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M. Rejkuba

Publications and source records attributed to M. Rejkuba.

At least 37 records · Page 2Linked to original sources

The outermost stellar halo of NGC 5128 (Centaurus A): Radial structure

The extended stellar halos of galaxies contain important clues for investigating their assembly history and evolution. We investigate the resolved stellar content and the extended halo of NGC 5128 as a function of galactocentric distance. We used HST images to resolve individual red giant branch (RGB) stars in 28 independent pointings. Star counts from deep VI color-magnitude diagrams reaching at least 1.5 mag below the tip of the RGB are used to derive the surface density distribution of the halo. The contamination by Milky Way stars is assessed with a new control field, with models, and by combining optical and near-IR photometry. We present a new calibration of the WFC3 F606W+F814W photometry to the ground-based VI photometric system. The photometry shows that the stellar halo of NGC 5128 is dominated by old RGB stars that are present in all fields. The V-band surface brightness changes from 23 to 32 mag/arcsec$^2$ between 8.3 kpc from the galaxy center to our outermost halo fields located 140 kpc away from the center along the major axis and 92 kpc along the minor axis. Within ~30 kpc, we also find evidence for a 2-3 Gyr old population traced by bright asymptotic giant branch stars. This population contributes only up to 10% in total stellar mass if it is 2 Gyr old, but a larger fraction of 30-40% is required if its age is 3 Gyr. The stellar surface density profile is well fit by a r$^{1/4}$ curve or a power-law $\sim r^{-3.1}$ over the full radial range, with no obvious break in the slope, but with large field-to-field scatter. The ellipticity measured from integrated-light photometry in the inner parts, $e=(b/a)=0.77$, flattens to $e=0.54 \pm 0.02$ beyond 30 kpc. Considering the flattening of the outer halo, the projection of the elliptical isophote on the semimajor axis for our most distant field reaches nearly 30 effective radii. [abridged]

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Extragalactic globular clusters with Euclid and other wide surveys

Globular clusters play a role in many areas of astrophysics, ranging from stellar physics to cosmology. New ground-based optical surveys complemented by observations from space-based telescopes with unprecedented near-infrared capabilities will help us solve the puzzles of their formation histories. In this context, the Wide Survey of the Euclid space mission will provide red and near-infrared data over about 15000 square degrees of the sky. Combined with optical photometry from the ground, it will allow us to construct a global picture of the globular cluster populations in both dense and tenuous environments out to tens of megaparsecs. The homogeneous photometry of these data sets will rejuvenate stellar population studies that depend on precise spectral energy distributions. We provide a brief overview of these perspectives.

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Hidden in the Haystack: Low-luminosity globular clusters towards the Milky Way bulge

Recent wide-area surveys have enabled us to study the Milky Way with unprecedented detail. Its inner regions, hidden behind dust and gas, have been partially unveiled with the arrival of near-IR photometric and spectroscopic datasets. Among recent discoveries, there is a population of low-mass globular clusters, known to be missing, especially towards the Galactic bulge. In this work, five new low-luminosity globular clusters located towards the bulge area are presented. They were discovered by searching for groups in the multi-dimensional space of coordinates, colours, and proper motions from the Gaia EDR3 catalogue and later confirmed with deeper VVV survey near-IR photometry. The clusters show well-defined red-giant branches and, in some cases, horizontal branches with their members forming a dynamically coherent structure in proper motion space. Four of them were confirmed by spectroscopic follow-up with the MUSE instrument on the ESO VLT. Photometric parameters were derived, and when available, metallicities, radial velocities and orbits were determined. The new clusters Gran 1 and 5 are bulge globular clusters, while Gran 2, 3, and 4 present halo-like properties. Preliminary orbits indicate that Gran 1 might be related to the Main Progenitor, or the so-called ''low-energy'' group, while Gran 2, 3 and 5 appear to follow the Gaia-Enceladus-Sausage. This study demonstrates that the Gaia proper motions, combined with the spectroscopic follow-up and colour-magnitude diagrams, are required to confirm the nature of cluster candidates towards the inner Galaxy. High stellar crowding and differential extinction may hide other low-luminosity clusters.

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On the Nitrogen variation in ~2 Gyr old massive star clusters in the Large Magellanic Cloud

We present ESO/VLT FORS2 low resolution spectroscopy of red giant branch stars in three massive, intermediate age ($\sim 1.7-2.3$ Gyr) star clusters in the Large Magellanic Cloud. We measure CH and CN index bands at 4300A, and 3883A, as well as [C/Fe] and [N/Fe] abundance ratios for 24, 21 and 12 member stars of NGC 1978, NGC 1651, NGC 1783, respectively. We find a significant intrinsic spread in CN in NGC 1978 and NGC 1651, a signal of multiple stellar populations (MPs) within the clusters. On the contrary, we report a null CN spread in NGC 1783 within our measurement precision. For NGC 1978, we separated the two populations in the CN distribution and we translated the CN spread into an internal N variation $Δ$[N/Fe]$=0.63\pm0.49$ dex. For NGC 1651 and NGC 1783, we put upper limits on the N abundance variations of $Δ$[N/Fe]$\leq 0.2, 0.4$ dex, respectively. The spectroscopic analysis confirms previous results from HST photometry, where NGC 1978 was found to host MPs in the form of N spreads, while slightly younger clusters (e.g. NGC 1783, $<$ 2 Gyr old) were not, within the limits of the uncertainties. It also confirms that intermediate age massive clusters show lower N abundance variations with respect to the ancient globular clusters, although this is in part due to the effect of the first dredge up at these stellar masses, as recently reported in the literature. We stress the importance of future studies to estimate the initial N abundance variations, free of stellar evolutionary mixing processes, by observing unevolved stars in young clusters.

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Discovery of new globular clusters in the Sagittarius dwarf galaxy

Context. Globular clusters (GCs) are witnesses of the past accretion events onto the Milky Way (MW). In particular, the GCs of the Sagittarius (Sgr) dwarf galaxy are important probes of an on-going merger. Aims. Our main goal is to search for new GC members of this dwarf galaxy using the VISTA Variables in the Via Lactea Extended Survey (VVVX) near-infrared database combined with the Gaia Early Data Release 3 (EDR3) optical database. Methods. We investigated all VVVX-enabled discoveries of GC candidates in a region covering about 180 sq. deg. toward the bulge and the Sgr dwarf galaxy. We used multiband point-spread function photometry to obtain deep color-magnitude diagrams (CMDs) and luminosity functions (LFs) for all GC candidates, complemented by accurate Gaia-EDR3 proper motions (PMs) to select Sgr members and variability information to select RR Lyrae which are potential GC members. Results. After applying a strict PM cut to discard foreground bulge and disk stars, the CMDs and LFs for some of the GC candidates exhibit well defined red giant branches and red clump giant star peaks. We selected the best Sgr GCs, estimating their distances, reddenings, and associated RR Lyrae. Conclusions. We discover 12 new Sgr GC members, more than doubling the number of GCs known in this dwarf galaxy. In addition, there are 11 other GC candidates identified that are uncertain, awaiting better data for confirmation.

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Towards a more complete sample of binary central stars of planetary nebulae with Gaia

Context: Many if not most planetary nebulae (PNe) are now thought to be the outcome of binary evolutionary scenarios. However only a few percent of PNe in the Milky Way are known to host binary systems. The high precision repeated observing and long time baseline of Gaia make it well suited to detect new close binaries through photometric variability. Aims: We aim to find new close binary central stars of PNe (CSPNe) using data from the Gaia mission, building towards a statistically significant sample of post common envelope, close binary CSPNe. Methods: As the vast majority of Gaia sources do not have published epoch photometry, we use the uncertainty in the mean photometry as a proxy for determining the variability of our CSPN sample in the second Gaia data release. We derive a quantity that expresses the significance of the variability, and consider what is necessary to build a clean sample of genuine variable sources. Results: Our selection recovers a large fraction of the known close binary CSPN population, while other CSPNe lying in the same region of the parameter space likely represent low-hanging fruit for ground-based confirmatory followup observations. Gaia epoch photometry for four of the newly identified variable sources confirms that the variability is genuine and consistent with binarity

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VVVX-Gaia Discovery of a Low Luminosity Globular Cluster in the Milky Way Disk

Milky Way globular clusters (MW GCs) are difficult to identify at low Galactic latitudes because of high differential extinction and heavy star crowding. The new deep near-IR images and photometry from the VISTA Variables in the Via Láctea Extended Survey (VVVX) allow us to chart previously unexplored regions. Our long term aim is to complete the census of MW GCs. The immediate goals are to estimate the astrophysical parameters, measuring their reddenings, extinctions, distances, total luminosities, proper motions, sizes, metallicities and ages. We use the near-IR VVVX survey database, in combination with Gaia DR2 optical photometry, and with the Two Micron All Sky Survey (2MASS) photometry. We report the detection of a heretofore unknown Galactic Globular Cluster at $RA =$ 14:09:00.0; $DEC=-$65:37:12 (J2000). We calculate a reddening of $E(J-K_s)=(0.3\pm 0.03)$ mag and an extinction of $A_{K_s}=(0.15\pm 0.01)$ mag for this new GC. Its distance modulus and corresponding distance were measured as $(m-M)=(15.93\pm0.03)$ mag and $D=(15.5\pm1.0)$ kpc, respectively. We estimate the metallicity and age by comparison with known GCs and by fitting PARSEC and Dartmouth isochrones, finding $[Fe/H]=(-0.70\pm0.2)$ dex and $t=(11.0\pm1.0)$ Gyr. The mean GC PMs from Gaia are $μ_{α^\ast}=(-4.68 \pm 0.47 )$ mas $yr^{-1}$ and $μ_δ=(-1.34 \pm 0.45)$ mas $yr^{-1}$. The total luminosity of our cluster is estimated to be $M_{Ks}=(-7.76\pm 0.5)$ mag. We have found a new low-luminosity, old and metal-rich globular cluster, situated in the far side of the Galactic disk, at $R_{G}=11.2$ kpc from the Galactic centre, and at $z=1.0$ kpc below the plane. Interestingly, the location, metallicity and age of this globular cluster are coincident with the Monoceros Ring (MRi) structure.

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Leveraging HST with MUSE: II. Na-abundance variations in intermediate age star clusters

Ancient ($>$10 Gyr) globular clusters (GCs) show chemical abundance variations in the form of patterns among certain elements, e.g. N correlates with Na and anti-correlates with O. Recently, N abundance spreads have also been observed in massive star clusters that are significantly younger than old GCs, down to an age of $\sim$2 Gyr. However, so far N has been the only element found to vary in such young objects. We report here the presence of Na abundance variations in the intermediate age massive star clusters NGC 416 ($\sim$6.5 Gyr old) and Lindsay 1 ($\sim$7.5 Gyr old) in the Small Magellanic Cloud, by combining HST and ESO-VLT MUSE observations. Using HST photometry we were able to construct ''chromosome maps'' and separate sub-populations with different N content, in the red giant branch of each cluster. MUSE spectra of individual stars belonging to each population were combined, resulting in high signal-to-noise spectra representative of each population, which were compared to search for mean differences in Na. We find a mean abundance variation of $Δ$[Na/Fe]$=0.18\pm0.04$ dex for NGC 416 and $Δ$[Na/Fe]$=0.24\pm0.05$ dex for Lindsay 1. In both clusters we find that the population that is enhanced in N is also enhanced in Na, which is the same pattern to the one observed in ancient GCs. Furthermore, we detect a bimodal distribution of core-helium burning Red Clump (RC) giants in the UV colour magnitude diagram of NGC 416. A comparison of the stacked MUSE spectra of the two RCs shows the same mean Na abundance difference between the two populations. The results reported in this work are a crucial hint that star clusters of a large age range share the same origin: they are the same types of objects, but only separated in age.

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The first detection of ultra-diffuse galaxies in the Hydra I cluster from VEGAS survey

In this paper we report on the discovery of 27 low-surface brightness galaxies, of which 12 are candidate ultra-diffuse galaxy (UDG) in the Hydra I cluster, based on deep observations taken as part of the VST Early-type Galaxy Survey (VEGAS). This first sample of UDG candidates in the Hydra I cluster represents an important step in our project that aims to enlarge the number of confirmed UDGs and, through study of statistically relevant samples, constrain the nature and formation of UDGs. This study presents the main properties of this class of galaxies in the Hydra I cluster. For all UDGs, we analyse the light and colour distribution, and provide a census of the globular cluster (GC) systems around them. Given the limitations of a reliable GC selection based on two relatively close optical bands only, we find that half of the UDG candidates have a total GC population consistent with zero. Of the other half, two galaxies have a total population larger than zero at 2$σ$ level. We estimate the stellar mass, the total number of GCs and the GC specific frequency ($S_N$). Most of the candidates span a range of stellar masses of $10^7-10^8$~M$_{\odot}$. Based on the GC population of these newly discovered UDGs, we conclude that most of these galaxies have a standard or low dark matter content, with a halo mass of $\leq 10^{10}$~M$_{\odot}$.

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Analysis of Red-Supergiants in VdBH 222

Recent surveys uncovered new Young Massive Clusters (YMCs) that host dozens of Red Supergiants (RSGs) in the inner Milky Way. These clusters are ideal for studying the most recent and violent star formation events in the inner Galaxy. However, due to the high extinction that affects the Galactic plane, they need to be studied through infrared (IR) spectroscopy. IR spectra of RSGs have proven to be powerful tools for obtaining chemical abundances. We present the first [Fe$/$H] measurement ($-$0.07$\pm$0.02) for the YMC VdBH 222 through analysis of its RSGs using VLT/X-shooter spectra. We find no evidence for Multiple Stellar Populations (MSPs) in this YMC, contrary to what is routinely observed in older massive clusters.

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Is Fornax 4 the nuclear star cluster of the Fornax dwarf spheroidal galaxy?

Fornax 4 is the most distinctive globular cluster in the Fornax dwarf spheroidal. Located close to the centre of the galaxy, more metal-rich and potentially younger than its four companions (namely, Fornax clusters number 1, 2, 3 and 5), it has been suggested to have experienced a different formation than the other clusters in the galaxy. Here we use HST/WFC3 photometry to characterize the stellar population content of this system and shed new light on its nature. By means of a detailed comparison of synthetic horizontal branch and red giant branch with the observed colour-magnitude diagrams, we find that this system likely hosts stellar sub-populations characterized by a significant iron spread up to $Δ$[Fe/H]$\sim$0.4 dex and possibly by also some degree of He abundance variations $Δ$Y$\sim0.03$. We argue that this purely observational evidence, combined with the other peculiarities characterizing this system, supports the possibility that Fornax 4 is the nuclear star cluster of the Fornax dwarf spheroidal galaxy. A spectroscopic follow-up for a large number of resolved member stars is needed to confirm this interesting result and to study in detail the formation and early evolution of this system and more in general the process of galaxy nucleation.

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The Tucana dwarf spheroidal galaxy: not such a massive failure after all

Isolated Local Group (LG) dwarf galaxies have evolved most or all of their life unaffected by interactions with the large LG spirals and therefore offer the opportunity to learn about the intrinsic characteristics of this class of objects. Here we explore the internal kinematic and metallicity properties of one of the three isolated LG dwarf spheroidal galaxies, i.e. the Tucana dSph. This is an intriguing system, as it has been found in the literature to have an internal rotation of up to 16 km/s, a much higher velocity dispersion than other dSphs of similar luminosity, and a possible exception to the too-big-too-fail problem. We present results for a new VLT/FORS2 spectroscopic dataset in the CaII triplet region for 50 candidate red giant branch stars in the direction of Tucana, which yielded line-of-sight velocity and metallicity ([Fe/H]) measurements of 39 effective members. This doubles the number of Tucana's stars with such measurements. In addition, we re-reduce and include in our analysis the other two spectroscopic datasets presented in the literature, the VLT/FORS2 sample by Fraternali et al. (2009) and the VLT/FLAMES one by Gregory et al. (2019). We measure a systemic velocity of $180.0\pm1.3$ km/s, consistently across the various datasets analyzed, and find that a dispersion-only model is moderately favored over models accounting also for internal rotation. Our best estimate of the internal velocity dispersion is $6.2_{-1.3}^{+1.6}$ km/s, much smaller than the values reported in the literature and in line with similarly luminous dSphs; this is consistent with Tucana not being an exception to the too-big-to-fail problem, nor living in a dark matter halo much more massive than those of its siblings. As for the metallicity properties, we do not find anything unusual; there are hints of the presence of a [Fe/H] gradient but more data are needed to pin its presence down.

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Kinematic and metallicity properties od the Aquarius dwarf galaxy from FORS2 MXU spectroscopy

Dwarf galaxies found in isolation in the Local Group (LG) are unlikely to have interacted with the large LG spirals, and therefore environmental effects should not be the main drivers of their evolution. We aim to provide insight into the internal mechanisms shaping LG dwarf galaxies by increasing our knowledge of the internal properties of isolated systems. We focus on the evolved stellar component of the Aquarius dwarf, whose kinematic and metallicity properties have only recently started to be explored. We have obtained spectroscopic data in the the near-infrared CaII triplet lines region with FORS2 at the Very Large Telescope for 53 red giant branch (RGB) stars, to derive line-of-sight velocities and [Fe/H] of the individual RGB stars. We have derived a systemic velocity of $-142.2^{+1.8}_{-1.8}$ km s$^{-1}$, in agreement with previous measurements from both the HI gas and stars. The internal kinematics of Aquarius appears to be best modelled by a combination of random motions (l.o.s. velocity dispersion of $10.3^{+1.6}_{-1.3}$ km s$^{-1}$) and linear rotation (with a gradient $-5.0^{+1.6}_{-1.9}$ km s$^{-1}$ arcmin$^{-1}$) along a P.A.=$139_{-27}^{+17}$ deg, consistent with the optical projected major axis. This rotation signal is significantly misaligned or even counter-rotating to that derived from the HI gas. We also find the tentative presence of a mild negative metallicity gradient and indications that the metal-rich stars have a colder velocity dispersion than the metal-poor ones. This work represents a significant improvement with respect to previous measurements of the RGB stars of Aquarius, as it doubles the number of member stars studied in the literature. We speculate that the misaligned rotation between the HI gas and evolved stellar component might have been the result of recent accretion of HI gas or re-accretion after gas-loss due to internal stellar feedback.

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A Color-Excess Extinction map of the Southern Galactic disk from the VVV and GLIMPSE Surveys

An improved high-resolution and deep A$_{Ks}$ foreground dust extinction map is presented for the Galactic disk area within $295^{\circ} \lesssim l \lesssim 350^{\circ}$, $-1.0^{\circ} \lesssim b \lesssim +1.0^{\circ}$. At some longitudes the map reaches up to $|b|\sim2.25^{\circ}$, for a total of $\sim$148 deg$^2$. The map was constructed via the Rayleigh-Jeans Color Excess (RJCE) technique based on deep near-infrared (NIR) and mid-infrared (MIR) photometry. The new extinction map features a maximum bin size of 1', and relies on NIR observations from the Two Micron All-Sky Survey (2MASS) and new data from ESO's Vista Variables in the Vía Láctea (VVV) survey, in concert with MIR observations from the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE). The VVV photometry penetrates $\sim$4 magnitudes fainter than 2MASS, and provides enhanced sampling of the underlying stellar populations in this heavily obscured region. Consequently, the new results supersede existing RJCE maps tied solely to brighter photometry, revealing a systematic underestimation of extinction in prior work that was based on shallower data. The new high-resolution and large-scale extinction map presented here is readily available to the community through a web query interface.

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Mapping the stellar age of the Milky Way bulge with the VVV. II. Deep JKs catalogs release based on PSF photometry

The bulge represents the best compromise between old and massive Galactic component, and as such its study is a valuable opportunity to understand how the bulk of the Milky Way formed and evolved. In addition, being the only bulge in which we can individually resolve stars in all evolutionary sequences, the properties of its stellar content provide crucial insights on the formation of bulges at large. We aim at providing a detailed and comprehensive census of the Milky Way bulge stellar populations by producing deep and accurate photometric catalogs of the inner ~300 sqdeg of the Galaxy. We perform DAOPHOT/ALLFRAME PSF-fitting photometry of multi-epochs J and Ks images provided by the VVV survey to obtain deep photometric catalogs. Artificial star experiments have been conducted on all images to properly assess the completeness and the accuracy of the photometric measurements. We present a photometric database containing nearly 600 million stars across the bulge area surveyed by the VVV. Through the comparison of derived color-magnitude diagrams of selected fields representative of different levels of extinction and crowding, we show the quality, completeness and depth of the new catalogs. With the exception of the fields located along the plane, this new photometry samples stars down to ~1-2 mag below the MS-TO with unprecedented accuracy. To demonstrate the tremendous potential inherent to this new dataset, we give few examples of possible applications such as: i) star counts studies through the dataset completeness map; ii) surface brightness map; and iii) cross-correlation with Gaia DR2. The database presented here represents an invaluable collection for the whole community, and we encourage its exploitation. The photometric catalogs including completeness information are publicly available through the ESO Science Archive.

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Globular cluster candidates in the Galactic bulge: Gaia and VVV view of the latest discoveries

Thanks to the recent wide-area photometric surveys, the number of star cluster candidates have risen exponentially in the last few years. Most detections, however, are based only on the presence of an overdensity of stars in a given region, or an overdensity of variable stars, regardless of their distance. As candidates, their detection has not been dynamically confirmed. Therefore, it is currently unknown how many, and which ones, of the published candidates, are true clusters, and which ones are chance alignments. We present a method to detect and confirm star clusters based on the spatial distribution, coherence in motion and appearance on the color-magnitude diagram. We explain and apply it to one new star cluster, and several candidate star clusters published in the literature. The presented method is based on data from the Second Data Release of Gaia complemented with data from the VISTA Variables in the Vía Láctea survey for the innermost bulge regions. It consists of a nearest neighbors algorithm applied simultaneously over spatial coordinates, star color, and proper motions, in order to detect groups of stars that are close in the sky, move coherently and define narrow sequences in the color-magnitude diagram, such as a young main sequence or a red giant branch. When tested in the bulge area ($-10<\ell\ {\rm (deg)}<+10$; $-10<b\ {\rm (deg)}<+10$) the method successfully recovered several known young and old star clusters. We report here the detection of one new, likely old star cluster, while deferring the others to a forthcoming paper. Additionally, the code has been applied to the position of 93 candidate star clusters published in the literature. As a result, only two of them are confirmed as coherently moving groups of stars at their nominal positions.

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Mapping the stellar age of the Milky Way bulge with the VVV. I. The method

Recent observational programmes are providing a global view of the Milky Way bulge that serves as template for detailed comparison with models and extragalactic bulges. A number of surveys (i.e. VVV, GIBS, GES, ARGOS, BRAVA, APOGEE) are producing comprehensive and detailed extinction, metallicity, kinematics and stellar density maps of the Galactic bulge with unprecedented accuracy. However, the still missing key ingredient is the distribution of stellar ages across the bulge. To overcome this limitation, we aim to age-date the stellar population in several bulge fields with the ultimate goal of deriving an age map of the Bulge. This paper presents the methodology and the first results obtained for a field along the Bulge minor axis, at $b=-6^\circ$. We use a new PSF-fitting photometry of the VISTA Variables in the Vía Láctea (VVV) survey data to construct deep color-magnitude diagrams of the bulge stellar population down to $\sim$ 2 mag below the Main Sequence turnoff. We find the bulk of the bulge stellar population in the observed field along the minor axis to be at least older than $\sim$ 7.5 Gyr. In particular, when the metallicity distribution function spectroscopically derived by GIBS is used, the best fit to the data is obtained with a combination of synthetic populations with ages in between $\sim$ 7.5 Gyr and 11 Gyr. However, the fraction of stars younger than $\sim$ 10 Gyr strongly depends upon the number of Blue Straggler Stars present in the bulge. Simulations show that the observed color-magnitude diagram of the bulge in the field along the minor axis is incompatible with the presence of a conspicuous population of intermediate-age/young (i.e. $\lesssim 5$ Gyr) stars.

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Time-series analyses of Cepheid and RR Lyrae variables in the wide-field variability surveys

We discuss time-series analyses of classical Cepheid and RR Lyrae variables in the Galaxy and the Magellanic Clouds at multiple wavelengths. We adopt the Fourier decomposition method to quantify the structural changes in the light curves of Cepheid and RR Lyrae variables. A quantitative comparison of Cepheid Fourier parameters suggests that the canonical mass-luminosity models that lie towards the red-edge of the instability strip show a greater offset with respect to observations for short-period Cepheids. RR Lyrae models are consistent with observations in most period bins. We use ensemble light curve analysis to predict the physical parameters of observed Cepheid and RR Lyrae variables using machine learning methods. Our preliminary results suggest that the posterior distributions of mass, luminosity, temperature and radius for Cepheids and RR Lyraes can be well-constrained for a given metal abundance, provided a smoother grid of models is adopted in various input physical parameters.

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