Lessons on Star-forming Ultra-diffuse Galaxies from The Stacked Spectra
  of 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 $\log_{10}(M_*/M_{\odot})\sim 8.57\pm0.29$, have the on-average
total-stellar-metallicity [M/H]$\sim -0.82\pm0.14$, iron-metallicity
[Fe/H]$\sim -1.00\pm0.16$, stellar age $t_*\sim5.2\pm0.5$ Gyr,
$\alpha$-enhancement [$\alpha$/Fe]$\sim 0.24\pm0.10$, and oxygen abundance
12+log(O/H)$\sim 8.16\pm0.06$, as well as central stellar velocity dispersion
$54\pm12$ km/s. 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]$\simeq-0.43(\pm0.26)$[Fe/H]$-0.14(\pm0.40)$.
