arXiv subjects

Guilherme Limberg

Publications and source records attributed to Guilherme Limberg.

At least 55 records · Page 3Linked to original sources

arXiv2024

The Fourth S-PLUS Data Release: 12-filter photometry covering $\sim3000$ square degrees in the southern hemisphere

The Southern Photometric Local Universe Survey (S-PLUS) is a project to map $\sim9300$ sq deg of the sky using twelve bands (seven narrow and five broadbands). Observations are performed with the T80-South telescope, a robotic telescope located at the Cerro Tololo Observatory in Chile. The survey footprint consists of several large contiguous areas, including fields at high and low galactic latitudes, and towards the Magellanic Clouds. S-PLUS uses fixed exposure times to reach point source depths of about $21$ mag in the $griz$ and $20$ mag in the $u$ and the narrow filters. This paper describes the S-PLUS Data Release 4 (DR4), which includes calibrated images and derived catalogues for over 3000 sq deg, covering the aforementioned area. The catalogues provide multi-band photometry performed with the tools \texttt{DoPHOT} and \texttt{SExtractor} -- point spread function (\PSF) and aperture photometry, respectively. In addition to the characterization, we also present the scientific potential of the data. We use statistical tools to present and compare the photometry obtained through different methods. Overall we find good agreement between the different methods, with a slight systematic offset of 0.05\,mag between our \PSF and aperture photometry. We show that the astrometry accuracy is equivalent to that obtained in previous S-PLUS data releases, even in very crowded fields where photometric extraction is challenging. The depths of main survey (MS) photometry for a minimum signal-to-noise ratio $S/N = 3$ reach from $\sim19.5$ for the bluer bands to $\sim21.5$ mag on the red. The range of magnitudes over which accurate \PSF photometry is obtained is shallower, reaching $\sim19$ to $\sim20.5$ mag depending on the filter. Based on these photometric data, we provide star-galaxy-quasar classification and photometric redshift for millions of objects.

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arXiv2024

The S-PLUS Ultra-Short Survey: first data release

This paper presents the first public data release of the S-PLUS Ultra-Short Survey (USS), a photometric survey with short exposure times, covering approximately 9300 deg$^{2}$ of the Southern sky. The USS utilizes the Javalambre 12-band magnitude system, including narrow and medium-band and broad-band filters targeting prominent stellar spectral features. The primary objective of the USS is to identify bright, extremely metal-poor (EMP; [Fe/H] $\leq -3$) and ultra metal-poor (UMP; [Fe/H] $\leq -4$) stars for further analysis using medium- and high-resolution spectroscopy.}{This paper provides an overview of the survey observations, calibration method, data quality, and data products. Additionally, it presents the selection of EMP and UMP candidates.}{The data from the USS were reduced and calibrated using the same methods as presented in the S-PLUS DR2. An additional step was introduced, accounting for the offset between the observed magnitudes off the USS and the predicted magnitudes from the very low-resolution Gaia XP spectra.}{This first release contains data for 163 observed fields totaling $\sim$324 deg$^{2}$ along the Celestial Equator. The magnitudes obtained from the USS are well-calibrated, showing a difference of $\sim 15$ mmag compared to the predicted magnitudes by the GaiaXPy toolkit. By combining colors and magnitudes, 140 candidates for EMP or UMP have been identified for follow-up studies.}{The S-PLUS USS DR1 is an important milestone in the search for bright metal-poor stars, with magnitudes in the range 10 $ < r \leq 14$. The USS is an ongoing survey; in the near future, it will provide many more bright metal-poor candidate stars for spectroscopic follow-up.

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arXiv2024

The Rise of the $R$-Process in the Gaia-Sausage/Enceladus Dwarf Galaxy

Neutron star mergers (NSMs) produce copious amounts of heavy r-process elements after a time delayed inspiral process. Once NSMs are present in a galaxy, r-process elements, such as Eu, are expected to significantly increase with time. Yet, there has been limited observational data in support of Eu increasing within Local Group galaxies. We have obtained high-resolution Magellan/MIKE observations of 43 metal-poor stars in the Gaia-Sausage/Enceladus tidally disrupted galaxy with $-2.5 < \rm{[Fe/H]} < -1$. For the first time, we find a clear rise in [Eu/Mg] with increasing [Mg/H] within one galaxy. We use a chemical evolution model to study how such a rise can result from the interplay of prompt and delayed r-process enrichment events. Delayed r-process sources are required to explain the rise and subsequent leveling off of [Eu/Mg] in this disrupted galaxy. However, the rise may be explained by delayed r-process sources with either short ($\sim 10$ Myr) or long ($\sim 500$ Myr) minimum delay times. Future studies on the nature of r-process sources and their enrichment processes in the GSE will require additional stars in the GSE at even lower metallicities than the present study.

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arXiv2024

Stellar Metallicities from DECam $u$-band Photometry: A Study of Milky Way Ultra-Faint Dwarf Galaxies

We conducted an in-depth analysis of candidate member stars located in the peripheries of three ultra-faint dwarf (UFD) galaxy satellites of the Milky Way: Boötes I (Boo1), Boötes II (Boo2), and Segue I (Seg1). Studying these peripheral stars has previously been difficult due to contamination from the Milky Way foreground. We used $u$-band photometry from the Dark Energy Camera (DECam) to derive metallicities to efficiently select UFD candidate member stars. This approach was validated on Boo1, where we identified both previously known and new candidate member stars beyond five half-light radii. We then applied a similar procedure to Boo2 and Seg1. Our findings hinted at evidence for tidal features in Boo1 and Seg1, with Boo1 having an elongation consistent with its proper motion and Seg1 showing some distant candidate stars, a few of which are along its elongation and proper motion. We find two Boo2 stars at large distances consistent with being candidate member stars. Using a foreground contamination rate derived from the \emph{Besançon} Galaxy model, we ascribed purity estimates to each candidate member star. We recommend further spectroscopic studies on the newly identified high-purity members. Our technique offers promise for future endeavors to detect candidate member stars at large radii in other systems, leveraging metallicity-sensitive filters with the Legacy Survey of Space and Time and the new, narrow-band Ca HK filter on DECam.

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arXiv2024

Extending the Chemical Reach of the H3 Survey: Detailed Abundances of the Dwarf-galaxy Stellar Stream Wukong/LMS-1

We present the first detailed chemical-abundance analysis of stars from the dwarf-galaxy stellar stream Wukong/LMS-1 covering a wide metallicity range ($-3.5 < \rm[Fe/H] \lesssim -1.3$). We find abundance patterns that are effectively indistinguishable from the bulk of Indus and Jhelum, a pair of smaller stellar streams proposed to be dynamically associated with Wukong/LMS-1. We confirmed a carbon-enhanced metal-poor star ($\rm[C/Fe] > +0.7$ and $\rm[Fe/H] \sim -2.9$) in Wukong/LMS-1 with strong enhancements in Sr, Y, and Zr, which is peculiar given its solar-level [Ba/Fe]. Wukong/LMS-1 stars have high abundances of $α$ elements up to $\rm[Fe/H] \gtrsim -2$, which is expected for relatively massive dwarfs. Towards the high-metallicity end, Wukong/LMS-1 becomes $α$-poor, revealing that it probably experienced fairly standard chemical evolution. We identified a pair of N- and Na-rich stars in Wukong/LMS-1, reminiscent of multiple populations in globular clusters. This indicates that this dwarf galaxy contained at least one globular cluster that was completely disrupted in addition to two intact ones previously known to be associated with Wukong/LMS-1, which is possibly connected to similar evidence found in Indus. From these $\geq$3 globular clusters, we estimate the total mass of Wukong/LMS-1 to be ${\approx}10^{10} M_\odot$, representing ${\sim}1$% of the present-day Milky Way. Finally, the [Eu/Mg] ratio in Wukong/LMS-1 continuously increases with metallicity, making this the first example of a dwarf galaxy where the production of $r$-process elements is clearly dominated by delayed sources, presumably neutron-star mergers.

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arXiv2024

Inferring dark matter subhalo properties from simulated subhalo-stream encounters

In the cold dark matter paradigm, our Galaxy is predicted to contain >10000 dark matter subhaloes in the $10^5-10^8M_\odot$ range which should be completely devoid of stars. Stellar streams are sensitive to the presence of these subhaloes, which can create small-scale features in streams if they pass closely enough. Modelling these encounters can therefore, potentially recover the subhalo's properties. In this work, we demonstrate this for streams generated in numerical simulations, modelled on eccentric orbits in a realistic Milky Way potential, which includes the Large Magellanic Cloud and the subhalo itself. We focus on a mock model of the ATLAS-Aliqa Uma stream and inject a $10^7 M_\odot$ subhalo, creating a similar discontinuous morphology to current observations. We then explore how well subhalo properties are recovered using mock stream observations, consisting of no observational errors, as well as assuming realistic observational setups. These setups include present day style observations, and what will be possible with 4MOST and Gaia DR5 in the future. We show that we can recover all parameters describing the impact even with uncertainties matching existing data, including subhalo positions, velocities, mass and scale radius. Modelling the subhalo on an orbit instead of assuming an impulse approximation, we greatly reduce the degeneracy between subhalo mass and velocity seen in previous works. However, we find a slight bias in the subhalo mass (~0.1 dex). This demonstrates that we should be able to reliably extract the properties of subhaloes with stellar streams in the near future.

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arXiv2024

Enrichment by Extragalactic First Stars in the Large Magellanic Cloud

The Large Magellanic Cloud (LMC) is the Milky Way's most massive satellite galaxy, which only recently (~2 billion years ago) fell into our Galaxy. Since stellar atmospheres preserve their natal cloud's composition, the LMC's recent infall makes its most ancient, metal-deficient ("low-metallicity") stars unique windows into early star formation and nucleosynthesis in a formerly distant region of the high-redshift universe. Previously, identifying such stars in the LMC was challenging. But new techniques have opened this window, now enabling tests of whether the earliest element enrichment and star formation in distant, extragalactic proto-galaxies deviated from what occurred in the proto-Milky Way. Here we present the elemental abundances of 10 stars in the LMC with iron-to-hydrogen ratios ranging from ~1/300th to ~1/12,000th of the Sun. Our most metal-deficient star is 50 times more metal-deficient than any in the LMC with available detailed chemical abundance patterns, and is likely enriched by a single extragalactic first star supernova. This star lacks significant carbon-enhancement, as does our overall sample, in contrast with the lowest metallicity Milky Way stars. This, and other abundance differences, affirm that the extragalactic early LMC experienced diverging enrichment processes compared to the early Milky Way. Early element production, driven by the earliest stars, thus appears to proceed in an environment-dependent manner.

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arXiv2024

200,000 Candidate Very Metal-poor Stars in Gaia DR3 XP Spectra

Very metal-poor stars ($\rm[Fe/H] < -2$) in the Milky Way are fossil records of early chemical evolution and the assembly and structure of the Galaxy. However, they are rare and hard to find. Gaia DR3 has provided over 200 million low-resolution ($R \approx 50$) XP spectra, which provides an opportunity to greatly increase the number of candidate metal-poor stars. In this work, we utilise the \texttt{XGBoost} classification algorithm to identify $\sim$200,000 very metal-poor star candidates. Compared to past work, we increase the candidate metal-poor sample by about an order of magnitude, with comparable or better purity than past studies. Firstly, we develop three classifiers for bright stars ($BP$ $<$ 16). They are Classifier-T (for Turn-off stars), Classifier-GC (for Giant stars with high completeness), and Classifier-GP (for Giant stars with high purity) with expected purity of 52\%/45\%/76\% and completeness of 32\%/93\%/66\% respectively. These three classifiers obtained a total of 11,000/111,000/44,000 bright metal-poor candidates. We apply model-T and model-GP on faint stars ($BP$ $>$ 16) and obtain 38,000/41,000 additional metal-poor candidates with purity 29\%/52\%, respectively. We make our metal-poor star catalogs publicly available, for further exploration of the metal-poor Milky Way.

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arXiv2024

The Power of High Precision Broadband Photometry: Tracing the Milky Way Density Profile with Blue Horizontal Branch stars in the Dark Energy Survey

Blue Horizontal Branch (BHB) stars, excellent distant tracers for probing the Milky Way's halo density profile, are distinguished in the $(g-r)_0$ vs $(i-z)_0$ color space from another class of stars, blue straggler stars (BSs). We develop a Bayesian mixture model to classify BHB stars using high-precision photometry data from the Dark Energy Survey Data Release 2 (DES DR2). We select $\sim2100$ highly-probable BHBs based on their $griz$ photometry and the associated uncertainties, and use these stars to map the stellar halo over the Galactocentric radial range $20 \lesssim R \lesssim 70$ kpc. After excluding known stellar overdensities, we find that the number density $n_\star$ of BHBs can be represented by a power law density profile $n_\star \propto R^{-α}$ with an index of $α=4.28_{-0.12}^{+0.13}$, consistent with existing literature values. In addition, we examine the impact of systematic errors and the spatial inhomogeneity on the fitted density profile. Our work demonstrates the effectiveness of high-precision $griz$ photometry in selecting BHB stars. The upcoming photometric survey from the Rubin Observatory, expected to reach depths 2-3 magnitudes greater than DES during its 10-year mission, will enable us to investigate the density profile of the Milky Way's halo out to the virial radius, unravelling the complex processes of formation and evolution in our Galaxy.

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arXiv2023

Ages and metallicities of stellar clusters using S-PLUS narrow-band integrated photometry: the Small Magellanic Cloud

The Magellanic Clouds are the most massive and closest satellite galaxies of the Milky Way, with stars covering ages from a few Myr up to 13 Gyr. This makes them important for validating integrated light methods to study stellar populations and star-formation processes, which can be applied to more distant galaxies. We characterized a set of stellar clusters in the Small Magellanic Cloud (SMC), using the $\textit{Southern Photometric Local Universe Survey}$. This is the first age (metallicity) determination for 11 (65) clusters of this sample. Through its 7 narrow bands, centered on important spectral features, and 5 broad bands, we can retrieve detailed information about stellar populations. We obtained ages and metallicities for all stellar clusters using the Bayesian spectral energy distribution fitting code $\texttt{BAGPIPES}$. With a sample of clusters in the color range $-0.20 < r-z < +0.35$, for which our determined parameters are most reliable, we modeled the age-metallicity relation of SMC. At any given age, the metallicities of SMC clusters are lower than those of both the Gaia Sausage-Enceladus disrupted dwarf galaxy and the Milky Way. In comparison with literature values, differences are $Δ$log(age)$\approx0.31$ and $Δ$[Fe/H]$\approx0.41$, which is comparable to low-resolution spectroscopy of individual stars. Finally, we confirm a previously known gradient, with younger clusters in the center and older ones preferentially located in the outermost regions. On the other hand, we found no evidence of a significant metallicity gradient.

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arXiv2023

All-sky Kinematics and Chemistry of Monoceros Stellar Overdensity

We explore the kinematic and chemical properties of Monoceros stellar overdensity by combining data from 2MASS, WISE, APOGEE, and $\text{Gaia}$. Monoceros is a structure located towards the Galactic anticenter and close to the disk. We identified that its stars have azimuthal velocity in the range of $200 < v_ϕ\,{\rm(km\,s^{-1})}< 250$. Combining their kinematics and spatial distribution, we designed a new method to select stars from this overdensity. This method allows us to easily identify the structure in both hemispheres and estimate their distances. Our analysis was supported by comparison with simulated data from the entire sky generated by $\texttt{Galaxia}$ code. Furthermore, we characterized, for the first time, the Monoceros overdensity in several chemical-abundance spaces. Our results confirm its similarity to stars found in the thin disk of the Galaxy and suggest an $\textit{in situ}$ formation. Furthermore, we demonstrate that the southern (Mon-S) and northern (Mon-N) regions of Monoceros exhibit indistinguishable chemical compositions.

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arXiv2023

S-PLUS: Photometric Re-calibration with the Stellar Color Regression Method and an Improved Gaia XP Synthetic Photometry Method

We present a comprehensive re-calibration of medium- and broad-band photometry from the Southern Photometric Local Universe Survey (S-PLUS) by leveraging two approaches: an improved Gaia XP Synthetic Photometry (XPSP) method with corrected Gaia XP spectra, the Stellar Color Regression (SCR) method with corrected Gaia EDR3 photometric data and spectroscopic data from LAMOST DR7. Through the use of millions of stars as standards per band, we demonstrate the existence of position-dependent systematic errors, up to 23 mmag for the Main Survey region, in the S-PLUS DR4 photometric data. A comparison between the XPSP and SCR methods reveals minor differences in zero-point offsets, typically within the range of 1 to 6 mmag, indicating the accuracy of the re-calibration, and a two- to three-fold improvement in the zero-point precision. During this process, we also verified and corrected for the systematic errors related to CCD position. The corrected S-PLUS DR4 photometric data will provide a solid data foundation for conducting scientific research that relies on high-calibration precision. Our results underscore the power of the XPSP method in combination with the SCR method, showcasing their effectiveness in enhancing calibration precision for wide-field surveys when combined with Gaia photometry and XP spectra, to be applied for other S-PLUS sub-surveys.

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arXiv2023

The Chemodynamical Nature of the Triangulum-Andromeda Overdensity

We present a chemodynamical study of the Triangulum-Andromeda overdensity (TriAnd) employing a sample of 31 candidate stars observed with the GRACES high-resolution ($R$=40,000) spectrograph at the Gemini North (8.1 m) telescope. TriAnd is a stellar substructure found toward the outer disk of the Milky Way, located at $R_{\rm GC}\sim 18$ kpc from the Sun, toward Galactic latitude $b \sim 25$°. Most stars in our sample have dynamical properties compatible with a disk stellar population. In addition, by applying an eccentricity cut, we are able to detect a stellar contamination that seems to be consistent with an accreted population. In chemical abundance space, the majority of our TriAnd candidates are similar to the outer thin-disk population, suggesting that the overdensity has an \textit{in situ} origin. Finally, the found accreted halo interlopers spatially overlapping with TriAnd should explain the historical discussion of the overdensity's nature due to its complex chemical patterns.

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arXiv2023

Chemodynamical Properties and Ages of Metal-Poor Stars in S-PLUS

Metal-poor stars are key to our understanding of the early stages of chemical evolution in the Universe. New multi-filter surveys, such as the Southern Photometric Local Universe Survey (S-PLUS), are greatly advancing our ability to select low-metallicity stars. In this work, we analyse the chemodynamical properties and ages of 522 metal-poor candidates selected from the S-PLUS data release 3. About 92% of these stars were confirmed to be metal-poor ([Fe/H] $\leq -1$) based on previous medium-resolution spectroscopy. We calculated the dynamical properties of a subsample containing 241 stars, using the astrometry from Gaia Data Release 3. Stellar ages are estimated by a Bayesian isochronal method formalized in this work. We analyse the metallicity distribution of these metal-poor candidates separated into different subgroups of total velocity, dynamical properties, and ages. Our results are used to propose further restrictions to optimize the selection of metal-poor candidates in S-PLUS. The proposed astrometric selection ($\mathrm{parallax}>0.85$ mas) is the one that returns the highest fraction of extremely metal-poor stars (16.3% have [Fe/H] $\leq -3$); the combined selection provides the highest fraction of very metal-poor stars (91.0% have [Fe/H] $\leq -2$), whereas the dynamical selection (eccentricity > 0.35 and diskness < 0.75) is better for targetting metal-poor (99.5% have [Fe/H] $\leq -1$). Using only S-PLUS photometric selections, it is possible to achieve selection fractions of 15.6%, 88.5% and 98.3% for metallicities below $-$3, $-$2 and $-$1, respectively. We also show that it is possible to use S-PLUS to target metal-poor stars in halo substructures such as Gaia-Sausage/Enceladus, Sequoia, Thamnos and the Helmi stream.

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arXiv2023

Phase-space Properties and Chemistry of the Sagittarius Stellar Stream Down to the Extremely Metal-poor ($\rm[Fe/H] \lesssim -3$) Regime

In this work, we study the phase-space and chemical properties of Sagittarius (Sgr) stream, the tidal tails produced by the ongoing destruction of Sgr dwarf spheroidal (dSph) galaxy, focusing on its very metal-poor (VMP; $\rm[Fe/H] < -2$) content. We combine spectroscopic and astrometric information from SEGUE and $Gaia$ EDR3, respectively, with data products from a new large-scale run of $\texttt{StarHorse}$ spectro-photometric code. Our selection criteria yields ${\sim}1600$ stream members, including ${>}200$ VMP stars. We find the leading arm ($b>0^\circ$) of Sgr stream to be more metal-poor, by ${\sim}0.2$ dex, than the trailing one ($b<0^\circ$). With a subsample of turnoff and subgiant stars, we estimate this substructure's stellar population to be ${\sim}1$ Gyr older than the thick disk's. With the aid of an $N$-body model of the Sgr system, we verify that simulated particles stripped earlier (${>}2$ Gyr ago) have present-day phase-space properties similar to lower-metallicity stream stars. Conversely, those stripped more recently (${<}2$ Gyr) are preferentially more akin to metal-rich ($\rm[Fe/H] > -1$) members of the stream. Such correlation between kinematics and chemistry can be explained by the existence of a dynamically hotter, less centrally-concentrated, and more metal-poor population in Sgr dSph prior to its disruption, implying that this galaxy was able to develop a metallicity gradient before its accretion. Finally, we discovered several carbon-enhanced metal-poor ($\rm[C/Fe] > +0.7$ and $\rm[Fe/H] \leq -1.5$) stars in Sgr stream, which is in tension with current observations of its remaining core where such objects are not found.

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arXiv2022

The SDSS-Gaia View of the Color-Magnitude Relation for Blue Horizontal-branch Stars

We present an updated sample of blue horizontal-branch (BHB) stars selected from the photometric and spectroscopic data from Sloan Digital Sky Survey and its associated project Sloan Extension for Galactic Understanding and Exploration (SEGUE). With this data, we selected candidates for A-type stars in the color-color space and then a mixture modeling technique was implemented in order to distinguish between BHB and main-sequence/blue-straggler stars based on their surface gravity values ($\log \rm{g}$) estimated by the SEGUE Stellar Parameter Pipeline. Our robust approach allows us to attribute individual probabilities of each star truly being in the BHB stage. Hence, our method is advantageous in comparison to previous SEGUE BHB selections that adopted simple $\log \rm{g}$ cuts. We also revisit the color-magnitude relation for these stars and propose two calibrations, based on updated distances for Galactic globular clusters, to estimate absolute magnitudes with $(g-r)_0$ and $(u-r)_0$ colors.

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arXiv2022

The Unmixed Debris of Gaia-Sausage/Enceladus in the Form of a Pair of Halo Stellar Overdensities

In the first billion years after its formation, the Galaxy underwent several mergers with dwarf satellites of various masses. The debris of Gaia-Sausage/Enceladus (GSE), the galaxy responsible for the last significant merger of the Milky Way, dominates the inner halo and has been suggested to be the progenitor of both the Hercules-Aquila Cloud (HAC) and Virgo Overdensity (VOD). We combine SEGUE, APOGEE, Gaia, and StarHorse distances to characterize the chemodynamical properties and verify the link between HAC, VOD, and GSE. We find that the orbital eccentricity distributions of the stellar overdensities and GSE are comparable. We also find that they have similar, strongly peaked, metallicity distribution functions, reinforcing the hypothesis of common origin. Furthermore, we show that HAC and VOD are indistinguishable from the prototypical GSE population within all chemical-abundance spaces analyzed. All these evidences combined provide a clear demonstration that the GSE merger is the main progenitor of the stellar populations found within these halo overdensities.

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arXiv2022

Reconstructing the Disrupted Dwarf Galaxy $Gaia$-Sausage/Enceladus Using its Stars and Globular Clusters

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

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