ , have the on-average total stellar metallicity [M/H] ∼ -0.82 ± 0.14, iron metallicity [Fe/H] ∼ -1.00 ± 0.16, stellar age t_* ∼ 5.2 ± 0.5 Gyr, α-enhancement [α/Fe] ∼ 0.24 ± 0.10, and oxygen abundance 12+log(O/H) ∼ 8.16 ± 0.06, as well as central stellar velocity dispersion 54 ± 12 km s^-1. On the star formation rate versus stellar mass diagram, these UDGs are located lower than the extrapolated star-forming main sequence from the massive spirals, but roughly follow the main sequence of low-surface-brightness dwarf galaxies. We find that these star-forming UDGs are not particularly metal-poor or metal-rich for their stellar masses, as compared with the metallicity-mass relations of the nearby typical dwarfs. With the UDG data of this work and previous studies, we also find a coarse correlation between [Fe/H] and magnesium-element enhancement [Mg/Fe] for UDGs: [Mg/Fe] ≃ -0.43(±0.26) [Fe/H] -0.14(±0.40).