Hubble Space Telescope survey of Magellanic Cloud star clusters. Photometry and astrometry of 113 clusters and early results

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Introduction
In the past years, our group has extensively used the Hubble Space Telescope (HST ) archive to study star clusters in both Magellanic Clouds (e.g.Milone et al. 2009, 2020, andreferences therein).The exquisite stellar photometry and astrometry provided by HST, together with the most advanced techniques for the analysis of astronomical images (e.g.Anderson et al. 2008;Sabbi et al. 2016;Bellini et al. 2017), has provided significant advances in understanding Magellanic-Cloud star clusters and their stellar populations.
Inspired by the discovery that the color-magnitude diagram (CMD) of the Large Magellanic Cloud (LMC) cluster NGC 1806 is not consistent with a single isochrone (Mackey & Broby Nielsen 2007), we started a series of papers to investigate the socalled extended-main sequence turn off phenomenon (eMSTO), in clusters with ages from about one to 2.3 Gyr.The main results include the discovery that the eMSTO is a common feature of Magellanic Cloud clusters (Milone et al. 2009), the early discoveries of split main sequence (MS) in young Magellanic Cloud clusters (Milone et al. 2013(Milone et al. , 2015(Milone et al. , 2016(Milone et al. , 2017)), and the characterization of the multiple populations in young and intermediateage LMC and Small Magellanic Cloud (SMC) clusters (Milone et al. 2018).We provided the first direct evidence, based on highresolution spectra, that the blue and red MS are made up of stellar populations with different rotation rates (Marino et al. 2018a) and the color and magnitude of an eMSTO star depend on stellar rotation (Dupree et al. 2017;Marino et al. 2018a).The highprecision photometry resulting from this project has been instrumental to shed light on the physical mechanisms that are responsible for generating multiple populations in young clusters and has been used both by our team and by other groups to constrain the effect of rotation and stellar mergers on the eMSTO and the split MS (e.g.Bastian & de Mink 2009;D'Antona et al. 2015D'Antona et al. , 2017;;Wang et al. 2022;Cordoni et al. 2022) and the contribution of variable stars on the eMSTO (Salinas et al. 2018).
Driven by these results, we decided to homogeneously analyze all archival images collected with the Ultraviolet and Visual Channel (UVIS) and the Near Infrared Channel (NIR) of Wide Field Camera 3 (WFC3) and with the Wide Field Channel of the Advanced Camera for Surveys (WFC/ACS) on board HST.In this work, we present high-precision stellar positions and magnitudes for stars in 101 fields of Magellanic Clouds that include 113 star clusters.
The paper is organized as follows.Section 2 describes the dataset and the methods used for homogeneously reducing the data and presents the CMDs.The methods for correcting the photometry for differential reddening and the differentialreddening maps are discussed in Section 3, while Section 4 is dedicated to the determination of the cluster centers.Absolute stellar proper motions are derived in Section 5. Section 6 provides some scientific cases that arise from early inspection of our catalogs.Finally, we report in the appendix the serendipitous discovery of one gravitational lens and two stellar clusters.

Data and data analysis
The dataset used in this paper comprises images collected through the UVIS/WFC3 and NIR/WFC3, and WFC/ACS on board HST.The images include 84 known star clusters in the Large Magellanic Cloud (LMC) and 29 clusters in the Small Magellanic Cloud (SMC).These clusters span wide intervals of age and stellar density, from sparse star-forming regions to old and dense GCs.The main properties of the available exposures are listed in Table 1.
Photometry and astrometry are obtained from calibrated, flat-fielded WFC3/NIR (_flt) exposures, while in the case of UVIS/WFC3 and WFC/ACS data we used the calibrated, flatfielded exposures corrected for the effects of the poor chargetransfer efficiency (CTE) of the detectors (_flc, Anderson & Bedin 2010).Stars are measured by means of distinct approaches that work best in different brightness regimes, as discussed in the following subsections.

First-pass photometry
We accounted for spatial variations of the Point-Spread Function (PSF) by using the grids of library PSFs provided by Jay Anderson for each filter and camera.The PSFs can change from one exposure to another due to focus variations produced by the breathing of HST, small guiding inaccuracies, and residual CTE.To derive the optimal PSF we perturbed the library PSFs by using a version of the Anderson et al. (2006) computer program adapted to UVIS/WFC3 and WFC/ACS (see also Bellini et al. 2013).In a nutshell, we divided each image into a grid containing n × n cells, with n ranging from 1 to 5. Bright, isolated, and unsaturated stars within each cell are fitted by the library PSF model, and the residuals of the fit are iteratively used to improve the PSF model itself.We calculated the appropriate PSF model of each star based on its location in the detector by linearly interpolating the four nearest PSFs of the grid (Anderson & King 2000).The number of cells in the grid has been fixed with the aim of obtaining the best quality-fit parameters for bright stars and depends on the number of available reference stars used to constrain the PSF perturbation in the cell.
These PSFs are then used to measure the magnitudes and positions of unsaturated stars in each image.Saturated stars in the UVIS/WFC3 and WFC/ACS images are measured using the methods by Gilliland (2004) and Gilliland et al. (2010).These authors noted that the total number of electrons of saturated stars in the UVIS/WFC3 and WFC/ACS detectors is conserved and this information is preserved in the _flt images with gain=2.Hence, we measured each saturated star in an aperture of 5-pixel radius and added the contiguous saturated pixels that had bled outside this radius (see Anderson et al. 2008, for details).
All catalogs derived from each filter and camera have been tied to the same photometric zero point, corresponding to the zero point of the deepest exposure in the filter that we used as a reference frame to construct the photometric master frame.To do this, we used the bright, unsaturated stars that are well-fitted by the PSF to calculate the difference between the magnitudes in the master frame and in each exposure.We used the mean of these magnitude differences to transform stars measured in each exposure into this reference frame.
Stellar positions are corrected for geometric distortion by using the solutions provided by Anderson & King (2006) for WFC/ACS and Bellini & Bedin (2009) and Bellini et al. (2011) for UVIS/WFC3.The coordinates of stars in all images of each cluster are transformed into a common reference system based on Gaia Early Data Release 3 (eDR3) catalogs (Gaia Collaboration et al. 2020), in such a way that the abscissa and the ordinate are aligned with the West and North direction, respectively.We first de-projected the right ascension and declination into the plane tangential to the center of the main cluster in the field.We assumed for these coordinates a scale factor of 0.04 arcsec per pixel.We first used bright, unsaturated stars that are wellfitted by the PSF to derive the six-parameter linear transformations used to convert the coordinates of all stars in each exposure into this reference frame.Then, we derived the 3σ-clipped average stellar positions to derive a new astrometric catalog, that we used as a master frame to improve the transformations.
do this, we used the FORTRAN computer program KS2 developed by Jay Anderson (e.g. Sabbi et al. 2016;Bellini et al. 2017;Nardiello et al. 2018), which is the evolution of kitchen sink, originally written to reduce WFC/ACS images (Anderson et al. 2008).KS2 exploits various iterations to find and measure stars.It first identifies the brightest and most isolated stars, calculates their fluxes and positions, and subtracts them from the image.In the subsequent iterations, it finds, measures, and subtracts stars that are gradually fainter and closer to neighbor stars.We used the stellar positions and magnitudes derived from first-pass photometry to generate appropriate masks for bright stars, including saturated ones.These masks optimize the detection and measurement of faint sources that are close to bright stars.They also minimize the detection of spurious sources that are typically associated with diffraction spikes and other structures of the stellar profile.
This program adopts three distinct methods to measure stars, each providing optimal photometry for different ranges of stellar luminosity and density.
-Method I is optimal for relatively bright stars.It provides accurate measurements of all stars that generate distinct peaks within their local 5×5-pixel raster after neighbor stars are subtracted.Each star is measured by using the PSF model corresponding to its position, while the sky level is estimated from the annulus between 4 and 8 pixels from the center of the star.
-Method II provides the best photometry for faint stars, which do have not enough flux to provide robust fits with the PSF.After subtracting neighbor stars, KS2 performs the aperture photometry of the star in the 5 × 5 pixel raster.Each pixel is properly weighted to ensure low weight to those pixels contaminated by nearby stars.The sky is calculated as in Method I.
-Method III provides the best photometry in very crowded regions and for faint stars when a large number of exposures are available.It works as Method II, but aperture photometry is calculated over a circle with a radius of 0.75 pixels and the local sky in the annulus between 2 and 4 pixels from the position measured during the finding stage.
Stellar fluxes and positions are measured in each exposure separately and then are properly averaged together to derive our best determinations of magnitudes and positions.Figure 1 compares the CMDs of stars in the field of view of Lindsay 1 obtained from the three methods.We have chosen this GC as an example because of the deep F275W and F814W photometry available, which comprises 16 and 7 exposures in F275W and F814W, with total integration times of 27,341s and 2,206s, respectively.A visual comparison of the top panels reveals that methods II and III are optimal for faint stars as they provide well-defined MSs.The latter method provides slightly better photometry for stars at the bottom of the MS alone, whereas Method II provides the best photometry for the remaining faint MS stars as highlighted in the middle panels, where we show the zoomed CMDs for MS stars with instrumental −6 <F275W< −4 mag1 .Clearly, the MS plotted in the central panel is much narrower and better defined than that shown in the left and right panels.On the contrary, Method I provides the best photometry for stars with bright instrumental magnitudes as demonstrated by the narrow red-giant and sub-giant branch (RGB and SGB) sequences in the bottom-left F555W vs. F555W−F814W CMDs.For each field, we derived three distinct catalogs from Methods I, II, and III.The science results shown in this paper, which are all focused on bright stars, are based on the photometry derived from Method I.

Photometry calibration
Photometry of each filter and camera has been calibrated to the Vega mag system by computing the aperture correction to the PSF-fit-derived magnitudes and applying to the corrected instrumental magnitude a photometric zero-point.To calculate the aperture corrections, we used unsaturated and isolated stars only.
We measured aperture magnitudes within circular regions of ∼0.4 and 0.5 arcsec radius for UVIS/WFC3 and WFC/ACS, respectively.To do this, we used the drizzled and CTE-corrected (_drc,) images, which are normalized to 1s exposure time.Aperture photometry has been calibrated by adding to these instrumental magnitudes the corresponding aperture corrections and the zero points (Bohlin 2016;Deustua et al. 2017).Finally, we calculated the 3 σ-clipped average of the difference between instrumental PSF magnitudes and calibrated aperture magnitudes for the stars in common.The resulting average values are then added to all the stars to derive calibrated magnitudes.

Quality parameters
The computer program KS2 computes for each star various parameters that can be used as diagnostics of the photometric and astrometric quality.For each filter it provides three main quantities: the RADXS parameter is a shape parameter that indicates the amount of flux that exceeds the predictions from the bestfitting PSF (Bedin et al. 2008).It is defined as RADXS = ( i,j pix i,j − PS F i,j )/10 −mag/2.5 where the sum is calculated within an annulus between 1.0 and 2.5 pixels from the center of the star and is normalized to the star's total flux.This quantity is negative when the object is sharper than the PSF (e.g.cosmic rays and PSF artifacts) and it is positive when the object is broader than the PSF (e.g.galaxies).The perfect PSF fit corresponds to RADXS =0. the quality-fit parameter, q f it, which is indicative of the goodness of the PSF fit.It is defined as q f it = i, j pix i,j PS F i,j i,j pix 2 i,j PS F 2 i,j , and it is calculated in a 5×5 pixel area centered on the star, and pix i,j and PS F i,j are the values of the pixel and the bestfitting PSF model, respectively, estimated in the pixel (i,j).It ranges from unit, in the case of a perfect fit, to zero. the root mean scatter of the magnitude determinations, rms.
As an example, in the top-left panels of Figure 2 we plot the RADXS and q f it parameters derived from F336W photometry of the star cluster Reticulum as a function of the F336W instrumental magnitude.Top-right panels show the analogous figures but for the F814W filter.The azure lines are drawn by hand with the criteria of separating the bulk of well-measured point-like sources from sources that are poorly fitted by the PSF model.The bottom panels compare the CMD of stars that pass the selection criteria in both filters and the CMD of stars that have been rejected in at least one filter.Although the magnitude rms is another diagnostic of photometric quality, we prefer not to use it to select the sample of stars with high-quality measurements to avoid excluding variable stars.
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The color-magnitude diagrams
In the four panels of Figure 3 we show the m F336W vs. m F336W − m F814W (left) and the m F555W vs. m F555W − m F814W (right) Hess diagrams of all the observed fields in the LMC (top) and SMC (bottom).Clearly, these diagrams reveal the complexity of stellar populations in the Magellanic Clouds, from bright and blue MSs composed of young and metal-rich stars to old and metal-poor stellar populations characterized by blue and faint MSs and faint RGBs.The CMDs are used to estimate age, distance modulus, (m−M) 0 , metallicity, [M/H], and reddening, E(B−V), by using isochrones from the Padova database (Marigo et al. 2017).To minimize the contamination of field stars, we excluded from the analysis the stars at a large distance from the cluster center.Moreover, we statistically subtracted the field stars from the CMD of cluster members by using the method of Gallart et al. (2003), in close analogy with what is done in previous papers from our group (e.g.Marino et al. 2014;Milone et al. 2018).In a nutshell, we defined by eye a region that is centered on the cluster and includes the bulk of cluster stars (hereafter cluster field) and a reference field with the same area, and at a large distance from the cluster center, which is mostly composed of field stars.We associated with each star in the reference field, the star in the cluster field at the smallest distance in the CMD, where the distance is defined as distance = (k × ∆color) 2 + (∆magnitude) 2 where ∆color and ∆magnitude are the color and magnitude differences, respectively, and k is a factor enhancing the difference in color with respect to the magnitude difference, which is derived as in Marino et al. (2014, see their section 3.1).These stars are excluded from the comparison with the isochrones.The cluster parameters and the best-fitting isochrones are used in Section 3 to estimate differential reddening maps and to investigate the eMSTO phenomenon (Section 6).To find the best-fitting isochrone, we used the CMD from the UVIS/WFC3 and/or WFC/ACS photometry providing the widest color baseline, thus maximizing the sensitivity to metallicity.However, when photometry in optical filters is available, we excluded the UV filters F225W, F275W, F336W, and F343N from the analysis to minimize the effect of multiple populations 2 .Indeed, these UV filters 2 These UV filters encompass various molecular bands that include carbon, nitrogen, and oxygen.Their fluxes are sensitive to the abundances of these elements, which are not constant within clusters with multiple populations.Hence, the CMDs made with UV filters may lead are sensitive to the potential effects due to stellar populations with different nitrogen and oxygen abundances, (e.g.Marino et al. 2008;Milone et al. 2020;Dondoglio et al. 2021), which are typical features of GCs older than ∼2.3 Gyr, and to stellar populations with different rotation rates (e.g.D' Antona et al. 2015;Milone et al. 2016;Li et al. 2017;Marino et al. 2018a), which are present in all clusters younger than ∼2 Gyr.
The observed CMDs are compared with grids of isochrones with different reddening values, distances, metallicities, and ages.The resulting best-fitting parameters are provided in Table 2 and are estimated as follows.
We first determined the isochrone and the values of reddening and distance modulus that, based on the visual comparison with the CMD, provide the best match with the CMD.Then, we improved the determination of the best-fitting parameters using the following iterative approach.We fixed the values of age, distance, and reddening and better constrained the cluster metallicity by comparing the slopes of the fiducial lines of the observed RGB and the MS of the CMDs, and the slope of the corresponding magnitude intervals of the isochrones.
Then, we assumed the metallicity value corresponding to the minimum difference between the slopes of the observed CMDs to less accurate determinations of the cluster parameters than optical CMDs.
Article number, page 5 of 37 Article number, page 6 of 37 and the isochrones to improve the estimates of reddening, age, and distance modulus.To do this, we adopted the criteria of obtaining the best match between the isochrone and the observed CMD, which may change for clusters with different ages.The best-fitting parameters of clusters older than ∼ 2.3 Gyr were estimated by determining the isochrone that best fits the CMD from the MSTO through the SGB (e.g.Dotter et al. 2010).Specifically, we calculated the χ 2 values of the distances in the CMD between the fiducial lines of the MSTO and SGB stars and the isochrone.The best-fitting values of age, reddening and distance modulus are derived by means of χ 2 minimization.A visual inspection at the CMDs reveals that all clusters between ∼ 10 Myr and ∼2.5 Gyr exhibit eMSTOs.Since the eMSTOs challenge their age determinations we provide two age values.We list in column 11 of Table 2 the age of the isochrone that best fits the lower part of the eMSTO.Clearly, this age value would represent the oldest cluster stars, if the eMSTO is entirely due to age variation.Alternatively, if the eMSTO is entirely due to rotation, our age estimate would provide an upper limit to cluster age, as the fast-rotating stars populate the lower part of the eMSTO (e.g.Dupree et al. 2017;Marino et al. 2018a,b;Kamann et al. 2020).Hence, we provide in column 12 of Table 2 the age of the isochrone that best fits the upper part of the eMSTO.In the clusters younger than ∼ 10 Myr, where it is challenging to identify the MSTO, our age determination is largely based on evolved stars.In these young clusters and in the clusters with the eMSTO, the age, distance modulus, and reddening were derived by eye.
To quantify the typical precision of the values of metallicity, age, reddening, and distance modulus inferred by the isochrones we applied the following procedure to four couples of clusters with different ages.The photometry of the clusters of each pair comes from datasets with large differences in the number of images and in the total exposure times.Hence, the range of uncertainties on the fitting parameter inferred from each couple of clusters would comprise the parameters' uncertainties of all studied clusters with similar ages.
We first linearly added to the slopes of the fiducial lines of the RGB and MS stars that were used to constrain the metallicity, the corresponding errors.Hence, we derived the best value of [Fe/H] that corresponds to the isochrone that provides the best match with the used slope.We repeated the same procedure but by using the slopes of the MS and RGB fiducials after subtracting the errors.We consider the semi-difference between the maximum and the minimum [M/H] value, ∆[M/H] as a quantity indicative of the precision of our metallicity estimate.
Similarly, we shifted each point of the fiducial line of the MS and the SGB to the bright and blue side of the CMD, perpendicular to the isochrone.We indicate the resulting line as blueshifted fiducial.The shift is applied in such a way that 68.27% of the stars on the blue side of the original fiducial line are located on the red side of the blue-shifted fiducial.We applied a similar procedure to derive a red-shifted fiducial line.Hence, we repeated four times the procedure described above to estimate the values of age, reddening, and distance modulus but by assuming the various combinations of the largest and minimum values of [M/H] and the blue-shifted and red-shifted fiducials.We consider the semi-differences between the maximum values of age (∆age), distance modulus, (∆(m−M) 0 ), and reddening (∆E(B−V)), as a proxy of the precision of the estimates of the corresponding quantities.
The results are listed in Table 3 for the pairs of clusters of old GCs NGC 2005 andNGC 1939 (ages of ∼ 13 Gyr), intermediate age clusters Kron 3 and Kron 1 (ages of ∼6-7 Gyr).We also investigated the ∼2 Gyr-old clusters NGC 1846 and Hodge 7 and the young clusters NGC 1866 and BSDL 1650 (ages of ∼300 Myr).

Differential reddening
To derive high-resolution reddening maps, we applied to our dataset the method originally developed by Milone et al. (2012) to correct the ACS/WFC F606W and F814W magnitudes of Galactic GCs for differential reddening (see also Bellini et al. 2017;Jang et al. 2022).The main difference of the adopted procedure is that the catalogs of several GCs comprise photometry in more than two bands.The main steps of our iterative method, which is illustrated in Figure 5 for NGC 416, can be summarized as follows: -We built the m F814W vs. m X − m F814W diagrams, where X=F275W, F336W, F343N, F438W, F555W, and F814W.
Each diagram has been used to gather information on differential reddening from a sample of reference stars.Reference stars are selected in the CMD region where the reddening direction defines a wide angle with the cluster fiducial line in such a way that we can easily disentangle the effect on stellar colors and magnitudes due to differential reddening from the shift due to photometric uncertainties.As an example, panel a of Figure 5 highlights in black the selected reference stars of NGC 416 in the m F814W vs. m F336W − m F814W CMD.-We first derived the reddening direction corresponding to each star as θ = arctan A X A X −A F814W , where A X and A F814W are the absorption coefficients in the X and F814W bands, respectively.To derive them, we identified the point on the best-fitting isochrone with the same m X magnitude as the reference star and calculate the m X and m F814W magnitude differences with the corresponding point of the isochrone with E(B−V)=0 mag.This procedure allows us to account for the dependence of reddening direction from the total amount of reddening and from its spectral type.As an example, panel a of Figure 5 shows the reddening direction associated with the reference star indicated by the red cross.
-We translated the CMD into a new reference frame where the origin corresponds to the reference stars as illustrated in panels a and b of Figure 5.This CMD is rotated counterclockwise by an angle θ so that the abscissa and the ordinate of the new reference frame are parallel and orthogonal, respectively, to the reddening direction.-We generated the fiducial line of MS, SGB, and RGB stars, which we plot as a continuous red line in panel b.To do this, we divided the sample of MS stars into 'ordinate' intervals.
For each bin, we calculated the median abscissa associated with the median 'ordinate' of the stars in the bin.The fiducial line has been derived by linearly interpolating these median points.-We calculated the distance of the reference star from the fiducial line along the reddening direction, ∆x as shown in panel b for a reference star of NGC 416 that we marked with a large red cross3 .
-We calculated the projection of ∆x along the m X − m F814W color direction, ∆ (m X − m F814W ) and plotted this quantity for the available X filters as shown in panel c of Figure 5.The observed values of ∆ (m X − m F814W ) are compared with corresponding quantities derived from the isochrones and corresponding to reddening variations ranging from ∆ E(B−V)=−0.3 to 0.3 mag in steps of 0.001 mag.The value of ∆ E(B−V) that provides the minimum χ 2 is assumed as the best differential-reddening estimate associated with the reference star marked with the red cross.
To derive the amount of differential reddening associated with each star in the catalog, we selected a sample of N spatially nearby reference stars, (light-blue crosses in Figure 5) as shown in panel d.The best determination of differential reddening is provided by the median of the ∆ E(B−V) values of these N neighbors.We excluded the target star from its own differential reddening determination.We derived various determinations of differential reddening by assuming different values of N, from 35 to 95 in steps of 5 and from 100 to 150 in steps of 10.For each determination, we calculated the pseudo-color distances between the value of x of the reference stars, corrected for differential reddening, and the fiducial line of Figure 5.We assumed that our best determination of differential reddening is given by the value of N that provides the minimum value of the r.m.s of these distances.In particular, we used N=75 for NGC 416.
As an example, Figure 6 shows the reddening map in the direction of NGC 416 and compares the original CMD to the CMD corrected for differential reddening.A collection of reddening maps for six clusters is provided in Figure 7.

Cluster centers
To determine the coordinates of the center of each star cluster we followed the procedure described in Cordoni et al. (2020b).In a nutshell, we first selected by eye a sample of probable cluster members based on their location in the CMD and smoothed their stellar spatial distribution with a Gaussian kernel of fixed size.The kernel size has been chosen with the criteria of favoring the overall shape of the cluster, instead of the smallscale structures.We derived five contour lines within 50 arcsec from the cluster center and interpolated each of them with an ellipse by using the algorithm by Halir & Flusser (1998).Our best cluster-center determination corresponds to the median value of the centers of the ellipses, while the corresponding uncertainty has been estimated as the dispersion of the center determinations inferred from each ellipse.Due to the low number of stars, it was not possible to apply the method above in 13 poorly-populated star clusters, namely BRHT 5b, BSDL 1650, KMK 8827, KMHK 1073, KMHK 8849, OGLE-CL-LMC390, NGC 1749, NGC 290, NGC 1850A, NGC 1858, NGC 1938and NGC 1966.For these clusters, we provide raw center determination based on the peak of the histogram distributions of the coordinates of the probable cluster members.Results are provided in Table 2.

Proper motions
To estimate the absolute proper motions of the studied clusters, we combined information from HST photometry and Gaia eDR3 ple).On the contrary, photometric errors are responsible for a random scatter along the fiducial line, but such a scatter is essentially not dependent on the reddening direction and the position of the star in the field of view.
proper motions.Specifically, for each cluster, we selected by eye stars that, based on their positions in all available CMDs, are probable cluster members.Then, we used the Gaia eDR3 catalog to select stars with magnitude g BP < 19.0 mag, which according to the criteria by Cordoni et al. (2018) have high-quality proper motions.The average proper motion of each cluster has been calculated as the 3-σ clipped average of the proper motions of selected cluster members for which are available both HST photometry and Gaia eDR3 high-quality proper motions.We estimated the corresponding uncertainty by following the method of Vasiliev (2019), which accounts for systematic errors.
The main steps of the procedure used to derive the absolute proper motion are illustrated in Figure 8 for NGC 1806.For this cluster, we have photometry in five photometric bands of UVIS/WFC3 and WFC/ACS.We constructed ten CMDs of stars in the FoV of NGC 1806 including four m F814W vs. m X − m F814W CMDs, where X=F336W, F343N, F435W, and F555W, three m F555W vs. m X − m F555W CMDs, where X=F336W, F343N, and F435W, two m F435W vs. m X − m F435W CMDs, where X=F336W and F343N, and the m F343N vs. m F336W − m F343N CMD.For each CMD, we selected by eye the stars that, based on their colors and magnitudes, are located on the main cluster evolutionary sequences.As an example, the stars that, based on their positions in all CMDs, likely belong to the RGB, AGB, and red clump of NGC 1806 are colored black in the three CMDs of Figure 8.The colored symbols mark stars with available Gaia eDR3 proper motions in both the CMDs and in the proper-motion diagram.The stars that do not belong to the RGB, AGB, and red clump of NGC 1806 in at least one CMD are represented with bluestarred symbols and are not included in the determination of the cluster proper motion.We also excluded the selected stars with proper motions that differ from the average cluster motion by more than three times the proper motion dispersion (i.e. the stars outside the black circle shown in the bottom-right panel of Figure 8 represented with aqua-starred symbols).The remaining stars are marked with red open dots.
Results are provided in Table 1.The left panels of Figure 9 show the positions of the studied LMC and SMC clusters relative to the SMC center.In the top-left panel, we associate to each cluster the corresponding proper-motion vector, while in the bottom-left panel we show the proper-motion residuals after subtracting to LMC and SMC clusters the average motion of the corresponding Magellanic Cloud from Gaia Collaboration et al. (2018) 4 .The proper motion diagram is plotted in the right panel of Figure 9 and reveals that, based on proper motions, all clusters are consistent with being either LMC or SMC members.

Proper motions from Gaia eDR3 and HST
For thirteen GCs, we take advantage of having more than one epoch observations with appropriate signal-to-noise ratio and temporal baselines to disentangle the internal kinematics of Magellanic Cloud stars and separate cluster members and field stars by using HST data alone.Detailed information on the HST images available for these clusters are provided in Table 4. Relative HST motions are then transformed into absolute motions based on Gaia eDR3 proper motions.
To derive relative proper motions we applied to our dataset the procedure described by Piotto et al. (2012) and described in the following for NGC 1978.In a nutshell, we first identified the distinct groups of images collected at the same epoch through the same filter and camera.We reduced each group of images, separately, as described in Section 2, and obtained the corresponding astrometric and photometric catalogs.
The reference frame defined by the first-epoch images collected through the reddest filter is adopted as a master frame.The coordinates of stars in each catalog are transformed into the master frame by means of six-parameter linear transformations (Anderson et al. 2006).To minimize the effect of possible small residual distortions we applied local transformations based on the nearest 70 reference stars.Target stars are never included in the calculation of their own transformations.
The abscissa and the ordinate of each star, expressed in milliarcsec, are plotted against the epoch, expressed in years, as shown in panels a1-a4 of Figure 10 for two stars in the field of view of NGC 1978.For simplicity, in this figure, we show the displacements DX and DY, and the time relative to the stellar position and time at the first epoch.These points are finally fitted with a weighted least-squares straight line, whose slope corresponds to the best proper motion estimate.
The selection of the stars used to derive the transformation is a critical step for accurate proper-motion determination.Hence, we selected bright and unsaturated stars that pass the criteria of selection discussed in Section 2.4.We derived proper motions relative to a sample of cluster members that have been selected iteratively.As a consequence, the average relative motion of the cluster is set to zero.We first identified probable cluster stars that, based on all available CMDs, lie on the main evolutionary sequences and used them to derive initial proper motion estimates.Then, we iteratively excluded those stars that do not share the same motion as the bulk of cluster members (i.e.stars with proper motions greater than three times the proper-motion dispersion of cluster stars).Panels b and c of Figure 10 mark with black points the probable cluster members that we selected for deriving stellar proper motions in the m F814W vs. m F555W −m F814W CMD and in the m F814W vs. DR = √ DX 2 + DY 2 plane, whereas aqua crosses are probable cluster members.Gray points mark the remaining stars with cluster-like proper motions, i.e. the sat- Similarly, the panels on the top represent the reddening variation as a function of the ordinate for stars in eight intervals of X.The field is centered around the center of NGC 416 (X,Y=6019,5507) and the X and Y axis are parallel to the right ascension and declination direction, respectively.We adopted a scale of 0.04 arcsec per pixel.urated stars, the faint stars, and the stars that do not lie on the main evolutionary sequences in the CMDs.
To transform relative proper motions into absolute ones we derived the difference between the relative proper motions derived from HST images and the absolute proper motions from Gaia eDR3 for an appropriate sample of stars.Specifically, this selected sample includes stars with high-quality relative proper motions (i.e.bright, unsaturated stars that pass the criteria of selection of Section 2.4).In addition, the selected sample includes stars that, based on the proper motion uncertainties and on the values of the Renormalized Unit Weight Error (RUWE), the astro-metric_gof_al (As_gof_al) parameters of the Gaia eDR3 catalog have accurate Gaia eDR3 absolute proper motions.We refer to papers by Cordoni et al. (2018Cordoni et al. ( , 2020a)), for details on the procedure.The sample includes both cluster and field stars, with the exception of a few stars with parallaxes significantly larger than zero.
The 3σ-clipped mean differences of the proper motion along each direction (µ α cosδ and µ δ ) are considered as the best estimate of the zero points of the motions and are used to convert relative proper motions into absolute ones.As an example, panels d1 and d2 of Figure 10 show the histogram distributions of the quantities ∆µ α cosδ=µ α cosδ-DX and ∆µ δ =µ δ -DY for stars in the field of view of NGC 1978.
The proper motion diagrams for NGC 1978 stars are plotted in the left panels of Figure 11 in four distinct magnitude bins.These diagrams can be used to separate the bulk of cluster members (black dots) from probable field stars (red crosses).
Here, the red circles that enclose the NGC 1978 stars have radii equal to 2.5σ, where σ is the average between the σ−clipped dispersion values of µ α cosδ and µ δ .For illustration purposes, we only mark in red the most-evident field stars with µ α cos δ > 1.6 mas/yr and a distance of more than 0.2 mas/yr from the average motion of NGC 1978, while the remaining stars are colored gray.The m F814W vs. m F555W − m F814W CMD of probable cluster members and field stars is shown in the right panel of Figure 11.

A saucerful of secrets
The photometry and astrometry of this work are exquisite tools to investigate various astrophysical topics.In this section, we provide further examples of science outcomes that arise from visual inspections of the photometric diagrams and of the propermotion diagrams.Specifically, in Section 6.1 we report the discovery of eMSTOs in the clusters KMHK 361 and NGC 265.Section 6.2 compares the CMDs of LMC clusters younger than ∼2.3 Gyr and investigates the color and magnitude distribution of eMSTO in clusters with different ages.Gaps and color discontinuities along the MS of NGC 1783 are investigated in Section 6.4 while Section 6.5 provides evidence of new features along the eMSTO and the upper MS of NGC 1783.Finally, Sec-Article number, page 10 of 37

Clusters without previous evidence of eMSTO
Figure 12 provides evidence that the CMDs of the star clusters KMHK 361 (age of 1.35 Gyr) and NGC 265 (age of 450 Myr) are not consistent with a single isochrone.In this figure, we compare the CMDs of stars in circular fields centered on the cluster (hereafter cluster fields) and in reference fields of the same area.We adopted radii of 20 and 24 arcsec for KMHK 361 and NGC 265, respectively, enclosing the bulk of cluster stars.To minimize the contamination from cluster stars, the reference fields are as far away from the cluster centers as possible, while still being within the FoV.By assuming a uniform distribution of field stars in the small HST field of view, the distribution of stars in the referencefield CMD is indicative of the contamination due to field stars.
Clearly, KMHK 361 exhibits an eMSTO, which cannot be explained by field-star contamination alone.Similarly, NGC 265 shows an intrinsic eMSTO.The upper MS is split in the F435W magnitude interval between ∼21 and 22 mag, with the red MS hosting about two-thirds of MS stars.The two MSs merge around m F435W ∼ 22.5 mag.The comparison between the CMDs of stars in the field and reference fields reveals that the split MS and the eMSTO are not due to field-star contamination.
The visual inspection of the CMDs from our survey suggests that all clusters with ages between ∼ 0.1 and ∼2.3 Gyr exhibit the eMSTO (Cordoni et al. in preparation).These findings corroborate the evidence that eMSTOs are common features of clusters younger than ∼2.3 Gyr, while split MSs are widespread phenom-ena among clusters younger than ∼0.8 Gyr (e.g.Milone et al. 2009;Milone & Marino 2022;Niederhofer et al. 2015;Goudfrooij et al. 2011;Li et al. 2017;Correnti et al. 2017).

The eMSTO in clusters of different age
Our dataset provides a unique opportunity for comparing CMDs of clusters with different ages derived with homogeneous methods.As an example, we take advantage of the collection of M F336W vs. M F336W − M F814W CMDs shown in Figure 13 to investigate how the eMSTO phenomenon changes as a function of cluster age.In this figure, star clusters are sorted by age, from ∼10 Myr (NGC 1818) to ∼2.5 Gyr (NGC 1978).The observed magnitudes have been converted into absolute ones by adopting the values of distance modulus and reddening listed in Table 2.
A visual inspection of this figure corroborates the previous conclusion that the split MS is visible in all LMC clusters younger than ∼800 Myr (from NGC 1818 to NGC 1953) and seems to disappear at older ages (Milone et al. 2018).The color separation between the blue and red MSs approaches its maximum value around the MSTO and decreases towards faint luminosities (Milone et al. 2016).As pointed out by Wang et al. (2022), the gap between the blue and red MSs significantly narrows down around M F336W = 1.0 mag, which is the luminosity level where the fraction of blue-MS stars approaches its minimum value (Milone et al. 2018).Noticeably, this magnitude value corresponds to an MS mass of ∼2.5 M , where the slowly rotating component of MS field stars disappears (Zorec & Royer 2012).
Article number, page 11 of 37 We also confirm that the eMSTO is a ubiquitous feature of LMC clusters younger than ∼2.3 Gyr.It is visible in all clusters where the turn-off is brighter than the MS bending around M F336W = 3.0 mag and disappears in NGC 1978 (e.g.Milone et al. 2009;Goudfrooij et al. 2014).Since the MS bending is due to a change in the stellar structure, the eMSTO is associated with stars with radiative envelopes alone.In addition, the split MS is visible among stars brighter than the MS bend.
Figure 13 reveals that the color and magnitude distributions of stars across the eMSTO significantly change from one cluster to another.As an example, the Hess diagrams plotted in the top panels (a1, a2, and a3) of Figure 14 suggest that most TO stars of NGC 1868 populate the bright and blue region of the eMSTO, whereas NGC 2173 shows higher stellar density on the bottomred side of its eMSTO.NGC 1852 seems to show an intermediate distribution.
To parametrize the stellar distribution of eMSTO stars in the CMDs, we adopted the procedure illustrated in Figure 14b for NGC 1852.We defined a new reference frame where the origin, O, is set by hand on the bright and blue side of the eMSTO, and the abscissa, X', envelopes the bright part of the eMSTO and points towards the red.We derived the red and blue fiducials of the eMSTO in the new reference frame and represented them as red and blue lines in the CMD of Figure 14b.To derive the fiducials, we follow the recipe by Milone et al. (2017), which is based on the naive estimator (Silverman 1986).We first divided the eMSTO into a series of bins with fixed pseudo-magnitude, δY'.The bins are defined over a grid of points separated by intervals of fixed pseudo-magnitude (s=δY/3).For each interval, we calculate the 4 th and the 96 th percentile of the X' distribution and associated these values with the mean pseudo-magnitude Y' of stars in the bin.These values are then linearly interpolated to derive the red and blue boundaries of the eMSTO.These lines are used to calculate the quantity that is defined in such a way that the stars on the blue and red fiducials have ∆ X =0 and 1, respectively.Figure 14 compares the kernel density (panel c) and the cumulative distributions of ∆ X (panel d) for NGC 1852 (black), NGC 1868 (aqua), and NGC 2173 (orange).We confirm the visual impression of a predominance of blue eMSTO stars in NGC 1868, whereas the ∆ X distribution of NGC 2173 is peaked towards the red.NGC 1852 has an intermediate distribution.
To quantify the ∆ X differences among the various clusters, we define two quantities: i) the area, A, below the cumulative curve shown in Figure 14 and ii) the median value of ∆ X , < ∆ X >.If the distribution is dominated by blue and bright MSTO stars we would expect large values of A and small values of < ∆ X >, while a predominance of faint and red eM-STO stars corresponds to small A and large < ∆ X >. Results are shown in Figure 15, where we plot both quantities against cluster age.LMC clusters (red dots in Figure 15) exhibit a strong anti-correlation between A and age and a correlation between < ∆ X > and age, as also indicated by the values of the Spearman's rank correlation coefficients of −0.91 and 0.92, respectively.Intriguingly, the ∼2 Gyr old SMC clusters NGC 411 and NGC 416 exhibit larger values of A and smaller values of < ∆ X > than LMC clusters with similar ages, with NGC 411 having the largest differences.The small statistical sample of clusters prevents us from reaching a firm conclusion on whether NGC 411 is an outlier or SMC and LMC clusters exhibit different trends.
The multiple populations of young and intermediate-age star clusters share common features that have been instrumental to shed light on the origin of split MSs and eMSTOs (see Milone & Marino 2022, for a recent review).As an example, the eM-STO width depends on cluster age.Specifically, if the eMSTO is interpreted as an age spread, the resulting age range is proportional to cluster age (e.g.Niederhofer et al. 2015;Cordoni et al. 2018).Moreover, the fractions of stars along the blue and the red MS correlate with stellar mass.The fraction of blue-MS stars varies from ∼ 40% among stars with masses of ∼ 1.5M to ∼ 15% among ∼ 2.5 − 3.0M stars.It arises again in more massive stars, up to ∼ 40% in ∼ 5.0M -stars.The fractions of blue-and red-MS stars do not depend on other properties of the host cluster like the global cluster's mass (Milone et al. 2018).These results have been instrumental to demonstrate that rota-Article number, page 12 of 37   The evidence that the ∆ X distribution of stars along the eM-STO depends on cluster age provides a potential further constraint to the eMSTO phenomenon.To start investigating the physical reasons responsible for the relations shown in Figure 15, we used stellar models from the Padova database (Marigo et al. 2017) to simulate a group of CMDs of non-rotating stellar populations with ages of 100, 200, 500, 1,000, 1,250, 1,500 and 2,000 Myrs and internal age spreads.We assumed a flat distribution and maximum width corresponding to the average age variations inferred by Cordoni et al. (2018) for Magellanic Cloud clusters with the same age.We derived the A and < ∆ X > quantities for each simulated CMD by using the same procedure adopted for real stars and plotted the resulting values against the oldest age of the simulated stellar population (open triangles of Figure 15).
Similarly, we simulated another group of CMDs for coeval stellar populations where 33% of stars have no rotation, whereas the remaining 67% of stars have rotation equal to 0.9 times the breakout value.The simulated diagrams have ages of 100, 150, 500, 800, and 1,250 Myr and are derived by means of Geneva models (Ekström et al. 2012(Ekström et al. , 2013;;Mowlavi et al. 2012;Wu et al. 2016).We assumed random viewing-angle distributions and adopted the gravity-darkening model by Espinosa Lara & Rieutord (2011) and the limb-darkening effect (Claret 2000).Stellar magnitudes for the available HST filters have been derived using the model atmospheres by Castelli & Kurucz (2003).The resulting A and < ∆ X > quantities are represented with filled diamonds in Figure 15.For completeness, we used the Geneva models to simulate non-rotating stellar populations with internal age spreads, in close analogy with what we did with the Padova models.Results are represented with filled triangles.
Clearly, the A and < ∆ X > quantities inferred from both groups of simulated diagrams provide poor fits to the observations.This fact indicates that internal age variation alone is not responsible for the eMSTO when we assume a flat age distribution for all clusters.Similarly, rotation alone is not responsible for the eMSTO when we assume two populations for all clusters: one of non-rotating stars and one of fast rotators with ω = 0.9ω c .
It is now widely accepted that the luminosity of eMSTO stars depends on gravity darkening and that its effect is strong for large values of the ratio between the rotational velocity and the critical velocity.Our results could indicate that this ratio increases when stars age on the MS as suggested by Hastings et al. (2020).
To properly constrain the contribution of rotation and age variation on the eMSTO, it is mandatory to extend the analysis to simulated diagrams that account for different internal age distributions, different rotation-rate distributions (e.g.Huang & Gies 2006;Huang et al. 2010;Goudfrooij et al. 2018), and that account for both age variations and stellar populations with different rotation rates.
The interpretation of the eMSTO phenomenon should also account for binary evolution effects (e.g.Wang et al. 2022).As an example, the stellar models by Wang et al. (2020) show that the fraction of evolutionary-driven mergers rises for smaller stellar masses, at the expense of the binaries that survive the mass transfer and produce spun-up accretors.An appropriate comparison between the observations illustrated in Figures 14 and 15 and the predictions of stellar models that account for binary evolution is mandatory to shed light on the effect of binary evolution on the eMSTO.

A population of UV-dim stars along the eMSTO of NGC 1783
The stellar proper motions derived from our dataset allow the partial separation of bright field stars from NGC 1783 cluster members, thus providing new insights on its stellar populations.
The left panels of Figure 16 show the proper-motion diagram for stars in the field of view of NGC 1783 in five magnitude bins.
The black circles are centered on the absolute proper motion of NGC 1783, and are used to separate probable cluster members (black points) from field stars (aqua crosses).The corresponding m F438W vs. m F438W − m F814W CMD (middle panel) highlights several characteristics of NGC 1783 in unprecedented detail.These include the eMSTO (Mackey et al. 2008;Milone et al. 2009;Goudfrooij et al. 2014) together with a well-populated sequence of MS-MS binaries with large mass ratio (Milone et al. 2009).The SGB also exhibits intrinsic broadening in color and magnitude, with the majority of stars populating the upper SGB.Moreover, the CMD reveals a broad, possibly dual, sequence of stars brighter and bluer than the turn-off.This blue sequence, which will be investigated in detail in Section 6.5 was first identified by Li et al. (2016) who associated it with the young stellar populations within NGC 1783.Their result has been challenged by Cabrera-Ziri et al. (2016) who suggested that the blue sequence is composed of field stars.
Here, we focus on the m F438W vs. m F275W − m F438W CMD of NGC 1783, which is illustrated in the right panel of Fig- ure 16.An unexpected feature of this CMD is the sparse cloud of stars on the red side of the eMSTO.These stars, which we dub UV-dim, are marked with red triangles in the left panel of Figure 17 where we reproduce the m F438W vs. m F275W − m F438W Article number, page 14 of 37 CMD zoomed around the eMSTO.UV-dim stars comprise a small fraction of ∼7% of the total number of eMSTO stars with 20.4 < m F555W < 21.5 mag.We used the same colors to represent these stars in the other panels of Figure 17 and showed that they define distinct sequences in both m F435W vs. m F343N − m F435W and m F555W vs. m F555W −m F814W CMDs.If the extreme position in the left-panel CMD is due to observational errors alone, the selected stars would have the same probability of having redder or bluer m F343N − m F435W and m F555W − m F814W colors than the bulk of MSTO stars.On the contrary, the presence of distinct sequences demonstrates that the extreme red m F275W − m F438W colors of the selected stars are intrinsic.We note that the Be stars, which are commonly observed in Magellanic Cloud clusters younger than ∼ 300 Myr (Keller et al. 2000;Bastian et al. 2017;Correnti et al. 2017;Milone et al. 2018), also exhibit redder colors than the bulk of eMSTO stars in CMDs composed of F275W and F336W filters.
In the following, we explore the possibility that the extreme F275W−F438W colors of UV-dim stars are an effect connected to the stellar rotation.It is well known that stellar rotation diminishes the effective temperature and the luminosity of a star, with fast-rotating MSTO stars being redder and dimmer than slow rotators.The position of a star along the eMSTO depends on the effects of limb and gravity darkening and on the viewing angle of the stellar rotation axes with respect to the line of sight.In this context, UV-dim stars would comprise of fast rotators that are seen equator-on, as these stars appear colder and fainter than pole-on fast rotators.
To qualitatively explore this suggestion, we produced simulations based on the isochrones from the Geneva database (Mowlavi et al. 2012;Ekström et al. 2012Ekström et al. , 2013;;Georgy et al. 2014) in close analogy with what we did in Section 6.2.In the top panels of Figure 18 we simulated a population of non-rotating stars (aqua points), which includes the 33% of the total number of stars, and a population of fast rotators, where the stellar rotation corresponds to 0.9 times the breakout value (ω/ω c = 0.9, black points).The simulated fraction of binaries is 0.3 and is similar to the observed binary fractions of intermediate-age LMC star clusters (Milone et al. 2009).
We note that non-rotating stars are located on the red and faint side of the eMSTO in the m F438W vs. m F275W − m F438W and m F435W vs. m F343N −m F435W CMDs, similarly to the clouds of UV-dim stars observed in the corresponding diagrams of NGC 1783.However, these stars define a narrow sequence that overlaps with the red portion of the eMSTO, in contrast with what is observed in the cloud of stars of NGC 1783 where we observe a broad color distribution that extends towards the red of the bulk of eMSTO stars.In addition, simulated stars exhibit fainter m F555W magnitudes and redder m F555W − m F814W colors than the bulk of eMSTO, in disagreement with what is observed in the m F555W vs. m F555W − m F814W CMD.Hence, we conclude that the cloud of stars in NGC 1783 is not consistent with a population of nonrotating stars.
In the bottom panels of Figure 18 we limit the analysis to fast-rotating stars only, where the position of a star in the eM-STO strongly depends on the limb and gravity darkening and on the viewing angle.We select by hand a sample of eMSTO stars with red m F275W − m F438W colors and faint m F438W magnitudes (red points in Figure 18).Clearly, the hypothesis that stars with a certain range of viewing angle correspond to the cloud of NGC 1783 stars is challenged by the position of the selected stars in the optical CMD, where they define a narrow sequence in the middle of the eMSTO.Further, it seems unlikely that the spread of the turnoff can be entirely attributed to the viewing angle of stars rotating close to breakout value ∼2 Gyrs after their formation.
As an alternative, circumstellar disks could be responsible for absorbing the UV radiation and the consequent cloud of stars on the red side of the eMSTO.Debris disks, possibly associated with planet formation, are frequently observed around A-type stars (e.g.Eiroa et al. 2013, and references therein).A challenge is the location of UV-dim stars in the m F555W vs. m F555W −m F814W CMD, which would imply that their disks poorly affect the emergent optical radiation.On the contrary, dust absorption is strongly dependent on the wavelength and is much more significant in the UV than in the optical.Hence, circumstellar dust in a disk could explain the location of these stars in the CMD (D'Antona et al., in preparation).
In this scenario, the disks are associated with stars that are currently non-rotating so that they can distribute along a narrow sequence in the optical CMD.If the disk formation is associated with rotation, these stars should have experienced fast rotation in their lifetime.Fig. 13: Collection of M F336W vs. M F336W − M F814W CMDs of LMC clusters younger than 2.5 Gyr.All panels have the same scale and are zoomed around the MS, while the insets highlight the MSTO.Clusters are sorted by age.

A zigzag across the MS of NGC 1783
A visual inspection of the CMD of Figure 16 shows another intriguing detail of the CMD of NGC 1783.As highlighted by the Hess diagram in the inset, the upper MS runs in a zigzag, with two main discontinuities (m F438W ∼ 22.0 and 22.4) and various sudden changes of slope around m F438W = 21.9, 22.1, 22.3 and 22.5.
We compare in Figure 19 the observed upper MS of NGC 1783 with the isochrones from Padova (left, Marigo et al. 2017).The faint MS discontinuity corresponds to effective temperature T eff = 6, 900K and mass M=1.26 M , whereas stars on the bright MS discontinuity have T eff = 7, 250K and M=1.19 M .
We tentatively associate the hotter gap of the NGC 1783 MS with the original Böhm-Vitense gap.A gap along the MS at T eff ∼ 7, 500K has been first predicted by Böhm-Vitense (1970) and observed in the nearest Galactic open clusters (e.g.Bohm-Vitense & Canterna 1974;de Bruijne et al. 2000de Bruijne et al. , 2001)).The Böhm-Vitense gap is associated with sudden changes in the structure of convective atmospheres.It has been interpreted as a color effect, due to the fact that the temperature gradient in deep atmospheric layers becomes smaller than the radiative gradient.As an alternative, it is the effect of temperature inhomogeneities produced by photospheric granulation (e.g.Boehm-Vitense 1982).
The colder discontinuity of the NGC 1783 MSs could correspond to a distinct MS gap, which was earlier investigated by D' Antona et al. (2002).Indeed, fainter MS gaps have been observed around T eff ∼ 7, 000K (e.g.Rachford & Canterna 2000).At this temperature, convection begins in stellar envelopes, and Article number, page 16 of 37  an increasing amount of the stellar exterior becomes convective as the mass and effective temperature decrease.Also, the eM-STO disappears below ∼ 7, 000K, confirming that fast-rotating MS stars are only present at hotter temperatures.Indeed, the external turbulence brakes the envelope rotation.Clearly, the change of stellar structure results in a variation of the MS slope.Recent works provide evidence of an MS kink at similar temperatures in several Galactic and Magellanic Cloud clusters, where the split MS, which is associated with stellar populations with different rotation rates, merges into a single MS (e.g. D'Antona et al. 2017;Milone et al. 2018;Marino et al. 2018a;Goudfrooij et al. 2018).
The fainter MS gap has been investigated in the Hyades by D' Antona et al. (2002) based on the full spectrum of turbulence model by Canuto et al. (1996), which predicts that the depth of the convective envelope suddenly changes within a narrow range of stellar mass and around T eff ∼ 6, 800K.They concluded that the gap is an effective-temperature effect associated with the sharp effective-temperature difference between stars that are only convective in the surface layers and stars with well-developed convective interiors.
However, these results are based on poorly-populated CMDs of open clusters, which often make it challenging to assess the statistical significance of the gaps.The high-precision HST photometry of populous star clusters may overcome this limitation and provides new insights on the MS region in the temperature range between ∼6,500K and 7,500K.
As shown in Figure 19, neither the isochrones from the Padova group nor those from the BaSTI (middle, Pietrinferni et al. 2004), and MESA (Choi et al. 2016;Dotter 2016;Paxton et al. 2011) databases reproduce the observed MS discontinuities.This fact corroborates the conclusion that these stellar models, poorly reproduce the CMD region where the stellar atmosphere changes from radiative to convective.

Search of multiple generations in NGC 1783
In the past years, astronomers have dedicated huge efforts to searching for young star clusters that are analogous to old GCs.Indeed, they may provide a snapshot of multiple populations shortly after their formation.The two sequences of stars in the field of view of the ∼1.5 Gyr-old cluster NGC 1783 are a hotly debated case because they are consistent with younger stellar populations of ∼440 and 520 Myr.After statistically subtracting the contribution of field stars from the CMD of stars around NGC 1783, Li et al. (2016) concluded that the blue MSs are cluster members.They suggested that these young stars are the signature of burst-like star formation and that NGC 1783 has experienced multiple bursts of star formation with an age difference of a few hundred million years.In this scenario, NGC 1783 is eventually the young counterpart of GCs with multiple populations.
This result has been challenged by Cabrera-Ziri et al. (2016), who suggested that the background subtraction method adopted by Li and collaborators may not remove contaminating field stars.Hence, they concluded that there is no evidence for multiple generations within NGC 1783 and that the young populations are field LMC stars along the same line of sight of NGC 1783.
As anticipated in Section 6.3, the m F438W vs. m F438W −m F814W CMD plotted in Figure 16 clearly reveals the stellar sequence first investigated by Li et al. (2016), whereas stellar proper motions allow disentangling the bulk of cluster members and field stars.To investigate whether NGC 1783 hosts a population of bright and hot MS stars, we combined information from photometry and stellar proper motions as illustrated in Figure 20.We first used the dashed rectangle plotted in the top-left panel of Figure 20 to select a sample of stars on the blue side of the cluster MSTO in the m F438W vs. m F438W − m F814W CMD.In the top-right panels, we compare the CMDs for stars in the dashed-line rectangle located within and outside a radius equal to 45 arcsec from the cluster's center.The external region has a ∼four-time wider area than the internal one.
The proper motion diagram plotted in the bottom-left panel of Figure 20 shows that NGC 1783 stars are partially separated Article number, page 17 of 37  from LMC stars.We draw the red circle to separate the bulk of cluster members from field stars and represent these stars with black circles and aqua-starred symbols, respectively, in the bottom-left and in the top panels of Figure 20.
We find that the sample of selected blue stars in the CMD comprises 18 field stars in the internal region, while 64 field stars belong to the external region.Their ratio of about four is comparable with the ratio of the corresponding field-of-view areas as expected if field stars have uniform spatial distribution.On the contrary, the number of stars with cluster-like proper motion in the internal and external field are 53 and 64 and are comparable  well reproduced by a function composed of the sum of two 3D Gaussian functions, that we derived by means of least squares minimization.For illustration purposes, we show in Figure 20 the histogram distributions of µ α cos δ and µ δ together with the corresponding two-dimensional Gaussian functions.
Clearly, the stars with cluster-like proper motions selected in the bottom-left panel of Figure 20 may also include field stars.To estimate the fraction of field stars that contaminate the sample of probable cluster members we used the best-fitting 3D Gaussian functions to simulate the proper motions plotted on the bottomright panel of Figure 20.Here, we show a subsample of 198 simulated stars, which is the same number of observed stars.Simulated field stars are represented with starred symbols and cluster stars with small dots.Clearly, a fraction of field stars (red starred symbols) have cluster-like proper motions while some cluster members (blue dots) lie outside the red circle.In particular, the fraction of field stars within the red circle, with respect to the number of cluster members is ∼5%.These facts demonstrate that the majority (∼ 95%) of stars with cluster-like proper motions selected in Figure 20 are cluster members.
In summary, our proper-motion-based results confirm the conclusion of Li and collaborators that the blue sequences are composed of genuine members of NGC 1783.More sophisticated analysis is mandatory to understand whether the blue sequence is associated with young stellar populations as suggested by Li and collaborators or whether it is composed of blue stragglers.The cluster members on the bright and blue side of the red clump are consistent both with young red clump stars and with binary systems composed of red-clump stars.The stellar concentrations around the center of each diagram are composed of cluster members and their broadening is mostly due to observational uncertainties.Indeed, the star-to-star scatter associated with the internal motions of cluster members is negligible with respect to proper motion errors at the distance of the Magellanic Clouds.On the contrary, field stars exhibit broad proper-motion distributions, which are significantly wider than what is expected from observational uncertainties alone.
We identified in each CMD a group of stars with blue m F336W − m F814W colors, which mostly comprise the young stellar populations of the host galaxy, and a group of old stars with red colors.Furthermore, we selected a sample of very-young LMC stars in NGC 1801 and NGC 1953 that define the bluest and brightest MS in their CMD (aqua triangles).The selected groups of old and young stars, identified in the CMDs, are highlighted with red and blue symbols, respectively, in the proper motion diagrams plotted in the third and fourth columns of panels.A visual inspection of these figures suggests that the proper motions of young and old SMC stars typically show different ellipticities, whereas the differences are less pronounced for LMC stellar populations.
Results are illustrated in Figure 23 and summarized in Table 5, where we provide for each population the median proper motions relative to the main cluster in the field, the ellipticity of the best-fitting ellipse that encloses 90% of stars ( = 1 − b/a, where a and b are the minor and major axes of the ellipse), and the position angle θ.As shown in Figure 21 Young LMC stars exhibit flatter proper-motion distributions than old LMC stars, in close analogy with what is observed for the SMC.However, the ellipses that best fit the proper motions of LMC stars in the fields of NGC 1755, and NGC 1953 have different orientations than the corresponding ellipses inferred for stars in the direction of NGC 1801.Very young stars in the field of view of NGC 1953 have more clustered proper motions with respect to the remaining young stars.Interestingly, the selected young stars show some hints of split MS in the CMD.A spectroscopic investigation is mandatory to understand whether the split is due to stellar populations with different rotation rates, similar to what is observed in the star clusters with similar ages, or to differences in distance, age, and/or chemical composition.The proper motion distributions of stars in the direction of the three analyzed LMC clusters are nearly circular, in contrast with what is observed for young stars in both Magellanic Cloud clusters and old SMC stars.
Article number, page 19 of 37 6.6.1.The massive star-forming region NGC 346 NGC 346 is a very young SMC star cluster (age ∼ 3 Myr, Bouret et al. 2003;Sabbi et al. 2007) that is responsible for the excitation of the surrounding HII region N 66.A stacked F814W image of NGC 346 and its neighborhoods is shown in the left panel of Figure 24 where we mark with an azure circle the central part of the NGC 346 star-forming region.
The intermediate-age star cluster BS 90 is also visible to the north of NGC 346 and is highlighted by the red circle in the left panel of Figure 24.The proper motion diagram of all stars with m F814W between 18.4 and 21.4 mag is plotted in the middle panel of Figure 24 and comprises stars with the best propermotion quality5 .Stars within the regions centered on NGC 346 and BS 90 (azure and red points, respectively) define two distinct clumps in the proper motion diagram, which are mostly composed of cluster members.We selected probable cluster members with proper motions smaller than four times the r.m.s of the proper motion distributions (stars within the circles) and calculated the median values of µ α cosδ and µ δ .Results are listed in Table 6.The fact that NGC 346 and BS 90 exhibit different proper motions demonstrates that they are distinct clusters projected onto the same field of view.
The probable members of NGC 346 and BS 90, selected from both stellar proper motions and positions, are marked with azure and red points in the CMD in the right panel of Figure 24.The sample of selected NGC 346 stars defines a well-populated MS and upper pre-MS, whose large broadening is indicative of a significant amount of differential reddening.On the contrary, BS 90 exhibits narrow SGB and RGB sequences, and a well-defined red clump, thus confirming that this cluster is poorly affected by differential reddening (Sabbi et al. 2007).Specifically, the value and estimated the 68.27 th percentile of the corresponding distribution (σ).We added three times σ to the median uncertainty of each bin and associated this value with the median magnitude of the stars in the bin.Finally, these points are linearly interpolated and the stars that are located below this line in the proper-motion uncertainty vs. magnitude plane are considered as well measured.
Article number, page 20 of 37 average reddening variation in the field of view within 36 arcsec from the center of BS 90 never exceeds ∆E(B−V)= 0.013 mag, with ∼ 68% of the stars having ∆E(B−V) values within 0.004 mag from the average reddening.This fact demonstrates that this cluster is in the foreground with respect to the region of NGC 346 and N 66.
The CMD of stars in the field of view of NGC 346 comprises stars in different evolutionary stages for which high-precision proper motions are available, including pre-MS stars, MS stars, and evolved stars in the SGB, RGB, and red-clump phases.As widely discussed in literature works (e.g.Sabbi et al. 2007;Cignoni et al. 2010Cignoni et al. , 2011))  proper motion diagram reveals that the bulk of MS stars (hereafter MS I stars, aqua points) exhibit a proper-motion distribution similar to the NGC 346 pre-MS stars.In addition, we note a tail of stars in the proper motion diagram that points towards the LMC and that we colored blue and name MS II.Both groups of selected MS stars seem diffused over the whole field, but the MS I stars define some stellar overdensities that trace the bar and possibly, some clumps of the Spur.We suggest that the MS II is mostly composed on SMC field stars that follow an elliptical proper motion distribution, in close analogy with what is observed for the other analyzed SMC young stars.On the contrary, MS I stars comprise both field SMC stars, and stars of the NGC 346 region.
Finally, the old SMC field stars are investigated in the bottom panels of Figure 25.Although this stellar population hosts some stars up to ages of more than 10 Gyr, it is mostly associated to a major star-formation episode that occurred between ∼ 3 and 5 Gyr ago.The RGB stars of the old populations with radial distance smaller than 36 arcsec from the center of BS 90 are marked with red points.These stars exhibit similar proper motion distribution as young stars and pre-MS stars in the star-forming region of BS 90 (bottom-middle panel) and are uniformly distributed across the entire field of view (bottom-right panel of Figure 25).Note, the motion of the bulk of old SMC field stars is significantly different from that of BS 90, despite this cluster having an age similar to most old field stars.

Summary and conclusions
We have used the HST archive to retrieve ACS/WFC, UVIS/WFC3, and NIR/WFC3 images of 101 fields in the direc-tion of the LMC and the SMC.These images include 29 SMC clusters and 84 LMC clusters.We derived high-precision photometry and astrometry by using the methods and the computer programs developed by Jay Anderson and his collaborators and obtained high-resolution reddening maps in the direction of each cluster.We provide accurate determinations of cluster centers and estimate distance modulus, reddening, metallicity, and age by comparing the CMDs with Padova isochrones (Marigo et al. 2017).Moreover, we calculated proper motions for cluster and field stars in twelve stellar fields that have been multi-epoch observations.
The exquisite photometry, astrometry, and proper motions presented in this paper have the potential to shed light on a variety of astrophysical phenomena.As an example, we present here some results that are evident from visual inspection of the CMDs and the proper motion diagrams.
-New insights into the eMSTO phenomenon.
The photometric catalogs, derived from homogeneous data reduction, allow accurate comparison of clusters with different ages.The analysis of the m F336W vs. m F336W − m F814W CMDs of 19 LMC clusters in a wide range of ages between ∼20 Myr and 2 Gyr, reveals that the distribution of stars along the eMSTO significantly changes from one cluster to another and depends on GC age.While the eMSTOs of young clusters are dominated by blue and bright eMSTO stars, the fraction of stars in the red and faint eMSTO increases in older clusters.This property of eMSTO stars provides a new observational constraint to understand the physical mechanism that is responsible for the eMSTO.We also provide the first evidence of eMSTO in  In addition to disentangling cluster members and field stars, proper motions allow the investigation of the internal kinematics of stellar populations in the Magellanic Clouds.We have identified two groups of young and old Magellanic-Cloud field stars in the FoVs of five SMC clusters, namely KRON 34, NGC 294, NGC 339, NGC 416, and NGC 419, and of three LMC clusters NGC 1755, NGC 1801and NGC 1953.The proper motions of young SMC stars exhibit elliptical distributions with high ellipticity values and major axes that point toward the LMC.The flattened proper-motion distributions would be associated with the Magellanic bridge and represent the dynamic signature of the flow motion of stars from the SMC to the LMC.Our results corroborate the evidence that SMC stars are affected by the LMC (e.g.Piatti et al. 2015).Old and young SMC stars exhibit different kinematics.The proper motions of the old SMC stars are also oriented towards the LMC and have elliptical distributions but with lower values of ellipticity and, in most cases, different centers.The different proper-motion distributions of old and young stars could reflect, in part, the presence of different young and old bridges.
The young and the old LMC stars also exhibit different motions on the plane of the sky.While the proper motions of the old populations show nearly circular distributions, young LMC stars have more flattened proper-motion distributions, with different orientations of the best-fitting ellipses.

Appendix. Serendipitous discoveries
We report the serendipitous findings of two new star clusters, hereafter clusters 1 and 2. Two zoom-ins of the region around cluster 1 are provided in the top-left panels of Figure 26, where we provide the monochromatic images in the F475W and F850LP bands.The cluster, which is centered around RA=00:45:21.28,DEC=−73:12:18.1, J2000 is clearly visible in the F850LP image, while the most prominent feature of the F475W image is a nebula that envelopes it.The top-right panel shows the m F775W vs. m F775W − m F850LP CMD for all stars in the WFC/ACS field that includes cluster 1.The bright star close to the cluster center is classified as the Hα emission-line star MA93-99 by Meyssonnier & Azzopardi (1993).We defined a circle centered on the cluster with a 4 arcsec radius (hereafter cluster region) and represented with black circles all stars within this region.We also plot the stars in Article number, page 23 of 37

Fig. 1 :
Fig. 1: Comparison of the instrumental F275W vs. F275W−F814W CMDs of stars in the field of view of the star cluster Lindsay 1 as derived from Method I (topleft), Method II (top-middle) and Method III (top-right).Well-measured stars are colored black, while stars with poor photometry are plotted with light gray dots.Azure crosses mark stars where the F814W magnitude is derived from saturated images.Middle panels are zoomed-in views of the top-panel CMD around the MS.Bottom panels compare the region of the instrumental F555W vs. F555W−F814W CMDs populated by bright stars with F555W< −9.75 mag.Calibrated magnitudes and colors are indicated by the top and right axes.

Fig. 2 :
Fig. 2: Top panels.RADXS and q f it parameters derived from F336W (left) and F814W (right) photometries of stars in the field of view of Reticulum.The azure lines separate wellmeasured stars (black dots) from poorly measured sources (gray crosses).The bottom panels show the instrumental F336W vs. F336W−F814W CMD for stars that pass the selection criteria in both filters (left) and for the remaining stars (right).

Fig. 4 :
Fig. 4: Stacked images and CMDs of stellar fields with different ages and stellar densities.North is up and East to the right.The top panels show the F475W image and the m F475W vs. m F475W − m F814W CMD of stars in the star-forming region around the very young cluster NGC 1966.The middle and bottom panels illustrate the F814W stacked images and the CMDs of the intermediate-age cluster NGC 2121 (age ∼ 3 Gyr) and the old GC NGC 2210 (age ∼ 12 Gyr), respectively.

Fig. 5 :
Fig. 5: This figure illustrates the procedure to estimate the amount of differential reddening associated with the target star represented with the large blue dot.Panel a shows the m F814W vs. m F336W − m F814W CMD of all the stars.Reference stars, are located between the two dotted gray lines and are colored black, whereas the neighboring reference stars are marked with light-blue crosses.The gray continuous lines are the abscissa and the ordinate of the rotated reference frame centered on the reference star marked with the large red cross, while the red arrow indicates the reddening direction.Panel b shows the same stars as panel a but in the rotated reference frame.The red continuous line is the fiducial of reference stars and the inset highlights the relative position between one reference star and the fiducial.Panel c represents the values of ∆x inferred from different filters (red dots).Gray crosses are the corresponding values derived for ∆ E(B−V) ranging from 0.01 to 0.10 mag in steps of 0.01 mag, while the black crosses provide the best fit to the observations and correspond to ∆ E(B−V)=0.058mag.Finally, the finding chart zoomed in around the target is illustrated in panel d.See the text for details.

Fig. 6 :
Fig. 6: Left.Comparison between the original m F814W vs. m F336W − m F814W CMD of NGC 416 (top) and the CMD corrected for differential reddening (bottom).Right.Differential-reddening map in the direction of NGC 416.The levels of gray are proportional to the reddening variation as indicated on the top-right.The panels on the right show ∆ E(B−V) against the abscissa for stars in eight ordinate intervals.Similarly, the panels on the top represent the reddening variation as a function of the ordinate for stars in eight intervals of X.The field is centered around the center of NGC 416 (X,Y=6019,5507) and the X and Y axis are parallel to the right ascension and declination direction, respectively.We adopted a scale of 0.04 arcsec per pixel.

Fig. 8 :
Fig. 8: This figure illustrates the procedure to identify stars that, based on the position in the CMDs from HST photometry and in the proper-motion diagram from GAIA eDR3, are probable members of NGC 1806.The probable members are represented with red circles in the CMDs plotted in the top panels and the bottom-left panel and in the proper motion diagram shown in the bottom-right panel.Stars that are not located on the main evolutionary sequences in at least one CMD are represented with blue-starred symbols.The arrow plotted in the proper-motion diagram indicates the mean cluster motion, while the circle is used to select the stars that are not included in the sample of probable cluster members, due to their large proper motions (aqua-starred symbols).See the text for details.

Fig. 9 :
Fig. 9: Left.Coordinates, in degrees, relative to the SMC center of the studied SMC and LMC clusters.The arrows in the top panel are indicative of the absolute proper motions of each cluster, while the bottom panel represents the proper motions of LMC and SMC clusters after subtracting the average motion of the corresponding galaxy.Right.Proper motions of stars brighter than g BP = 16.0 mag in the region around the LMC and the SMC (black points).The studied LMC and SMC clusters are plotted in all panels with red and aqua dots, respectively.

Fig. 10 :
Fig. 10: Procedure to estimate absolute proper motions.Panels a1 and a2 show the displacements along the X and Y directions in four epochs of a probable field star (blue triangles) relative to the mean motion of NGC 1978.Similarly, panels a3 and a4 show the displacements of a candidate cluster member (red dots).The m F814W vs. m F555W − m F814W CMD of stars in the field of view of NGC 1978 is plotted in panel b, while panel c shows relative stellar proper motions against m F814W .Aqua crosses are probable field stars selected on the basis of their proper motions.The stars used as references to calculate relative proper motions are colored black, while the remaining stars with cluster-like proper motions are gray.Panels d1 and d2 show the histogram of the difference between our relative proper motions and the absolute proper motions from Gaia eDR3.

Fig. 11 :
Fig. 11: Proper motion diagrams of stars in the field of view of NGC 1978 in four F814W magnitude intervals (left).The m F814W vs. m F555W − m F814W CMD of stars in the left panels is plotted on the right.Stars within the red circles plotted in the left panels are considered probable cluster members and are colored black, whereas the most-evident field stars are represented with red crosses.The remaining stars are colored gray.See the text for details.

Fig. 12 :
Fig. 12: CMDs of the clusters KMHK 361 and NGC 265 without previous evidence of eMSTOs.Stars in the cluster field and reference field of each cluster are represented with black points and aqua crosses, respectively.See text for details.

Fig. 14 :
Fig. 14: m F336W vs. m F336W −m F814W Hess diagrams of NGC 1868 (a1), NGC 1852 (a2), and NGC 2173 (a3) zoomed around the eMSTO.The blue and red lines are the boundaries of the eM-STOs.Panel b illustrates the scheme to derive the ∆ X quantity for eMSTO stars, while the corresponding kernel-density distributions and cumulative distributions are plotted in panels c and d, respectively, for NGC 1868 (aqua), NGC 1852 (black) and NGC 2173 (orange).See the text for details.

Fig. 15 :
Fig.15: Area below the ∆ X cumulative curve, A, (left) and median ∆ X value as a function of cluster age for LMC (red dots) and SMC (aqua dots) clusters with the eMSTO.Open and filled triangles are inferred from simulated CMDs of non-rotating stellar populations with different ages derived from the Padova and Geneva database, respectively.The diamonds correspond to coeval stellar populations with different rotation rates from the Geneva database.See text for details.

Fig. 16 :
Fig. 16: Proper motion diagrams of stars in the field of view of NGC 1783 in five F438W magnitude intervals (left).The m F438W vs. m F438W − m F814W CMD for stars in the left panels is plotted on the middle.Stars within the black circles plotted in the proper motion diagrams are considered probable cluster members and are colored black, whereas field stars are represented with aqua crosses.The right panel shows the m F438W vs. m F275W − m F438W CMD for probable cluster members, while the inset represents the Hess diagram of the CMD region around the upper MS.

Fig. 18 :
Fig. 18: Simulated CMDs of two stellar populations of fastrotating stars (ω/ω c = 0.9, black points) and non-rotating stars (aqua points).Red points in the bottom-panel diagrams mark the sample of fast rotating stars selected by hand and located on the red side of the eMSTO in the m F438W vs. m F275W − m F438W CMD.Simulations are derived from Geneva isochrones.

Fig. 19 :
Fig. 19: Reproductions of the m F438W vs. m F275W − m F438W CMD of Figure 16 zoomed around the upper MS.The red, blue, and green lines superimposed on each CMD are the best-fitting nonrotating isochrones from the Padova (left), BaSTI (middle), and MESA (right) databases.A rotating MESA isochrone with ω = 0.4ω c , with ω c being the breakout velocity, is plotted in the right panel in cyan.

6. 6 .
Figures 21 and 22 show the CMDs and the proper motion diagrams of stars in the fields of view of five SMC clusters, namely Kron 34, NGC 294, NGC 339, NGC 416, and NGC 419, and three LMC clusters, namely NGC 1755, NGC 1801 and NGC 1953.Since we focus on the internal kinematics of LMC and SMC stars, we restrict the analysis to the magnitude interval that provides the most precise proper-motion determinations.The stellar concentrations around the center of each diagram are composed of cluster members and their broadening is mostly due , young SMC stars exhibit flat proper motion distributions, where the eccentricity of the best-fitting ellipses ranges from ∼ 0.3 in NGC 416 to ∼ 0.6 in NGC 339.The proper motion distributions of the old stellar populations have smaller eccentricity values, between ∼ 0.1 in NGC 416 and NGC 339 and ∼ 0.3 in NGC 419.In all cases, the major axis of the best-fitting ellipses roughly follows the direction North West -South East, thus pointing towards the LMC.Similar conclusions are derived by Massari et al. (2021) based on high-precision proper motions and stellar photometry from HST of NGC 419.These authors demonstrated that it is possible to separate cluster members from SMC field stars by using stellar kinematics.Moreover, they identified a kinematic stellar component that they associated with the Magellanic Bridge.Although our results do not provide evidence for populations of field stars with distinct kinematics, the flattened proper motion distributions would reflect the flow motion of stars from the SMC to the LMC.Further evidence of SMC star clusters showing a relative motion pointing towards the LMC is provided by Zivick et al. (2018); Piatti (2021); Dias et al. (2021); Schmidt et al. (2022).

Fig. 20 :
Fig. 20: Top.Reproductions of the CMDs of NGC 1783 of Figure 16.Right panels are zoomed-in views of the CMD region on the bright-blue side of the MSTO (dashed rectangle in the top-left panel) for stars with radial distances from the cluster center smaller and larger than 45 arcsec.Bottom.Proper motion diagram of stars plotted in the top-left panel (left).The red circle separates stars with a cluster-like motion from the bulk of field stars.Black points and aqua-starred symbols mark the selected bright-blue stars.The corresponding histogram distributions for µ α cos δ and µ δ are also represented on the top and right side of the panel.The best fit bi-Gaussian functions are represented with gray lines, and the two Gaussian components are colored aqua and red.The bottomright panel shows the simulated proper motions for cluster members and field stars.Black and blue dots indicate NGC 1783 stars with cluster-like and field-like proper motions, respectively, while red color is used to distinguish field stars with cluster-like proper motions from the remaining field stars (aqua starred symbols).

Fig. 21 :
Fig. 21: First-column panels show the CMDs of stars in the field of view of five SMC clusters with available proper motions.The corresponding proper motion diagrams are plotted in the second column, while the third and fourth columns represent the proper motions of candidate old and young field stars selected in the CMDs and colored red and blue, respectively.Red and blue ellipses provide the best-fitting of the distributions of candidate old and young field stars in the proper motion diagram.The Hess diagrams of the proper-motion distributions are shown in all proper-motion diagrams.
, this field hosts a conspicuous population of pre-MS stars that are highlighted in the top-left panel of Figure 25.In particular, we used orange and yellow colors to represent two samples of pre-MS I and pre-MS II stars with high-precision proper motions, which lie respectively inside and outside the central region of NGC 346.The remaining pre-MS stars are colored black.As indicated in Table 6, the proper motion distributions of the two groups of pre-MS stars share the same mean motion as NGC 346 indicating that stars in both the central region and in the outskirts share the same mean motions (top-middle panel of Figure 25), although the latter exhibits a wider proper motion dispersion.The distribution of pre-MS stars across the field of view highlights the distinctive structure of the NGC 346 region described by Contursi et al. (2000), including the low-density filament oriented to the north-east direction (spur), and the fan-shaped structure (bar), that hosts the majority of pre-MS stars.MS stars are investigated in the middle panels of Figure 25, and comprise stars of the young population of the SMC.The Article number, page 21 of 37

Fig. 22 :
Fig. 22: Similar to Figure 21 but for the LMC clusters NGC 1755, NGC 1801, and NGC 1953.Very young stars in the fields of view of NGC 1801 and NGC 1953 are represented with aqua triangles.

Fig. 23 :
Fig. 23: Positions of candidate young LMC and SMC stars relative to the center of the SMC (top).The bottom panel shows the density distributions of candidate old LMC and SMC stars.The ellipses that provide the best fit of proper-motion distributions in young and old stars in the fields of eight clusters are colored blue and red, respectively.

Fig. 24 :
Fig. 24: Stacked F814W WFC/ACS image of the SMC field that includes the clusters NGC 346 and BS 90, which are highlighted by the azure and red circle, respectively (left).The middle panel shows the proper motion diagram, while the m F814W vs. m F555W −m F814W CMD is represented in the right panel.Only stars in the F814W magnitude interval between the two horizontal lines in the CMD are plotted in the proper-motion diagram, where the stars in the NGC 346 and BS 90 regions defined in the left panel are colored blue and red, respectively.Blue and red symbols in the right-panel CMD mark proper-motion selected cluster members in the NGC 346 and BS 90 regions.See text for details.

Fig. 25 :
Fig. 25: The three left panels are reproductions of the m F814W vs. m F555W − m F814W CMDs for stars in the field of view of NGC 346 and are used to select various groups of stars that we represented with colored symbols.The middle panels show the proper motions for stars in the magnitude interval delimited by the horizontal lines in the corresponding CMDs, whereas the right panels show the coordinates of the selected stars.The top panels are focused on candidate pre-MS stars.Specifically, bright pre-MS within 28 arcsec from the center of NGC 346 (pre-MS I sample) are represented with orange symbols, the remaining bright pre-MS stars (pre-MS II sample) are colored yellow, while the black symbols in the top panels mark faint pre-MS stars.Bright MS stars are investigated in the middle panels.Blue and aqua colors mark MS I and MS II stars, which have radial distances larger than 28 arcsec from the center of NGC 346, but different proper motion distributions.The remaining bright-MS stars are colored black.The bottom panels highlight the selected RGB stars with radial distances from the center of BS 90 larger (red) and smaller than 60 arcsec (black).

Fig. 26 :
Fig. 26: Top panels.Stacked images in F475W and F850LP centred on the cluster 1 discovered in this paper (left).The m F775W vs. m F775W − m F850LP diagram is plotted on the right for all stars in the ACS/WFC field (gray points), stars in the cluster 1 field (black circles) and in the reference field (aqua crosses).Bottom panels.Stacked image in F160W for the discovered cluster 2 (left) and m F160W vs. m F110W − m F160W CMD (right).Gray, black, and aqua symbols indicate stars in the WFC3/NIR field, stars in the cluster field, and in the reference field, respectively.
the LMC intermediate-age cluster KMHK 361 and in the SMC young

Table 2 :
Cluster-center coordinates, average proper motions, distance modulus, reddening, metallicities, and ages for the studied clusters.

Table 2 :
Cluster-center coordinates, average proper motions, distance modulus, reddening, metallicities, and ages for the studied clusters.

Table 3 :
The quantities listed in this table are indicative of the precision of values of distance modulus, reddening, age, and metallicity inferred from isochrone fitting.The horizontal lines separate the couples of clusters with similar ages and different photometric qualities.See text for details.
Article number, page 33 of 37

Table 4 :
Description of the dataset of the thirteen GCs with HST proper-motion determinations.For completeness, we include information on F275W images, although they are not used for deriving proper motions.

Table 4 :
Description of the dataset of the thirteen GCs with HST proper-motion determinations.For completeness, we include information on F275W images, although they are not used for deriving proper motions.
Article number, page 35 of 37