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Omega Centauri ($\omega$ Cen) is the Milky Way's most massive globular cluster and is likely the stripped nucleus of an accreted dwarf galaxy. In this paper, we analyze $\omega$ Cen's kinematics using data from oMEGACat, a comprehensive catalog of $\omega$ Cen's central regions, including 1.4 million proper motion measurements and 300,000 spectroscopic radial velocities. Our velocity dispersion profiles and kinematic maps are consistent with previous work but improve on their resolution, precision, and spatial coverage. The cluster's 3D dispersion is isotropic in the core, with increasing radial anisotropy at larger radii. The 2D kinematic maps show an elongation of the velocity dispersion field comparable to the flattening observed photometrically. We find good agreement between proper motions and line-of-sight velocity dispersion and measure a kinematic distance of 5494$\pm$61 pc, the most precise kinematic distance to $\omega$ Cen available. The subset of data with precise metallicity measurements shows no correlation between metallicity and kinematics, supporting the picture of well-mixed stellar populations within the half-light radius of $\omega$ Cen. Finally, we study the degree of energy equipartition using a large range of stellar masses. We find partial energy equipartition in the center that decreases towards large radii. The spatial dependence of the radial energy equipartition is stronger than the tangential energy equipartition. Our kinematic observations can serve as a new reference for future dynamical modeling efforts that will help to further disentangle the complex mass distribution within $\omega$ Cen., Comment: 31 pages, 23 Figures, 4 Tables. Accepted for publication in ApJ. Data products available under: https://doi.org/10.5281/zenodo.14978551 more...

The Galactic bulge hosts the Milky Way's oldest stars, possibly coming from disrupted globular clusters (GCs) or the bulge's primordial building blocks, making these stars witnesses to the Galaxy's early chemical enrichment. The Galactic bar currently dominates the bulge's region, altering the orbits of objects formed before its formation and complicating the trace of the field stars' original clusters. Here, we present the discovery of a fossil record of this evolution, SOS1 -- a star trapped in the bar, exhibiting significant enhancements in nitrogen, sodium, and aluminum, typical of second-generation GC stars. SOS1 also shows an s-process Ce enhancement, suggesting an old age and early enrichment by fast-rotating massive stars in the Galaxy's earliest phases. With the purpose of finding the SOS1's parent GC, we derive its precise chemodynamical properties by combining high-precision proper motions from Gaia with APOGEE detailed chemical abundances. Our analysis suggests that SOS1 was possibly stripped from the GC Terzan 5 by the Galactic bar's gravitational influence approximately 350 Myr ago. We also found chemical similarities suggesting that SOS1 belonged to the most metal-poor, ancient, and peripheral stellar population of Terzan 5. These results not only support the hypothesis that Terzan 5 is a remnant of a primordial building block of the Galactic bulge, but also suggest this cluster continues losing stars to the bar. Our method highlights how powerful the use of chemodynamical properties in the Gaia era is for tracing the Galaxy's evolutionary history., Comment: Accepted for publication in ApJ Letters. 13 pages, 4 Figures (+ 3 in Appendix), and 1 Table (+ 1 in Appendix) more...

Dwarf galaxies are known to exhibit an unusual richness in numbers of globular clusters (GCs), property quantified by the specific frequency ($S_N$), which is high for dwarf and giant elliptical galaxies, but with a minimum for intermediate-mass galaxies. In this work we study the role that GC evolution has in setting this trend, for which we use ${\it N}$-body simulations to evolve GCs in dwarf galaxies and quantify their disruption efficiency. We selected five individual dwarf galaxies from a high-resolution cosmological simulation, which includes GC formation and follow-up of their paths inside the host galaxy. Then, the tidal history of each GC is coupled to NBODY6++GPU to produce ${\it N}$-body models that account for both, the interaction of GCs with their galactic environment and their internal dynamics. This results in a GC mass loss parameterization to estimate dissolution times and mass loss rates after a Hubble time. GC evolution is sensitive to the particular orbital histories within each galaxy, but the overall result is that the amount of mass that GC systems lose scales with the mass (and density) of the host galaxy, i.e., the GC mass loss efficiency is lowest in low-mass dwarfs. After a 12 Gyr evolution all simulated GC systems retain an important fraction of their initial mass (up to 25%), in agreement with the high GC to field star ratios observed in some dwarfs, and supports the scenario in which GC disruption mechanisms play an important role in shaping the GC specific frequency in dwarf galaxies., Comment: 16 pages, 11 figures, 4 tables. Accepted for publication in MNRAS more...

The information on Galactic assembly time is imprinted on the chemodynamics of globular clusters. This makes them important probes that help us to understand the formation and evolution of the Milky Way. Discerning between in-situ and ex-situ origin of these objects is difficult when we study the Galactic bulge, which is the most complex and mixed component of the Milky Way. To investigate the early evolution of the Galactic bulge, we analysed the globular cluster NGC 6355. We derived chemical abundances and kinematic and dynamic properties by gathering information from high-resolution spectroscopy with FLAMES-UVES, photometry with the Hubble Space Telescope, and Galactic dynamic calculations applied to the globular cluster NGC 6355. We derive an age of $13.2\pm1.1$ Gyr and a metallicity of [Fe/H]$=-1.39\pm0.08$ for NGC 6355, with $\alpha$-enhancement of [$\alpha$/Fe]$=+0.37\pm0.11$. The abundance pattern of the globular cluster is compatible with bulge field RR Lyrae stars and in-situ well-studied globular clusters. The orbital parameters suggest that the cluster is currently confined within the bulge volume when we consider a heliocentric distance of $8.54\pm0.19$ kpc and an extinction coefficient of $R_V = 2.84\pm0.02$. NGC 6355 is highly likely to come from the main bulge progenitor. {Nevertheless, it still} has a low probability of being formed from an accreted event because its age is uncertain and because of the combined [Mg/Mn] [Al/Fe] abundance. Its relatively low metallicity with respect to old and moderately metal-poor inner Galaxy clusters may suggest a low-metallicity floor for globular clusters that formed in-situ in the early Galactic bulge., Comment: 20 pages, 26 figures, and 9 tables. Astronomy & Astrophysics, in press. Some minor corrections more...

We combine spectroscopic, photometric, and astrometric information from APOGEE data release 17 and $Gaia$ early data release 3 to perform a self-consistent characterization of $Gaia$-Sausage/Enceladus (GSE), the remnant of the last major merger experienced by the Milky Way, considering stars and globular clusters (GCs) altogether. Our novel set of chemodynamical criteria to select genuine stars of GSE yields a metallicity distribution function with a median [Fe/H] of $-1.22$ dex and $0.23$ dex dispersion. Stars from GSE present an excess of [Al/Fe] and [Mg/Mn] (also [Mg/Fe]) in comparison to surviving Milky Way dwarf satellites, which can be explained by differences in star-formation efficiencies and timescales between these systems. However, stars from Sequoia, another proposed accreted halo substructure, essentially overlap the GSE footprint in all analyzed chemical-abundance spaces, but present lower metallicities. Among probable GCs of GSE with APOGEE observations available, we find no evidence for atypical [Fe/H] spreads with the exception of $\omega$ Centauri ($\omega$Cen). Under the assumption that $\omega$Cen is a stripped nuclear star cluster, we estimate the stellar mass of its progenitor to be $M_\star \approx 1.3 \times 10^9 M_\odot$, well-within literature expectations for GSE. This leads us to envision GSE as the best available candidate for the original host galaxy of $\omega$Cen. We also take advantage of $Gaia$'s photometry and APOGEE metallicities as priors to determine fundamental parameters for eight high-probability ($>$70%) GC members of GSE via statistical isochrone fitting. Finally, the newly determined ages and APOGEE [Fe/H] values are utilized to model the age-metallicity relation of GSE., Comment: Accepted for ApJ. New version matches the accepted one. Added/removed some references and included some clarifications on Section 3.4 more...

Palomar 6 (Pal~6) is a moderately metal-poor globular cluster projected towards the Galactic bulge. A full analysis of the cluster can give hints on the early chemical enrichment of the Galaxy and a plausible origin of the cluster. The aim of this study is threefold: a detailed analysis of high-resolution spectroscopic data obtained with the UVES spectrograph at the Very Large Telescope (VLT) at ESO, the derivation of the age and distance of Pal~6 from Hubble Space Telescope (HST) photometric data, and an orbital analysis to determine the probable origin of the cluster. High-resolution spectra of six red giant stars in the direction of Palomar 6 were obtained at the $8$m VLT UT2-Kueyen telescope equipped with the UVES spectrograph in FLAMES$+$UVES configuration. Spectroscopic parameters were derived through excitation and ionisation equilibrium of \ion{Fe}{I} and \ion{Fe}{II} lines, and the abundances were obtained from spectrum synthesis. From HST photometric data, the age and distance were derived through a statistical isochrone fitting. Finally, a dynamical analysis was carried out for the cluster assuming two different Galactic potentials. Four stars that are members of Pal~6 were identified in the sample, which gives a mean radial velocity of $174.3\pm1.6$ km\,s$^{-1}$ and a mean metallicity of [Fe/H]$\,=-1.10\pm0.09$ for the cluster. We found an enhancement of $\alpha$-elements (O, Mg, Si, and Ca) $0.29<\,$[X/Fe]$\,<0.38$ and the iron-peak element Ti of [Ti/Fe]$\,\sim+0.3$. The odd-Z elements (Na and Al) show a mild enhancement of [X/Fe]$\,\sim +0.25$. The abundances of both first- (Y and Zr) and second-peak (Ba and La) heavy elements are relatively high, with $+0.4<\,$[X/Fe]$\,<+0.60$ and $+0.4<\,$[X/Fe]$\,<+0.5$, respectively. The r-element Eu is also relatively high with [Eu/Fe]$\,\sim +0.6$. $\mathbf{\left[Truncated\right]}$, Comment: 23 pages, 26 figures, and 12 tables. References added, typos corrected, published version more...

We present results from a study of fifteen red giant members of the intermediate-metallicity globular cluster (GC) FSR 1758 using high-resolution near-infrared spectra collected with the Apache Point Observatory Galactic Evolution Experiment II survey (APOGEE-2), obtained as part of CAPOS (the bulge Cluster APOgee Survey). Since its very recent discovery as a massive GC in the bulge region, evoking the name Sequoia, this has been an intriguing object with a highly debated origin, and initially led to the suggestion of a purported progenitor dwarf galaxy of the same name. In this work, we use new spectroscopic and astrometric data to provide additional clues to the nature of FSR 1758. Our study confirms the GC nature of FSR 1758, and as such we report for the first time the existence of the characteristic N-C anti-correlation and Al-N correlation, revealing the existence of the multiple-population phenomenon, similar to that observed in virtually all GCs. Furthermore, the presence of a population with strongly enriched aluminium makes it unlikely FSR 1758 is the remnant nucleus of a dwarf galaxy, as Al-enhanced stars are uncommon in dwarf galaxies. We find that FSR 1758 is slightly more metal rich than previously reported in the literature, with a mean metallicity [Fe/H] between $-1.43$ to $-1.36$ (depending on the adopted atmospheric parameters), and with a scatter within observational error, again pointing to its GC nature. Overall, the $\alpha$-enrichment ($\gtrsim+0.3$ dex), Fe-peak (Fe, Ni), light- (C, N), and odd-Z (Al) elements follow the trend of intermediate-metallicity GCs. ... A new examination of its dynamical properties with the \texttt{GravPot16} model favors an association with the Gaia-Enceladus-Sausage accretion event. Thus, paradoxically, the cluster that gave rise to the name of the Sequoia dwarf galaxy does not appear to belong to this specific merging event., Comment: 15 pages, 8 pages, 3 Tables. Abridged abstract. Accepted for publication in Astronomy & Astrophysics (A&A) more...

We identified 8 additional stars as members of the Helmi stream (HStr) in the combined GALAH+ DR3 and $Gaia$ EDR3 catalog. By consistently reevaluating claimed members from the literature, we consolidate a sample of 22 HStr stars with parameters determined from high-resolution spectroscopy and spanning a considerably wider (by $\sim$0.5 dex) metallicity interval ($-2.5 \lesssim \rm[Fe/H] < -1.0$) than previously reported. Our study focuses on $\alpha$ (Mg and Ca) and neutron-capture (Ba and Eu) elements. We find that the chemistry of HStr is typical of dwarf spheroidal (dSph) galaxies, in good agreement with previous $N$-body simulations of this merging event. Stars of HStr constitute a clear declining sequence in $\rm[\alpha/Fe]$ for increasing metallicity up to $\rm[Fe/H] \sim -1.0$. Moreover, stars of HStr show a median value of $+$0.5 dex for $\rm[Eu/Fe]$ with a small dispersion ($\pm$0.1 dex). Every star analyzed with $\rm[Fe/H] < -1.2$ belong to the $r$-process enhanced ($\rm[Eu/Fe] > +0.3$ and $\rm[Ba/Eu] < 0.0$) metal-poor category, providing remarkable evidence that, at such low-metallicity regime, stars of HStr experienced enrichment in neutron-capture elements predominantly via $r$-process nucleosynthesis. Finally, the extended metallicity range also suggests an increase in $\rm[Ba/Eu]$ for higher $\rm[Fe/H]$, in conformity with other surviving dwarf satellite galaxies of the Milky Way., Comment: 9 pages (+2 appendix), 4 figures. Accepted for publication in ApJ Letters more...

Recent developments in Machine Learning and Deep Learning depend heavily on cloud computing and specialized hardware, such as GPUs and TPUs. This forces those using those models to trust private data to cloud servers. Such scenario has prompted a large interest on Homomorphic Cryptography and Secure Multi-Party Computation protocols that allow the use of cloud computing power in a privacy-preserving manner. When comparing the efficiency of such protocols, most works in literature resort to complexity analysis that gives asymptotic higher-bounding limits of computational cost when input size tends to infinite. These limits may be very different from the actual cost or execution time, when performing such computations over small, or average-sized datasets. We argue that Monte Carlo methods can render better computational cost and time estimates, fostering better design and implementation decisions for complex systems, such as Privacy-Preserving Machine Learning Frameworks. more...

The central (`bulge') region of the Milky Way is teeming with a significant fraction of mildly metal-deficient stars with atmospheres that are strongly enriched in cyanogen ($^{12}$C$^{14}$N). Some of these objects, which are also known as nitrogen-enhanced stars, are hypothesised to be relics of the ancient assembly history of the Milky Way. Although the chemical similarity of nitrogen-enhanced stars to the unique chemical patterns observed in globular clusters has been observed, a direct connection between field stars and globular clusters has not yet been proven. In this work, we report on high-resolution, near-infrared spectroscopic observations of the bulge globular cluster NGC 6723, and the serendipitous discovery of a star, 2M18594405$-$3651518, located outside the cluster (near the tidal radius) but moving on a similar orbit, providing the first clear piece of evidence of a star that was very likely once a cluster member and has recently been ejected. Its nitrogen abundance ratio ([N/Fe]$\gtrsim + 0.94$) is well above the typical Galactic field-star levels, and it exhibits noticeable enrichment in the heavy $s$-process elements (Ce, Nd, and Yb), along with moderate carbon enrichment; all characteristics are known examples in globular clusters. This result suggests that some of the nitrogen-enhanced stars in the bulge likely originated from the tidal disruption of globular clusters., Comment: Astronomy & Astrophysics, in press. 16 pages, 8 figures, 2 tables more...

We present the first high-resolution abundance analysis of the globular cluster VVV~CL001, which resides in a region dominated by high interstellar reddening towards the Galactic Bulge. Using \textit{H}-band spectra acquired by the Apache Point Observatory Galactic Evolution Experiment (APOGEE), we identified two potential members of the cluster, and estimate from their Fe I lines that the cluster has an average metallicity of [Fe/H] = $-2.45$ with an uncertainty due to systematics of 0.24 dex. We find that the light-(N), $\alpha$-(O, Mg, Si), and Odd-Z (Al) elemental abundances of the stars in VVV~CL001 follow the same trend as other Galactic metal-poor globular clusters. This makes VVV~CL001 possibly the most metal-poor globular cluster identified so far within the Sun's galactocentric distance and likely one of the most metal-deficient clusters in the Galaxy after ESO280-SC06. Applying statistical isochrone fitting, we derive self-consistent age, distance, and reddening values, yielding an estimated age of $11.9^{+3.12}_{-4.05}$ Gyr at a distance of $8.22^{+1.84}_{-1.93}$ kpc, revealing that VVV~CL001 is also an old GC in the inner Galaxy. The Galactic orbit of VVV~CL001 indicates that this cluster lies on a halo-like orbit that appears to be highly eccentric. Both chemistry and dynamics support the hypothesis that VVV~CL001 could be an ancient fossil relic left behind by a massive merger event during the early evolution of the Galaxy, likely associated with either the Sequoia or the \textit{Gaia}-Enceladus-Sausage structures., Comment: Accepted for publication in The Astrophysical Journal Letters. 9 pages, 4 figures, 1 table more...

The presence of nitrogen-enriched stars in globular clusters provides key evidence for multiple stellar populations (MPs), as has been demonstrated with globular cluster spectroscopic data towards the bulge, disk, and halo. In this work, we employ the VVV Infrared Astrometric Catalogue (VIRAC) and the DR16 SDSS-IV release of the APOGEE survey to provide the first detailed spectroscopic study of the bulge globular cluster UKS~1. Based on these data, a sample of six selected cluster members was studied. We find the mean metallicity of UKS~1 to be [Fe/H]$=-0.98\pm0.11$, considerably more metal-poor than previously reported, and a negligible metallicity scatter, typical of that observed by APOGEE in other Galactic globular clusters. In addition, we find a mean radial velocity of $66.1\pm12.9$ km s$^{-1}$, which is in good agreement with literature values, within 1$\sigma$. By selecting stars in the VIRAC catalogue towards UKS~1, we also measure a mean proper motion of ($\mu_{\alpha}\cos(\delta)$, $\mu_{\delta}$) $=$ ($-2.77\pm0.23$,$-2.43\pm0.16$) mas yr$^{-1}$. We find strong evidence for the presence of MPs in UKS~1, since four out of the six giants analysed in this work have strong enrichment in nitrogen ([N/Fe]$\gtrsim+0.95$) accompanied by lower carbon abundances ([C/Fe]$\lesssim-0.2$). Overall, the light- (C, N), $\alpha$- (O, Mg, Si, Ca, Ti), Fe-peak (Fe, Ni), Odd-Z (Al, K), and the \textit{s}-process (Ce, Nd, Yb) elemental abundances of our member candidates are consistent with those observed in globular clusters at similar metallicity. Furthermore, the overall star-to-star abundance scatter of elements exhibiting the multiple-population phenomenon in UKS~1 is typical of that found in other global clusters (GCs), and larger than the typical errors of some [X/Fe] abundances. Results from statistical isochrone fits in the VVV colour-magnitude diagrams indicate an age ..., Comment: 16 pages, 9 figures, 3 tables, A&A (in press) more...

The Bayesian isochrone fitting using the Markov chain Monte Carlo algorithm is applied, to derive the probability distribution of the parameters age, metallicity, reddening, and absolute distance modulus. We introduce the \texttt{SIRIUS} code by means of simulated color-magnitude diagrams, including the analysis of multiple stellar populations. The population tagging is applied from the red giant branch to the bottom of the main sequence. Through sanity checks using synthetic {\it HST} color-magnitude diagrams of globular clusters we verify the code reliability in the context of simple and multiple stellar populations. In such tests, the formal uncertainties in age or age difference, metallicity, reddening, and absolute distance modulus can reach $400$ Myr, $0.03$ dex, $0.01$ mag, and $0.03$ mag, respectively. We apply the method to analyse NGC 6752, using Dartmouth stellar evolutionary models. Assuming a single stellar population, we derive an age of $13.7\pm0.5$ Gyr and a distance of $d_{\odot}=4.11\pm 0.08$ kpc, with the latter in agreement within $~3\sigma$ with the inverse Gaia parallax. In the analysis of the multiple stellar populations, three {populations} are clearly identified. From the Chromosome Map and UV/Optical two-color diagrams inspection, we found a fraction of stars of $25\pm5$, $46\pm7$, and $29\pm5$ per cent, for the first, second, and third generations, respectively. These fractions are in good agreement with the literature. An age difference of $500\pm410$ Myr between the first and the third generation is found, with the uncertainty decreasing to $400$ Myr when the helium enhancement is taken into account., Comment: 17 pages, 11 figures, 3 tables. Accepted for publication in ApJ more...

Globular clusters (GCs) are the most ancient stellar systems in the Milky Way. Therefore, they play a key role in the understanding of the early chemical and dynamical evolution of our Galaxy. Around $40\%$ of them are placed within $\sim4$ kpc from the Galactic center. In that region, all Galactic components overlap, making their disentanglement a challenging task. With Gaia DR2, we have accurate absolute proper motions for the entire sample of known GCs that have been associated with the bulge/bar region. Combining them with distances, from RR Lyrae when available, as well as radial velocities from spectroscopy, we can perform an orbital analysis of the sample, employing a steady Galactic potential with a bar. We applied a clustering algorithm to the orbital parameters apogalactic distance and the maximum vertical excursion from the plane, in order to identify the clusters that have high probability to belong to the bulge/bar, thick disk, inner halo, or outer halo component. We found that $\sim 30\%$ of the clusters classified as bulge GCs based on their location are just passing by the inner Galaxy, they appear to belong to the inner halo or thick disk component, instead. Most of GCs that are confirmed to be bulge GCs are not following the bar structure and are older than the epoch of the bar formation., Comment: 17 pages, 9 figures, 7 tables. Accepted for publication in MNRAS more...

The VISCACHA (VIsible Soar photometry of star Clusters in tApii and Coxi HuguA\footnote{LMC and SMC names in the Tupi-Guarani language spoken by native people in Brazil}) Survey is an ongoing project based on deep and spatiallyresolved photometric observations of Magellanic Cloud star clusters, collected using the SOuthern Astrophysical Research (SOAR) telescope together with the SOAR Adaptive Module Imager. So far we have used $>$300h of telescope time to observe $\sim$150 star clusters, mostly with low mass ($M < 10^4 M_{\odot}$) on the outskirts of the LMC and SMC. With this high-quality data set, we homogeneously determine physical properties using deep colour-magnitude diagrams (ages, metallicities, reddening, distances, mass, luminosity and mass functions) and structural parameters (radial density profiles, sizes) for these clusters which are used as a proxy to investigate the interplay between the Magellanic Clouds and their evolution. We present the VISCACHA survey and its initial results, based on our first two papers. The project's long term goals and expected legacy to the community are also addressed., Comment: 4 pages, 2 figures, to appear in the proceedings of the IAUS351 "Star Clusters: From the Milky Way to the Early Universe", A. Bragaglia, M.B. Davies, A. Sills & E. Vesperini, eds more...

The VISCACHA (VIsible Soar photometry of star Clusters in tApii and Coxi HuguA) Survey is an ongoing project based on deep photometric observations of Magellanic Cloud star clusters, collected using the SOuthern Astrophysical Research (SOAR) telescope together with the SOAR Adaptive Module Imager. Since 2015 more than 200 hours of telescope time were used to observe about 130 stellar clusters, most of them with low mass (M < 10$^4$ M$_\odot$) and/or located in the outermost regions of the Large Magellanic Cloud and the Small Magellanic Cloud. With this high quality data set, we homogeneously determine physical properties from statistical analysis of colour-magnitude diagrams, radial density profiles, luminosity functions and mass functions. Ages, metallicities, reddening, distances, present-day masses, mass function slopes and structural parameters for these clusters are derived and used as a proxy to investigate the interplay between the environment in the Magellanic Clouds and the evolution of such systems. In this first paper we present the VISCACHA Survey and its initial results, concerning the SMC clusters AM3, K37, HW20 and NGC796 and the LMC ones KMHK228, OHSC3, SL576, SL61 and SL897, chosen to compose a representative subset of our cluster sample. The project's long term goals and legacy to the community are also addressed., Comment: 21 pages, 21 figures more...