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NGC 1052-DF2, an ultra diffuse galaxy (UDG), has been the subject of intensedebate. Its alleged absence of dark matter, and the brightness and numberexcess of its globular clusters (GCs) at an initially assumed distance of20Mpc, suggested a new formation channel for UDGs. We present the firstsystematic spectroscopic analysis of both the stellar body and the GCs (six ofwhich were previously known, and one newly confirmed member) of this galaxyusing MUSE@VLT. Even though NGC 1052-DF2 does not show any spatially extendedemission lines we report the discovery of three planetary nebulae (PNe). Weconduct 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 ofall 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 noevidence for a variation of age and metallicity in the GC population with theavailable spectra. The significantly more metal-rich stellar body with respectto its associated GCs, the age of the population, its metallicity and alphaenrichment, are all in line with other dwarf galaxies. NGC 1052-DF2 thus fallson the same empirical mass-metallicity relation as other dwarfs, for the fulldistance range assumed in the literature. We find that both debated distanceestimates (13 and 20 Mpc) are similarly likely, given the three discovered PNe.

The ultra-diffuse galaxy NGC 1052-DF2 with MUSE: II. The population of DF2: stars, clusters and planetary nebulae