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E. Pancino

Publications and source records attributed to E. Pancino.

At least 19 recordsLinked to original sources

The role of mass transfer efficiency in stability criteria: Implementation in SEVN and a test on blue stragglers and binary compact objects

Context: The stability of mass transfer through Roche-lobe overflow plays a key role in shaping the outcome of binary interactions. However, the criterion for mass transfer stability remains one of the main open questions in the theory of binary evolution. Aims: We develop a mass transfer stability prescription that accounts for mass and angular momentum loss, and implement it in the population synthesis code SEVN. We assess its impact relative to the standard formalism used in SEVN, using blue stragglers and binary compact objects as illustrative cases. Methods: We derive an expression for the response of the Roche-lobe radius to mass loss in the general case where the mass and angular momentum of the system are not conserved. On the basis of this formulation, we construct a new mass transfer stability criterion that modifies the standard approach only through the Roche-lobe response term. Results: Population synthesis simulations with SEVN show that the new criterion allows stable mass transfer in binaries with higher donor-to-accretor mass ratios, leading to an overall increase in the predicted number of blue stragglers and promoting their formation in wider orbits. This contributes to reconciling the differences between theory and observations. For binary compact objects, the impact of the new stability criterion varies across system types, with the strongest effects occurring in binaries containing at least one neutron star. In particular, for low mass transfer efficiency, the new criterion enhances the contribution of channels involving stable mass transfer and leads to a larger number of systems, including gravitational wave progenitors. Conclusion: The inclusion of a new, simple, yet more consistent prescription for mass transfer stability has proven that refining this criterion can significantly improve our understanding of the formation channels of specific stellar populations.

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The Hubble Missing Globular Cluster Survey. III. Astro-photometric catalogs, artificial-star tests, and improved absolute proper motions

The Hubble Missing Globular Cluster Survey (MGCS) has taken one of the last opportunities to complete the census of Galactic globular clusters (GCs) started by past Hubble Space Telescope (HST) programs, securing high-resolution data for 34 GCs never observed before by HST. The previous papers in the series have highlighted the astrometric and photometric potential of the project by analyzing a subsample of targets. We present, and release to the community, the official astro-photometric catalogs of the MGCS for all GCs imaged by this project. We describe the data reduction using state-of-the-art techniques designed for HST. We discuss the photometric calibration and show, for the first time, the synergy with the Gaia catalog to ensure homogeneous photometry across our data set. We compute artificial-star tests that can be used to assess systematics and the completeness level of our data. We combined HST and Gaia data to refine the absolute proper motions of our GCs, reaching a precision $\sim$3 times better than that of Gaia alone. We used these new proper motions to update (and to determine for the first time for five systems) the associations between GCs and their putative galaxy progenitors. This work continues decades-long efforts of large Treasury programs in sharing precise and accurate atlases to the community for studying GCs across a wide range of scientific endeavors.

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Revisiting the near infrared Calcium triplet as metallicity indicator

The near-infrared Calcium II Triplet (CaT), around 850nm, is a key metallicity indicator for red giant stars. We present a revised [Fe/H] calibration as a function of CaT line strengths and four luminosity indicators, including the $Gaia$ $G$-band, together with the classical $V$, $I$, and $K_s$ bandpasses. For this purpose, we used a sample of 366 red giant stars belonging to 25 globular and open clusters, complemented by 52 extremely metal-poor field giant stars. The CaT line strengths are determined by fitting Gaussian-Lorentzian combination profiles using the Python lmfit package, which utilises the algorithms implemented therein. The derived calibration is valid for a wide metallicity range, $-4$\,dex$ \lesssim \mathrm{[Fe/H]} \lesssim +0.15$, and for ages older than $\sim$200 Myr. In addition, we performed a detailed assessment of how factors such as spectral resolution, spectral quality (expressed through the signal-to-noise ratio), and the algorithms used to constrain the line profiles affect the measured line strengths and the resulting metallicities.

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The Hubble Missing Globular Cluster Survey. II. Survey membership tools and kinematic analysis of NGC 6749

The Hubble Missing Globular Cluster Survey has secured high quality astro photometric data in two bands for 34 clusters never observed with HST. When combined with Gaia positional measurements, this data set enables the investigation of the bulk motion and the internal kinematics of these poorly studied clusters to an unprecedented level of detail. Focusing on the case of NGC 6749, we here showcase how the combined Gaia HST proper motions have a quality sufficient to accurately assess the cluster stellar membership, determine its absolute proper motion with a precision superior to Gaia, and to investigate its kinematic profile for the first time. Proper motions are determined using the public code GAIAHUB, which for NGC 6749 combines data sets separated in time by 8 years. The resulting measurements improve the precision of Gaia proper motions by a factor of 10 at the faint end, and enable recovering the proper motion for 662 stars for which Gaia could only measure the positions. These proper motions are efficient in decontaminating the colour magnitude diagram of NGC 6749, and make it possible to compare the efficacy of a method of statistical decontamination that relies only on the photometric information extracted from the HST parallel fields. Finally, using the sample of best measured proper motions we determine the velocity dispersion and anisotropy profiles of NGC 6749, that reveal an isotropic behaviour in the cluster inner regions and a slight radial anisotropy outside 1.5 half light radii. The proper motions and the code to statistically decontaminate the clusters color magnitude diagram are made available as public products of the survey.

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Cluster Ages to Reconstruct the Milky Way Assembly (CARMA). III. NGC 288 as the first Splashed globular cluster

The system of globular clusters (GCs) in the Milky Way (MW) comprises a mixture of both in situ and accreted clusters. Tracing the origin of GCs provides invaluable insights into the formation history of the MW. However, reconciling diverse strands of evidence is often challenging. A notable example is NGC 288, where despite significant efforts in the literature, the available chrono-chemodynamical data have yet to provide a definitive conclusion regarding its origin. On the one hand, all post-Gaia dynamical studies indicate an accreted origin for NGC 288 from the Gaia-Sausage-Enceladus (GSE) dwarf galaxy. On the other hand, NGC 288 has been found to be 2.5 Gyr older than other GSE GCs at the same metallicity, this suggesting a different (and possibly in situ) origin. In this work, we address the unresolved question on the origin of NGC 288 by analyzing its chrono-chemical properties in an unprecedentedly homogeneous framework. First, we compare the location of NGC 288 in the age-metallicity plane with that of other two in situ GCs at similar metallicity, namely NGC 6218 and NGC 6362. The age estimates obtained within the homogeneous framework of the CARMA collaboration show that the three clusters are coeval, reinforcing the contrast with the dynamical interpretation. Then, we compare the abundances with a sample of in situ and accreted clusters at similar metallicity, finding again consistency with the chemistry of in situ systems. To reconcile these results with its orbital properties, we propose a scenario where NGC 288 formed in the proto-disc of the MW, and then was dynamically heated by the interaction with the GSE merger. This is a fate that resembles that of proto-disc stars undergoing the so-called Splash event. Therefore, NGC 288 demonstrates the importance of a homogeneous chrono-chemodynamical information in the interpretation of the origin of MW GCs.

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Survey of Surveys. II. Stellar parameters for 23 millions of stars

In the current panorama of large surveys, the vast amount of data obtained with different methods, data types, formats, and stellar samples, is making an efficient use of the available information difficult. The Survey of Surveys is a project to critically compile survey results in a single catalogue, facilitating the scientific use of the available information. In this second release, we present two new catalogs of stellar parameters (Teff, logg, and [Fe/H]). To build the first catalog, SoS-Spectro, we calibrated internally and externally stellar parameters from five spectroscopic surveys (APOGEE, GALAH, Gaia-ESO, RAVE, and LAMOST) and externally on the PASTEL database. The second catalog, SoS-ML catalog, is obtained by using SoS-Spectro as a reference to train a multi-layer perceptron, which predicts stellar parameters based on two photometric surveys, SDSS and SkyMapper. As a novel approach, we build on previous parameters sets, from Gaia DR3 and Andrae et al. (2023), aiming to improve their precision and accuracy. We obtain a catalog of stellar parameters for around 23 millions of stars, which we make publicly available. We validate our results with several comparisons with other machine learning catalogs, stellar clusters, and astroseismic samples. We find substantial improvements in the parameters estimates compared to other Machine Learning methods in terms of precision and accuracy, especially in the metal-poor range, as shown in particular when validating our results with globular clusters. We believe that there are two reasons behind our improved results at the low-metallicity end: first, our use of a reference catalog, the SoS-Spectro, which is calibrated using high-resolution spectroscopic data; and second, our choice to build on pre-existing parameter estimates from em Gaia and Andrae et al., rather than attempting to obtain our predictions from survey data alone.

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The $Hubble$ Missing Globular Cluster Survey. I. Survey overview and the first precise age estimate for ESO452-11 and 2MASS-GC01

We present the $Hubble$ Missing Globular Cluster Survey (MGCS), a $Hubble$ $Space$ $Telescope$ Treasury Program dedicated to the observation of all kinematically confirmed Milky Way globular clusters that missed previous $Hubble$ imaging. After introducing the aims of the programme and describing its target clusters, we showcase the first results of the survey. These are related to two clusters, one located at the edge of the Milky Way bulge and observed in optical bands, namely ESO452-11, and one located in the Galactic disc observed in the near-IR, namely 2MASS-GC01. For both clusters, the deep colour-magnitude diagrams obtained from the MGCS observations reach several magnitudes below their main-sequence turn-off and thus enable the first precise estimate of their age. By using the methods developed in the Cluster Ages to Reconstruct the Milky Way Assembly (CARMA) project, we find ESO452-11 to be an old metal-intermediate globular cluster, with ${\rm [M/H]}\simeq-0.80^{+0.08}_{-0.11}$ and an age of ${\rm t}=13.59^{+0.48}_{-0.69}$ Gyr. Its location on the age-metallicity relation makes it consistent with an in situ origin, in agreement with its dynamical properties. On the other hand, the results for 2MASS-GC01 highlight it as a young metal-intermediate cluster, with an age of ${\rm t}=7.22^{+0.93}_{-1.11}$ Gyr at ${\rm [M/H]}=-0.73^{+0.06}_{-0.06}$. Despite the large associated uncertainty, our age estimate for this extremely extincted cluster indicates it to be either the youngest globular cluster known to date or a massive and compact open cluster, which is consistent with its almost circular, disc-like orbit

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The Survey of Surveys: machine learning for stellar parametrization

We present a machine learning method to assign stellar parameters (temperature, surface gravity, metallicity) to the photometric data of large photometric surveys such as SDSS and SKYMAPPER. The method makes use of our previous effort in homogenizing and recalibrating spectroscopic data from surveys like APOGEE, GALAH, or LAMOST into a single catalog, which is used to inform a neural network. We obtain spectroscopic-quality parameters for millions of stars that have only been observed photometrically. The typical uncertainties are of the order of 100K in temperature, 0.1 dex in surface gravity, and 0.1 dex in metallicity and the method performs well down to low metallicity, were obtaining reliable results is known to be difficult.

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MUSE adaptive-optics spectroscopy confirms dual active galactic nuclei and strongly lensed systems at sub-arcsec separation

The novel Gaia Multi Peak (GMP) technique has proven to be able to successfully select dual and lensed AGN candidates at sub-arcsec separations. Both populations are important because dual AGN represent one of the central, still largely untested, predictions of lamdaCDM cosmology, and compact lensed quasars allow to probe the central regions of the lensing galaxies. In this work, we present high spatial resolution spectroscopy of twelve GMP-selected systems. We use the the adaptive-optics assisted integral-field spectrograph MUSE at VLT to resolve each system and study the nature of each component. All the targets reveal the presence of two components confirming the GMP selection. We classify five targets as dual AGN, two as lensed systems, and five as a chance alignment of a star and and AGN. Having separations between 0.30" and 0.86", these dual and lensed systems are, to date, among the most compact ever discovered at z >0.3. This is the largest sample of distant dual AGN with sub-arcsec separations ever presented in a single paper.

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OCCASO V. Chemical-abundance trends with Galactocentric distance and age

Context. Open clusters provide valuable information on stellar nucleosynthesis and the chemical evolution of the Galactic disc, as their age and distances can be measured more precisely with photometry than for field stars. Aims. Our aim is to study the chemical distribution of the Galactic disc using open clusters by analysing the existence of gradients with Galactocentric distance, azimuth or height from the plane and dependency with age. Methods. High-resolution spectra (R>60 000) of 194 stars belonging to 36 open clusters are used to determine atmospheric parameters and chemical abundances with two independent methods: equivalent widths and spectral synthesis. The sample has been complemented with 63 clusters with high-resolution spectroscopy from literature. Results. We measure local thermodynamic equilibrium abundances for 21 elements: α (Mg, Si, Ca, and Ti), odd-Z (Na and Al), Fe-peak (Fe, Sc, V, Cr, Mn, Co, Ni, Cu, and Zn), and neutron-capture (Sr, Y, Zr, Ba, Ce, and Nd). We also provide non-local thermodynamic equilibrium abundances for elements when corrections are available. We find inner disc young clusters enhanced in [Mg/Fe] and [Si/Fe] compared to other clusters of their age. For [Ba/Fe] we report an age trend flattening for older clusters (age<2.5 Ga). The studied elements follow the expected radial gradients as a function of their nucleosynthesis groups, which are significantly steeper for the oldest systems. For the first time, we investigate the existence of an azimuthal gradient, finding some hints of its existence among the old clusters (age>2 Ga).

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Differential reddening in 48 globular clusters: An end to the quest for the intracluster medium

For decades, it has been theorized that a tenuous but detectable intracluster medium should be present in globular clusters, which is continuously replenished by the gas and dust ejected by bright giants and periodically cleared by interactions with the Galactic disk. However, dedicated searches, especially in infrared and radio wavelengths, have returned mostly upper limits, which are lower than theoretical expectations by several orders of magnitude. We profited from recent wide-field photometry for 48 Galactic globular clusters to compute high-resolution maps of differential reddening, which can be used to correct any photometric catalog in these areas for reddening variations. Using 3D reddening maps from the literature, we evaluated the amount of foreground extinction. This allowed us to estimate the masses of the intracluster medium in our sample clusters, with an accuracy of one order of magnitude. Our estimates agree with the few available literature detections and with theoretical expectations. Because the discrepancy between observations and expectations only concerns literature upper limits, we explored possible reasons why they could be underestimated and we show that two recent discoveries can explain the discrepancy. The first is the recent discovery that the intracluster medium in 47 Tuc is not centrally concentrated. This is also supported by our maps, which in the majority of cases do not show a central reddening concentration. The second is the discovery that the dust in metal-poor ([Fe/H] less than about -1 dex) globular clusters is dominated by iron grains rather than silicates, which undermines previous dust mass estimates from observed upper limits. We conclude that current evidence, including our maps, does not contradict theoretical expectations and the problem of the missing intracluster medium is no longer an issue.

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SpectroTranslator: a deep-neural network algorithm to homogenize spectroscopic parameters

The emergence of large spectroscopic surveys requires homogenising on the same scale the quantities they measure in order to increase their scientific legacy. We developed the SpectroTranslator, a data-driven deep neural network algorithm that can convert spectroscopic parameters from the base of one survey to another. The algorithm also includes a method to estimate the importance that the various parameters play in the conversion from base A to B. As a showcase, we apply the algorithm to transform effective temperature, surface gravity, metallicity, [Mg/Fe] and los velocity from the base of GALAH into the APOGEE base. We demonstrate the efficiency of the SpectroTranslator algorithm to translate the spectroscopic parameters from one base to another using parameters directly by the survey teams, and are able to achieve a similar performance than previous works that have performed a similar type of conversion but using the full spectrum rather than the spectroscopic parameters, allowing to reduce the computational time, and to use the output of pipelines optimized for each survey. By combining the transformed GALAH catalogue with the APOGEE catalogue, we study the distribution of [Fe/H] and [Mg/Fe] across the Galaxy, and we find that the median distribution of both quantities present a vertical asymmetry at large radii. We attribute it to the recent perturbations generated by the passage of a dwarf galaxy across the disc or by the infall of the Large Magellanic Cloud. Although several aspects still need to be refined, in particular how to deal in an optimal manner with regions of the parameter space meagrely populated by stars in the training sample, the SpectroTranslator already shows its capability and promises to play a crucial role in standardizing various spectroscopic surveys onto a unified basis.

astro-ph.GA

The Gaia-ESO Survey: new spectroscopic binaries in the Milky Way

The Gaia-ESO Survey (GES) is a large public spectroscopic survey which acquired spectra for more than 100000 stars across all major components of the Milky Way. In addition to atmospheric parameters and stellar abundances that have been derived in previous papers of this series, the GES spectra allow us to detect spectroscopic binaries with one (SB1), two (SB2) or more (SBn $\ge$ 3) components. Cross-correlation functions (CCFs) have been re-computed thanks to a dozen spectral masks probing a range of effective temperatures, surface gravities and metallicities. By optimising the mask choice for a given spectrum, the new computed so-called Nacre (Narrow cross-correlation experiment) CCFs are narrower and allow to unblend more stellar components than standard masks. The Doe (Detection of Extrema) extremum-finding code then selects the individual components and provides their radial velocities. From the sample of HR10 and HR21 spectra corresponding to 37565 objects, the present study leads to the detection of 322 SB2, ten (three of them being tentative) SB3, and two tentative SB4. In particular, compared to our previous study, the Nacre CCFs allow us to multiply the number of SB2 candidates by $\approx$ 1.5. The colour-magnitude diagram reveals, as expected, the shifted location of the SB2 main sequence. A comparison between the SB identified in Gaia DR3 and the ones detected in the present work is performed and the complementarity of the two censuses is discussed. An application to mass-ratio determination is presented, and the mass-ratio distribution of the GES SB2 is discussed. When accounting for the SB2 detection rate, an SB2 frequency of $\approx$ 1.4% is derived within the present stellar sample of mainly FGK-type stars. As primary outliers identified within the GES data, SBn spectra produce a wealth of information and useful constraints for the binary population synthesis studies.

astro-ph.SR

GMP-selected dual and lensed AGNs: selection function and classification based on near-IR colors and resolved spectra from VLT/ERIS, KECK/OSIRIS, and LBT/LUCI

The Gaia-Multi-Peak (GMP) technique can be used to identify large numbers of dual or lensed AGN candidates at sub-arcsec separation, allowing us to study both multiple SMBHs in the same galaxy and rare, compact lensed systems. The observed samples can be used to test the predictions of the models of SMBH merging once 1) the selection function of the GMP technique is known, and 2) each system has been classified as dual AGN, lensed AGN, or AGN/star alignment. Here we show that the GMP selection is very efficient for separations above 0.15'' when the secondary (fainter) object has magnitude G<20.5. We present the spectroscopic classification of five GMP candidates using VLT/ERIS and Keck/OSIRIS, and compare them with the classifications obtained from: a) the near-IR colors of 7 systems obtained with LBT/LUCI, and b) the analysis of the total, spatially-unresolved spectra. We conclude that colors and integrated spectra can already provide reliable classifications of many systems. Finally, we summarize the confirmed dual AGNs at z>0.5 selected by the GMP technique, and compare this sample with other such systems from the literature, concluding that GMP can provide a large number of confirmed dual AGNs at separations below 7 kpc.

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Search for lithium-rich giants in 32 open clusters with high-resolution spectroscopy

Lithium-rich giant stars are rare and their existence challenges our understanding of stellar structure and evolution. We profit from the high-quality sample gathered with HARPS and UVES, in order to search for Li-rich giants and to identify the Li enrichment mechanisms responsible. We derive stellar parameters for 247 stars belonging to 32 open clusters, with 0.07 Ga < ages < 3.6 Ga. We employed the spectral synthesis technique code FASMA for the abundance analysis of 228 stars from our sample. We also determined ages, distances, and extinction using astrometry and photometry from Gaia and PARSEC isochrones to constrain their evolutionary stage. Our sample covers a wide range of stellar masses from 1 to more than 6 solar masses where the majority of the masses are above 2 solar masses. We have found 14 canonical Li-rich giant stars which have experienced the first dredge-up. This corresponds to 6% of our total sample, which is higher than what is typically found for field stars. Apart from the canonical limit, we use the maximum Li abundance of the progenitor stars as a criterion for Li enrichment. We find Li enhancement also among eight stars which have passed the first dredge up and show strong Li lines based on the fact that stars at the same evolutionary stage in the same cluster have significantly different Li abundances. We confirm that giants with higher Li abundance correspond to a higher fraction of fast-rotating giants, suggesting a connection between Li enhancement and stellar rotation as predicted by stellar models. Our Li-rich giants are found in various evolutionary stages implying that no unique Li production mechanism is responsible for Li enrichment but rather different intrinsic or external mechanisms can be simultaneously at play.

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The Gaia-ESO Survey: Preparing the ground for 4MOST & WEAVE galactic surveys. Chemical evolution of lithium with machine learning

With its origin coming from several sources (Big Bang, stars, cosmic rays) and given its strong depletion during its stellar lifetime, the lithium element is of great interest as its chemical evolution in the Milky Way is not well understood at present. To help constrain stellar and galactic chemical evolution models, numerous and precise lithium abundances are necessary for a large range of evolutionary stages, metallicities, and Galactic volume. In the age of stellar parametrization on industrial scales, spectroscopic surveys such as APOGEE, GALAH, RAVE, and LAMOST have used data-driven methods to rapidly and precisely infer stellar labels (atmospheric parameters and abundances). To prepare the ground for future spectroscopic surveys such as 4MOST and WEAVE, we aim to apply machine learning techniques to lithium measurements and analyses. We trained a convolution neural network (CNN), coupling Gaia-ESO Survey iDR6 stellar labels (Teff, log(g), [Fe/H], and A(Li)) and GIRAFFE HR15N spectra, to infer the atm parameters and lithium abundances for ~40,000 stars. We show that the CNN properly learns the physics of the stellar labels, from relevant spectral features through a broad range of evolutionary stages and stellar parameters. The Li feature at 6707.8 A is successfully singled out by our CNN, among the thousands of lines. Rare objects such as Li-rich giants are found in our sample. This level of performance is achieved thanks to a meticulously built, high-quality, and homogeneous training sample. The CNN approach is very well adapted for the next generations of spectroscopic surveys aimed at studying (among other elements) lithium, such as the 4MIDABLE-LR/HR (4MOST Milky Way disk and bulge low- and high-resolution) surveys. In this context, the caveats of ML applications should be appropriately investigated, along with the realistic label uncertainties and upper limits for abundances.

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Gaia Data Release 3: The Galaxy in your preferred colours. Synthetic photometry from Gaia low-resolution spectra

Gaia Data Release 3 provides novel flux-calibrated low-resolution spectrophotometry for about 220 million sources in the wavelength range 330nm - 1050nm (XP spectra). Synthetic photometry directly tied to a flux in physical units can be obtained from these spectra for any passband fully enclosed in this wavelength range. We describe how synthetic photometry can be obtained from XP spectra, illustrating the performance that can be achieved under a range of different conditions - for example passband width and wavelength range - as well as the limits and the problems affecting it. Existing top-quality photometry can be reproduced within a few per cent over a wide range of magnitudes and colour, for wide and medium bands, and with up to millimag accuracy when synthetic photometry is standardised with respect to these external sources. Some examples of potential scientific application are presented, including the detection of multiple populations in globular clusters, the estimation of metallicity extended to the very metal-poor regime, and the classification of white dwarfs. A catalogue providing standardised photometry for ~220 million sources in several wide bands of widely used photometric systems is provided (Gaia Synthetic Photometry Catalogue; GSPC) as well as a catalogue of $\simeq 10^5$ white dwarfs with DA/non-DA classification obtained with a Random Forest algorithm (Gaia Synthetic Photometry Catalogue for White Dwarfs; GSPC-WD).

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A Wide-Field View on Multiple Stellar Populations in 28 Milky Way Globular Clusters

The majority of Galactic globular clusters (GCs) contain multiple stellar populations displaying specific chemical abundance variations. In particular, GCs generally contain a `primordial' population with abundances similar to field stars, along with an `enriched' population exhibiting light element anomalies. In this paper we present a homogeneous and wide-view analysis of multiple stellar populations in 28 Galactic GCs. By using a combination of HST photometry together with wide-field, ground-based photometry we are able to analyse between 84% and 99% of all stars in each cluster. For each GC, we classify stars into separate sub-populations using the well-established $C_{\rm{UBI}}$ colour index, and investigate the spatial distributions of these populations. Our results show that dynamically young GCs can contain either centrally concentrated enriched or primordial populations, or no centrally concentrated population. Dynamically old GCs show fully mixed populations as expected. The existence of clusters born with centrally concentrated primordial (and homogeneously mixed) populations exacerbates the mass-budget problem facing many cluster formation scenarios. The diversity in these results also highlights the need for additional theories that can account for the wide variety of initial conditions that we find. We finally investigate the enriched star fraction as a function of different global parameters in our GC sample, using also data for young and low-mass clusters from the Small- and Large Magellanic Clouds and confirm earlier results that the enriched star fraction strongly correlates with the initial mass of a cluster.

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