Discovery of a red ultra-diffuse galaxy in a nearby void based on its globular cluster luminosity function

Distance determinations of extremely-low-surface-brightness galaxies are expensive in terms of spectroscopic time. Because of this, their distances are often inferred by associating such galaxies with larger structures such as groups or clusters, leading to a systematic bias by selecting objects in high density environments. Here we report the discovery of a red ultra-diffuse galaxy (S82-DG-1: $r_{\mathrm{eff}}$ = 1.6 kpc; $<\mu _{g}>$ = 25.7 mag arcsec$^{-2}$; $g-i$ = 0.78 mag) located in a nearby cosmic void. We used multi-band luminosity functions of its globular clusters to obtain the distance to S82-DG-1, at 28.7$_{-3.6}^{+4.2}$ Mpc. Follow-up deep spectroscopy with the GTC telescope yields a redshift of 3353 $\pm$ 29 km s$^{-1}$, making its association with the NGC 1211 galaxy (one of the most isolated galaxies known) highly likely. Both galaxies have compatible distances and redshifts, share a high peculiar velocity ($\sim$1000 km s$^{-1}$) and lie within a void of radius 7 Mpc. The local surface density is $\Sigma_5 \sim 0.06$ Mpc$^{-2}$, an order of magnitude smaller than the field population and similar to the voids found in the GAMA survey. Our work shows: i) The high potential of using optical ground-based photometry of associated globular clusters to explore distances to ultra-diffuse galaxies and ii) the presence of red ultra-diffuse galaxies even in the most sparse environments, suggesting a wide range of formation mechanisms.