(abridged) We provide Ks photometry for roughly 39,000 stars and H-bandphotometry for about 11,000 stars within a field of about 40"x40", centred onSgr A*. In addition, we provide Ks photometry of about 3,000 stars in a verydeep central field of 10"x10", centred on Sgr A*. We find that the Ksluminosity function (KLF) is rather homogeneous within the studied field anddoes not show any significant changes as a function of distance from thecentral black hole on scales of a few 0.1 pc. By fitting theoretical luminosityfunctions to the KLF, we derive the star formation history of the nuclear starcluster. We find that about 80% of the original star formation took place 10Gyr ago or longer, followed by a largely quiescent phase that lasted for morethan 5 Gyr. We clearly detect the presence of intermediate-age stars of about 3Gyr in age. This event makes up about 15% of the originally formed stellar massof the cluster. A few percent of the stellar mass formed in the past few 100Myr. Our results appear to be inconsistent with a quasi-continuous starformation history. The stellar density increases exponentially towards Sgr A*at all magnitudes between Ks=15 to 19. We also show that the precise propertiesof the stellar cusp around Sgr A* are hard to determine because the starformation history suggests that the star counts can be significantlycontaminated, at all magnitudes, by stars that are too young to be dynamicallyrelaxed. We find that the probability of observing any young (non-millisecond)pulsar in a tight orbit around Sgr A* and beamed towards Earth is very low. Weargue that typical globular clusters, such as they are observed in and aroundthe Milky Way today, have probably not contributed to the nuclear cluster'smass in any significant way. The nuclear cluster may have formed followingmajor merger events in the early history of the Milky Way.

X-ray emitting atmospheres of non-rotating early-type galaxies and theirconnection to central active galactic nuclei have been thoroughly studied overthe years. However, in systems with significant angular momentum, processes ofheating and cooling are likely to proceed differently. We present an analysisof the hot atmospheres of six lenticulars and a spiral galaxy to study theeffects of angular momentum on the hot gas properties. We find an alignmentbetween the hot gas and the stellar distribution, with the ellipticity of theX-ray emission generally lower than that of the optical stellar emission,consistent with theoretical predictions for rotationally-supported hotatmospheres. The entropy profiles of NGC 4382 and the massive spiral galaxy NGC1961 are significantly shallower than the entropy distribution in othergalaxies, suggesting the presence of strong heating (via outflows orcompressional) in the central regions of these systems. Finally, we investigatethe thermal (in)stability of the hot atmospheres via criteria such as the TI-and C-ratio, and discuss the possibility that the discs of cold gas present inthese objects have condensed out of the hot atmospheres.

It has been proposed that S0 galaxies are either fading spirals or the resultof galaxy mergers. The relative contribution of each pathway, and theenvironments in which they occur remains unknown. Here we investigate stellarand gas kinematics of 219 S0s in the SAMI Survey to look for signs of multipleformation pathways occurring across the full range of environments. We identifya large range of rotational support in their stellar kinematics, whichcorrespond to ranges in their physical structure. We find thatpressure-supported S0s with $v/{\sigma}$ below 0.5 tend to be more compact andfeature misaligned stellar and gas components, suggesting an external originfor their gas. We postulate that these S0s are consistent with being formedthrough a merger process. Meanwhile, comparisons of ellipticity, stellar massand S\'ersic index distributions with spiral galaxies shows that therotationally supported S0s with $v/{\sigma}$ above 0.5 are more consistent witha faded spiral origin. In addition, a simulated merger pathway involving acompact elliptical and gas-rich satellite results in an S0 that lies within thepressure-supported group. We conclude that two S0 formation pathways areactive, with mergers dominating in isolated galaxies and small groups, and thefaded spiral pathway being most prominent in large groups ($10^{13} < M_{halo}< 10^{14}$).