Studies of galaxy surveys in the context of the cold dark matter paradigmhave shown that the mass of the dark matter halo and the total stellar mass arecoupled through a function that varies smoothly with mass. Their average ratioM_{halo}/M_{stars} has a minimum of about 30 for galaxies with stellar massesnear that of the Milky Way (approximately 5x10^{10} solar masses) and increasesboth towards lower masses and towards higher masses. The scatter in thisrelation is not well known; it is generally thought to be less than a factor oftwo for massive galaxies but much larger for dwarf galaxies. Here we report theradial velocities of ten luminous globular-cluster-like objects in theultra-diffuse galaxy NGC1052-DF2, which has a stellar mass of approximately2x10^8 solar masses. We infer that its velocity dispersion is less than 10.5kilometers per second with 90 per cent confidence, and we determine from thisthat its total mass within a radius of 7.6 kiloparsecs is less than 3.4x10^8solar masses. This implies that the ratio M_{halo}/M_{stars} is of order unity(and consistent with zero), a factor of at least 400 lower than expected.NGC1052-DF2 demonstrates that dark matter is not always coupled with baryonicmatter on galactic scales.

We recently found an ultra diffuse galaxy (UDG) with a half-light radius ofR_e = 2.2 kpc and little or no dark matter. The total mass of NGC1052-DF2 wasmeasured from the radial velocities of bright compact objects that areassociated with the galaxy. Here we analyze these objects using a combinationof HST imaging and Keck spectroscopy. Their average size is <r_h> = 6.2+-0.5 pcand their average ellipticity is <{\epsilon}> = 0.18+-0.02. From a stacked Keckspectrum we derive an age >9 Gyr and a metallicity of [Fe/H] = -1.35+-0.12.Their properties are similar to {\omega} Centauri, the brightest and largestglobular cluster in the Milky Way, and our results demonstrate that theluminosity function of metal-poor globular clusters is not universal. Thefraction of the total stellar mass that is in the globular cluster system issimilar to that in other UDGs, and consistent with "failed galaxy" scenarioswhere star formation terminated shortly after the clusters were formed.However, the galaxy is a factor of ~1000 removed from the relation betweenglobular cluster mass and total galaxy mass that has been found for othergalaxies, including other UDGs. We infer that a dark matter halo is not aprerequisite for the formation of metal-poor globular cluster-like objects inhigh redshift galaxies.

We present hydrodynamical N-body models which demonstrate that ellipticalgalaxies can transform into S0s by acquiring a disc. In particular, we showthat the merger with a massive gas-rich satellite can lead to the formation ofa baryonic disc around an elliptical. We model the elliptical as a massive,compact galaxy which could be observed as a 'red nugget' in the high-zuniverse. This scenario contrasts with existing S0 formation scenarios in theliterature in two important ways. First, the progenitor is an elliptical galaxywhereas scenarios in the literature typically assume a spiral progenitor.Second, the physical conditions underlying our proposed scenario can exist inlow-density environments such as the field, in contrast to scenarios in theliterature which typically address dense environments like clusters and groups.As a consequence, S0s in the field may be the most likely candidates to haveevolved from elliptical progenitors. Our scenario also naturally explainsrecent observations which indicate that field S0s may have older bulges thandiscs, contrary to cluster S0s which seem to have older discs than bulges.

MaNGA provides the opportunity to make precise spatially resolvedmeasurements of the IMF slope in galaxies owing to its unique combination ofspatial resolution, wavelength coverage and sample size. We derive radialgradients in age, element abundances and IMF slope analysing optical andnear-infrared absorption features from stacked spectra out to the half-lightradius of 366 early-type galaxies with masses $9.9 - 10.8\;\log M/M_{\odot}$.We find flat gradients in age and [$\alpha$/Fe] ratio, as well as negativegradients in metallicity, consistent with the literature. We further derivesignificant negative gradients in the [Na/Fe] ratio with galaxy centres beingwell enhanced in Na abundance by up to 0.5 dex. Finally, we find a gradient inIMF slope with a bottom-heavy IMF in the centre (typical mass excess factor of1.5) and a Milky Way-type IMF at the half-light radius. This pattern ismass-dependent with the lowest mass galaxies in our sample featuring only ashallow gradient around a Milky Way IMF. Our results imply the localIMF-$\sigma$ relation within galaxies to be even steeper than the globalrelation and hint towards the local metallicity being the dominating factorbehind the IMF variations. We also employ different stellar population modelsin our analysis and show that a radial IMF gradient is found independently ofthe stellar population model used. A similar analysis of the Wing-Ford bandprovides inconsistent results and further evidence of the difficulty inmeasuring and modelling this particular feature.

We report the discovery of a new low-redshift galaxy-scale gravitationallens, identified from a systematic search of publicly available MUSEobservations. The lens galaxy, 2MASXJ04035024-0239275, is a giant elliptical at$z$ = 0.06604 with a velocity dispersion of $\sigma$ = 314 km s$^{-1}$. Thelensed source has a redshift of 0.19165 and forms a pair of bright imageseither side of the lens centre. The Einstein radius is 1.5 arcsec, projectingto 1.8 kpc, which is just one quarter of the galaxy effective radius. Aftercorrecting for an estimated 19 per cent dark matter contribution, we find thatthe stellar mass-to-light ratio from lensing is consistent with that expectedfor a Milky Way initial mass function (IMF). Combining the new system withthree previously-studied low-redshift lenses of similar $\sigma$, the derivedmean mass excess factor (relative to a Kroupa IMF) is $\langle\alpha\rangle$ =1.09$\pm$0.08. With all four systems, the intrinsic scatter in $\alpha$ formassive elliptical galaxies can be limited to $<0.32$, at 90 per centconfidence.