The ultra-diffuse galaxy NGC 1052-DF2 with MUSE: II. The population of
  DF2: stars, clusters and planetary nebulae
  NGC 1052-DF2, an ultra diffuse galaxy (UDG), has been the subject of intense
debate. Its alleged absence of dark matter, and the brightness and number
excess of its globular clusters (GCs) at an initially assumed distance of
20Mpc, suggested a new formation channel for UDGs. We present the first
systematic spectroscopic analysis of both the stellar body and the GCs (six of
which were previously known, and one newly confirmed member) of this galaxy
using MUSE@VLT. Even though NGC 1052-DF2 does not show any spatially extended
emission lines we report the discovery of three planetary nebulae (PNe). We
conduct full spectral fitting on the UDG and the stacked spectra of all GCs.
The UDG's stellar population is old, 8.9$\pm$1.5 Gyr, metal-poor, with [M/H] =
$-$1.07$\pm$0.12 with little or no $\alpha$-enrichment. The stacked spectrum of
all GCs indicates a similar age of 8.9$\pm$1.8 Gyr, but lower metallicity, with
[M/H] = $-$1.63$\pm$0.09, and similarly low $\alpha$-enrichment. There is no
evidence for a variation of age and metallicity in the GC population with the
available spectra. The significantly more metal-rich stellar body with respect
to its associated GCs, the age of the population, its metallicity and alpha
enrichment, are all in line with other dwarf galaxies. NGC 1052-DF2 thus falls
on the same empirical mass-metallicity relation as other dwarfs, for the full
distance range assumed in the literature. We find that both debated distance
estimates (13 and 20 Mpc) are similarly likely, given the three discovered PNe.
