Constraining the formation of NGC 1052-DF2 from its unusual globular cluster population

The ultra-diffuse galaxy (UDG) NGC 1052-DF2 has a low dark matter content and hosts a very unusual globular cluster (GC) population, with a median luminosity ~4 times higher than in most galaxies and containing about 5 per cent of the galaxy's stars. We apply a theoretical model that predicts the initial cluster mass function as a function of the galactic environment to investigate the origin of DF2's peculiar GC system. Using the GC mass function, the model constrains the star-forming conditions in the galaxy during the formation of its GCs, ~9 Gyr ago. We predict that the GCs formed in an environment with very high gas surface density, $\Sigma _{\rm ISM}\gtrsim 10^3\rm \,{M_\odot}\rm \,{pc}^{-2}$, and strong centrifugal support, $\Omega \gtrsim 0.7\rm \,{Myr}^{-1}$, similar to nearby circumnuclear starbursts and the central region of the Milky Way. The extreme conditions required to form the observed GC population imply a very high cluster formation efficiency of ≈87 per cent, and contrast strongly with the current diffuse nature of the galaxy. Since a nuclear starburst would lead to the rapid in-spiral of the GCs and is ruled out by the absence of a nuclear star cluster, we propose that the GCs plausibly formed during a major merger at z ~ 1.3. The merger remnant must have undergone significant expansion of its stellar (and perhaps also its dark matter) component to reach its low present surface brightness, leading to the interesting possibility that it was the formation of DF2's extreme GC population that caused it to become a UDG. If true, this strong structural evolution would have important implications for understanding the origins of UDGs.