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We present Magellan/IMACS and Magellan/MIKE spectroscopy of the ultra-faint dwarf (UFD) galaxy Pictor~II (Pic~II) that is located only 12 kpc from the Large Magellanic Cloud (LMC). From the IMACS spectroscopy, we identify 13 member stars and measure a mean heliocentric velocity of , a velocity dispersion of , a mean metallicity of , and an upper limit on the metallicity dispersion of . We measure detailed elemental abundances for the brightest star, finding $\text{[Fe/H]}=-3.3$, high [ $\alpha$/Fe] ratios, and no detectable neutron capture elements, similar to stars in other UFDs. However, this star has an unusually high [Sc/Fe] ratio. The dynamical mass-to-light ratio ( $M/L={760}_{-420}^{+910}{M}_{\odot }{L}_{\odot }^{-1}$), size, and chemical abundances confirms that Pic~II is a dark matter-dominated dwarf galaxy. We perform detailed orbit modeling of Pic~II in a combined Milky Way (MW) and LMC potential and find that Pic~II is highly likely to be a long-term LMC satellite. Furthermore, we find that Pic II is likely still bound to the LMC today. Pic~II is the seventh LMC-associated UFD and among the most metal-poor UFDs known. We further update the morphological parameters with deeper Dark Energy Camera (DECam) photometry, compute the dark matter properties for dark matter indirect detection searches, verify the extremely low metallicity with narrowband CaHK imaging, and briefly discuss tidal influences of the LMC and MW. 

Abstract We report the discovery and spectroscopic confirmation of an ultra-faint Milky Way satellite in the constellation of Leo. This system was discovered as a spatial overdensity of resolved stars observed with Dark Energy Camera (DECam) data from an early version of the third data release of the DECam Local Volume Exploration (or DELVE) survey. The low luminosity ( $M_V=-3.56_{-0.37}^{+0.47}$; $L_V=2300_{-700}^{+1200}{L}_{\odot }$), large size ( $R_{1/2}=90_{-30}^{+30}$pc), and large heliocentric distance ( $D=111_{-6}^{+9}$kpc) are all consistent with the population of ultra-faint dwarf galaxies (UFDs). Using Keck/DEIMOS observations of the system, we were able to spectroscopically confirm nine member stars, while measuring a tentative mass-to-light ratio of $700_{-500}^{+1400}{M}_{\odot }/L_{\odot }$and a nonzero metallicity dispersion of ${\sigma }_{[\mathrm{Fe}/\mathrm{H}]}=0.19_{-0.11}^{+0.14}$, further confirming Leo VI’s identity as a UFD. While the system has a highly elliptical shape, $ϵ=0.54_{-0.29}^{+0.19}$, we do not find any conclusive evidence that it is tidally disrupting. Moreover, despite the apparent on-sky proximity of Leo VI to members of the proposed Crater-Leo infall group, its smaller heliocentric distance and inconsistent position in energy–angular momentum space make it unlikely that Leo VI is part of the proposed infall group. 

Abstract We present the discovery of Aquarius III, an ultra-faint Milky Way satellite galaxy identified in the second data release of the DECam Local Volume Exploration survey. Based on deeper follow-up imaging with DECam, we find that Aquarius III is a low-luminosity ( $M_V=-{2.5}_{-0.5}^{+0.3};$ $L_V={850}_{-260}^{+380}{L}_{\odot }$), extended ( $r_{1/2}={41}_{-8}^{+9}$pc) stellar system located in the outer halo (D_⊙= 85 ± 4 kpc). From medium-resolution Keck/DEIMOS spectroscopy, we identify 11 member stars and measure a mean heliocentric radial velocity of $v_{\mathrm{sys}}=-{13.1}_{-0.9}^{+1.0}\mathrm{km}{\mathrm{s}}^{-1}$for the system and place an upper limit ofσ_v< 3.5 km s⁻¹(σ_v< 1.6 km s⁻¹) on its velocity dispersion at the 95% (68%) credible level. Based on calcium-triplet metallicities of the six brightest red giant members, we find that Aquarius III is very metal-poor ([Fe/H]= − 2.61 ± 0.21) with a statistically significant metallicity spread ( ${\sigma }_{\left[\mathrm{Fe}/\mathrm{H}\right]}={0.46}_{-0.14}^{+0.26}$dex). We interpret this metallicity spread as strong evidence that the system is a dwarf galaxy as opposed to a star cluster. Combining our velocity measurement with Gaia proper motions, we find that Aquarius III is currently situated near its orbital pericenter in the outer halo (r_peri= 78 ± 7 kpc) and that it is plausibly on first infall onto the Milky Way. This orbital history likely precludes significant tidal disruption from the Galactic disk, notably unlike other satellites with comparably low velocity dispersion limits in the literature. Thus, if further velocity measurements confirm that its velocity dispersion is truly belowσ_v≲ 2 km s⁻¹, Aquarius III may serve as a useful laboratory for probing galaxy formation physics in low-mass halos. 

We introduce a new (ϵₚ, δₚ)-differentially private algorithm for the k-means clustering problem. Given a dataset in Euclidean space, the k-means clustering problem requires one to find k points in that space such that the sum of squares of Euclidean distances between each data point and its closest respective point among the k returned is minimised. Although there exist privacy-preserving methods with good theoretical guarantees to solve this problem, in practice it is seen that it is the additive error which dictates the practical performance of these methods. By reducing the problem to a sequence of instances of maximum coverage on a grid, we are able to derive a new method that achieves lower additive error than previous works. For input datasets with cardinality n and diameter Δ, our algorithm has an O(Δ² (k log² n log(1/δₚ)/ϵₚ + k √(d log(1/δₚ))/ϵₚ)) additive error whilst maintaining constant multiplicative error. We conclude with some experiments and find an improvement over previously implemented work for this problem.