A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. I. Data and Stellar Population Characterization

The data set was acquired with MUSE (Bacon et al. 2014), an integral field spectrograph mounted at the UT4 of the Very Large Telescope at the Paranal Observatory in Chile, between 2015 June 29 and September 19 in run 095.B-0585(A) (PI: Lützgendorf).

A total of 16 pointings, with a field of view (FOV) of $59\buildrel{\prime\prime}\over{.} 9\times 60\buildrel{\prime\prime}\over{.} 0$ each, create a 4 × 4 mosaic that covers a contiguous area out to ∼2.5 times the half-light radius of M54 (R_HL = 082, Harris 1996, 2010 edition), equivalent to ∼25 times its core radius (R_c = 009, Harris 1996, 2010 edition). The estimated tidal radius of M54 is ${R}_{{\rm{t}}}=9\buildrel{\,\prime}\over{.} 87$ (assuming a King-model central concentration of c = 2.04; Harris 1996, 2010 edition).

Due to overlaps between neighboring pointings, the observations cover an FOV of ∼35 × 35 (1' corresponds to 8.27 pc at an assumed distance of 28.4 kpc; Siegel et al. 2011). This results in a total FOV of 29 pc × 29 pc. The data have a wavelength coverage of 4800–9300 Å and a spectral resolution increasing with wavelength from R ∼ 1750 to R ∼ 3750. The spatial sampling is 02 pixel^–1. Each field was observed with three exposures, applying offsets in rotation of 90° between them (no dithering) to increase the homogeneity of the data across the FOV. The exposure time for each of the three exposures was chosen to be 400 s for the inner 4 pointings and 610 s for the outer 12 pointings. This was done to avoid saturation of the innermost crowded region with high surface brightness. During the observations, the air mass varied from 1.0 to 1.9, and the seeing between 05 and 12. Figure 1 shows the color image of the 4 × 4 mosaic obtained from the MUSE data using synthetic i, r, and z filters.

Zoom In Zoom Out Reset image size

The data reduction was performed using the MUSE pipeline (version 1.2.1; Weilbacher et al. 2014). The pipeline includes all tasks for the data reduction process: bias creation/subtraction, flat-fielding, illumination correction, and wavelength calibration. Before combining the single exposures, they were flux-calibrated using a standard star and corrected for the barycentric motion of Earth.

We extract individual stellar spectra with PampelMuse (Kamann et al. 2013). This tool takes a photometric catalog as a reference for the positions and magnitudes of the stars in the FOV. It models the change in the point-spread function (PSF) as a function of wavelength and allows deblending of sources efficiently even in crowded and dense regions. A reference stellar catalog for M54 was published by Siegel et al. (2007) as part of the ACS Survey of Galactic Globular Clusters (Sarajedini et al. 2007). The catalog includes source positions and F606W (V) and F814W (I) magnitudes with their respective uncertainties. Its total coverage is larger than the MUSE data set FOV.

We extract the spectra of ∼55,000 stars from the entire field. For our subsequent analysis we only consider the spectra with signal-to-noise ratio (S/N) ≥ 10, which are labeled by PampelMuse as good extracted spectra. Within the entire MUSE FOV, we extract good spectra for a total of ∼7000 different stars in the magnitude range of $22\lt {\rm{F}}814{\rm{W}}\lt 13$ (I band).

In our stellar sample we do not include main-sequence (MS) stars below the oldest turnoff point since they are fainter than $I\sim 21$ and their spectra are typically below our S/N = 10 threshold.

From the spectral fitting performed by ULySS we obtain the LOS velocities for each star.

Since the space motion of the nucleus can mimic the effect of an additional rotation component, we correct the LOS velocity values for this effect, known as perspective rotation, using Equation (6) in van de Ven et al. (2006). We use the absolute proper motion of the cluster M54 V_W = −2.82 ± 0.11 mas yr⁻¹ and V_N = −1.51 ± 0.14 mas yr⁻¹ (Sohn et al. 2015). These values are in good agreement with the recent values based on Gaia data by Vasiliev (2019). We obtain correction values between −0.3 and 0.3 km s⁻¹.

In Appendix A, we discuss the agreement between velocity measurements derived for stars observed in multiple MUSE pointings.

The position of the Sgr dSph with respect to the Milky Way and the large FOV of the MUSE data mosaic result in a considerable amount of contamination of nonmember stars in our Sgr dSph NSC sample. We determine the membership probability based on the iterative expectation maximization technique using "clumPy"⁹ (Kimmig et al. 2015). We use our LOS velocity measurements and the distance of the stars to the center of the cluster M54 as input values (no metallicity estimates considered).

This procedure is described in detail by Walker et al. (2009) and later with some variations by Kimmig et al. (2015). The technique iteratively estimates the mean velocity and velocity dispersion of the cluster plus the membership probability of each star until all the parameters converge. We use a foreground/background contamination model for the Milky Way based on the Besançon model of the Galaxy (Robin et al. 2003).

The membership probability obtained with the expectation maximization technique for each star is represented by color in the radius versus velocity plot in Figure 3. From our total sample of 7000 stars we consider those with probability ≥70% to be members of the Sgr dSph NSC, leaving a total of 6651 members.

Zoom In Zoom Out Reset image size

We obtain a maximum likelihood mean LOS velocity for the member stars (dark red points) of 141.34 ± 0.18 km s⁻¹ and a central velocity dispersion of 16.31 ± 0.28 km s⁻¹. The quoted numbers are the median ±1σ values of the posterior distribution. The LOS velocity estimate is in good agreement with previous works, e.g., ${V}_{{LOS}}\sim 141$ km s⁻¹ by Bellazzini et al. (2008) for the metal-poor and metal-rich populations. From this point, the analysis is carried out on a sample that only includes the members of the Sgr dSph NSC determined by this technique.

In the color–magnitude diagram (CMD) in Figure 4 we show the full sample of extracted single stellar spectra. Member stars of the Sgr dSph NSC (probability ≥70%) are color-coded by the S/N logarithm, while nonmembers (probability <70%) are shown in gray. The stellar photometry information in F606W (V) and F814W (I) filters is extracted from the M54 HST reference catalog.

Zoom In Zoom Out Reset image size

The top panel of Figure 5 shows the metallicity histogram for the member stars of the Sgr dSph NSC. This metallicity distribution is highly consistent with the one presented by Mucciarelli et al. (2017) for a total of 76 stars in a radius range of $0\buildrel{\,\prime}\over{.} 0\lt R\leqslant 2\buildrel{\,\prime}\over{.} 5$. We cross-matched our sample with those from Carretta et al. (2010a) and Mucciarelli et al. (2017), and we compare the measurements for the stars we have in common. The values are consistent within the errors. We obtain a mean difference of 0.15 ± 0.03 dex, when comparing with Carretta et al. (2010a), with a standard deviation of σ = 0.16. From the comparison with Mucciarelli et al. (2017), we obtain a mean difference of 0.05 ± 0.02 dex with a standard deviation of σ = 0.17. This comparison is included in Appendix B.

Zoom In Zoom Out Reset image size

In the bottom panel, we present the relation between radius and metallicity for the sample of 6651 stars as derived with ULySS, color-coded by the metallicity uncertainties. Two clear distributions in metallicity become apparent: a metal-poor population at [Fe/H] = −1.5 and a metal-rich population around [Fe/H] = −0.3 with a separation at [Fe/H] = −0.8. The median metallicity uncertainty is 0.05 dex.

The top panels in Figure 6 show the CMD color-coded by metallicity (hereafter CMD+metallicity) corresponding to all the Sgr dSph NSC members (and a zoom-in onto the turnoff region; top right panel). We overplotted in blue, green, and orange isochrones from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) corresponding to different stellar populations in the Sgr dSph NSC, using as a reference the work by Siegel et al. (2007). We are able to see stars in different evolutionary stages: turnoff point (TO), red giant branch (RGB), horizontal branch (HB), asymptotic giant branch (AGB), red clump (RC), and even the extreme horizontal branch (EHB) and the blue plume (BP). The CMD shows clear evidence for an old metal-poor population, as well as at least two distinct younger populations with metallicity ≳−0.4 that agree well with the 4.5–6 Gyr isochrone highlighted by Siegel et al. (2007).

Zoom In Zoom Out Reset image size

For our complete sample of member stars we estimate a mean metallicity of [Fe/H] = −1.06, with a standard deviation of σ = 0.64. For the metal-poor stars ([Fe/H] < −0.8) we obtain a mean metallicity of [Fe/H] = −1.45 and a standard deviation of σ = 0.32. This is in good agreement with previous works, such as Brown et al. (1999) and Da Costa & Armandroff (1995) with an estimate of [Fe/H] = −1.55, and later by Carretta et al. (2010a), who estimated a metallicity of [Fe/H] = −1.559 ± 0.021 dex.

In the case of the stars in the metal-rich regime ([Fe/H] > −0.8), we obtain a mean value of [Fe/H] = −0.27 and a standard deviation of σ = 0.29. In this case, the metallicity measurement differs from previous studies. Carretta et al. (2010a) obtained a value of [Fe/H] = −0.622 ± 0.068 dex, and Mucciarelli et al. (2017) obtained [Fe/H] = −0.52 ± 0.02 dex. A possible explanation for this difference is discussed in Section 4.1.

We repeated the metallicity measurements with a second method, using Ca ii triplet lines, and obtained consistent metallicity measurements using the two independent methods (see Appendix C).

Valuable information about the SFH of the Sgr dSph NSC can be obtained from age and metallicity estimates together. For the age estimates of individual stars we use a grid of isochrones, which we compare with the magnitudes and colors of the stars as measured from the HST photometry in V (F606W) and I (F814W) bands with their respective uncertainties (${\sigma }_{V}$, ${\sigma }_{I}$), and metallicities Z, obtained from the MUSE spectra, including their uncertainties ${\sigma }_{Z}$. We set the metallicity uncertainty to 0.1 dex when lower than that value. We consider age the only free parameter of the model.

We use Bayes's theorem to estimate the ages through the posterior probability as

$$\begin{eqnarray}&&\ P(\tau | {V}_{\mathrm{obs}},{I}_{\mathrm{obs}},{Z}_{\mathrm{obs}})\propto \,P({V}_{\mathrm{obs}},{I}_{\mathrm{obs}},{Z}_{\mathrm{obs}}| \tau )\times P(\tau ),\end{eqnarray} \tag{ 1 }$$

where the normalized likelihood function P(V_obs, I_obs, Z_obs $|$ τ) of the observables at a given age is a trivariate Gaussian:

$$\begin{eqnarray}&&\begin{array}{l}P({V}_{\mathrm{obs}},{I}_{\mathrm{obs}},{Z}_{\mathrm{obs}}| \tau )\\ \,=\,\displaystyle \frac{1}{\ {\sigma }_{{V}_{\mathrm{obs}}}\,{\sigma }_{{I}_{\mathrm{obs}}}\,{\sigma }_{{Z}_{\mathrm{obs}}}\,{\left(2\pi \right)}^{3/2}}\exp \displaystyle \frac{-{\left({V}_{\mathrm{obs}}-{V}_{0}\right)}^{2}}{2{\sigma }_{{V}_{\mathrm{obs}}}}\\ \,\,\times \,\exp \displaystyle \frac{\ -{\left({I}_{\mathrm{obs}}-{I}_{0}\right)}^{2}}{2{\sigma }_{{I}_{\mathrm{obs}}}^{2}}\exp \displaystyle \frac{\ -{\left({Z}_{\mathrm{obs}}-{Z}_{0}\right)}^{2}}{2{\sigma }_{{Z}_{\mathrm{obs}}}^{2}},\end{array}\end{eqnarray} \tag{ 2 }$$

where V₀, I₀, and Z₀ denote the real magnitudes and metallicity of the star given its age and the σ values represent the independent errors in each measurement. We marginalize over the unknown true magnitudes and metallicity of the star by integrating over the isochrones (see, e.g., Pont & Eyer 2004 for a similar approach).

Due to the lack of extended horizontal branch isochrone models, we have excluded stars with colors between V − I = −0.2 and 0.4 and I in the range of 21–17 in our age analysis.

Initially, we used a flat prior in age P(τ) for all the remaining stars. The age–metallicity relation (AMR) found for the TO region stars turned out to be very well represented by the empirical model published by Layden & Sarajedini (2000). On the other hand, the obtained ages for a fraction of metal-poor RGB stars were lower than expected for such a metallicity regime. This degeneracy could be a consequence of high abundance of elements like oxygen, which has been reported to display a high spread in this metal-poor population (Carretta et al. 2010a). In fact, VandenBerg et al. (2012) showed the impact of different elements abundances on computed evolutionary tracks at similar [Fe/H] values and how this affects the color of the stars and thus their position in the CMD. After this examination of the initial ages, to guard against systematic age uncertainties, we set a weak Gaussian age prior P(τ) to their model with a standard deviation of 3 Gyr for the age estimates of all extracted member stars from the MUSE cube.

We built the isochrone grid with a resolution of 0.2 Gyr with ages from 0.2 to 15 Gyr from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) assuming the HST/ACS WFC photometric system. The metallicity range is from −2.495 to 0.500 dex with steps of 0.005 dex, considering [α/Fe] = 0.0. We correct the isochrone magnitudes by extinction of ${A}_{V}=0.377$ and ${A}_{I}=0.233$ from NED.¹⁰ These are obtained using the calibration published by Schlafly & Finkbeiner (2011) for the F606W and F814W bands for a reddening of $E(B-V)=0.15$ estimated in the central $5^{\prime}$ radius of M54 (Schlegel et al. 1998) with ${R}_{V}=3.1$. We shifted the grid of isochrones adopting a distance modulus of $(m-{M}_{0})=17.27$ (Siegel et al. 2007). For comparison, we performed the same analysis considering a reddening of $E(B-V)=0.16$ and a distance modulus of $(m-{M}_{0})=17.13$ (Sollima et al. 2010), obtaining consistent age estimates. We take the mode of the likelihood distribution of ages as the best age estimate and the highest density interval that accommodates 68% of the probability as the age uncertainty.

The CMD for the clean stellar sample color-coded by age (hereafter CMD+age) is presented in the bottom left panel of Figure 6, with a zoom-in of the TO region in the bottom right panel of the figure. Three isochrones based on those presented in Siegel et al. (2007) are overplotted; they are also from the Dartmouth Stellar Evolution Database (Dotter et al. 2008).

We use Gaussian Mixture Models (GMMs) in age–metallicity space to separate the stars into distinct multiple populations. To this aim, we used only TO region stars, where we obtain the most reliable age estimates as we describe in Section 3.4. We tested GMMs with three, four, and five components and found that a GMM with four components gives the best representation of our data set based on the Akaike Information Criterion (Akaike 1974). We optimized the GMM using the affine-invariant Markov chain Monte Carlo (MCMC) algorithm (Goodman & Weare 2010; Foreman-Mackey et al. 2013). We then computed the probabilities of all stars in the observed sample of belonging to any of the GMM defined populations. The fourth Gaussian component of the GMM captures outliers and is not further considered in our analysis.

We estimate the mean and spread in both age and metallicity for each of the subpopulations. We start by taking stars with a high probability (>50%) of belonging to each subpopulation. We then perform a maximum likelihood fit for the ages and metallicities of these stars using a two-dimensional Gaussian and accounting for the observational uncertainties in each stars' age and metallicity. The result is a mean and intrinsic spread in both age and metallicity for each population. We assumed that the [Fe/H] probability distribution functions (pdf's) are Gaussian and integrated numerically over the non-Gaussian individual stellar age pdf's. From the results of this procedure we define three different subpopulations as follows:

• 1.  
  YMR: young metal-rich (red), with mean age of 2.16 ± 0.03 Gyr and mean [Fe/H] = −0.04 ± 0.01.
• 2.  
  IMR: intermediate-age metal-rich (orange), with mean age of 4.28 ± 0.09 Gyr and mean [Fe/H] = −0.29 ± 0.01.
• 3.  
  OMP: old metal-poor (blue), with mean age of 12.16 ± 0.05 Gyr and mean [Fe/H] = −1.41 ± 0.01.

We find that the YMR population has an intrinsic 1σ spread of 0.20 ± 0.03 Gyr in age and 0.12 ± 0.01 dex in metallicity; the IMR population has an intrinsic spread of 1.16 ± 0.07 Gyr in age and 0.16 ± 0.01 dex in metallicity; the OMP population has an intrinsic spread of 0.92 ± 0.04 Gyr in age and 0.24 ± 0.01 dex in metallicity. The uncertainties are represented by the standard deviation in each parameter in the converged part of the MCMC, thus obtaining low errors. The age–metallicity correlation coefficients, ρ, for the three populations are ${\rho }_{\mathrm{YMR}}=-0.35$, ${\rho }_{\mathrm{IMR}}=-0.70$, and ${\rho }_{\mathrm{OMP}}=-0.97$.

To check for consistency, we use the same method to estimate the intrinsic spread in metallicity for stars with $I\leqslant 16.5$ mag, where the S/N of the stars is mostly >100. This leaves a total of 22 stars for the YMR (5% of YMR sample) and 208 for the OMP (∼9% of OMP sample). For the YMR subpopulation we obtain an intrinsic 1σ spread of 0.11 ± 0.06 dex, and 0.13 ± 0.03 dex for the OMP subpopulation. The spread for the YMR subpopulation derived from the brightest stars is consistent with the one measured for the stars of all magnitudes. For the OMP subpopulation, we observe a difference of 0.11 dex. This can be a consequence of the low number of stars in comparison with the entire sample and the effects of the age uncertainties at the RGB region, which can be more uncertain, as we mention in the previous section. Since these values are obtained from a reduced fraction of the entire sample (<10%), we will consider the intrinsic spread measured from the sample at all magnitudes.

The AMR is presented in Figure 7, where we include all stars for which ages were measured and have relative age errors ≤40%. The overplotted crosses represent the intrinsic spreads of the different populations: YMR in red, IMR in orange, and OMP in blue. The intrinsic age and metallicity spreads, together with the age–metallicity correlation coefficient ρ, define the inclination angle of the crosses for each subpopulation. We discuss the possible origin of these populations in Section 5.

Zoom In Zoom Out Reset image size

For the RC stars in the sample we were able to obtain reliable measurements in metallicity and found that they all fall in the metal-rich regime. The complexity of this stage of stellar evolution prevents us from getting reliable ages for the RC stars from simple isochrone fits. Due to this effect, the RC stars were not considered to belong to any of the subpopulations when we decompose the stars into subpopulations via the maximum likelihood method. For completeness, these stars are shown in Figure 7 and fall on the diagram clustered together as the overdensity at ∼1 Gyr in a metallicity range of $-0.5\lt [\mathrm{Fe}/{\rm{H}}]\lt 0.0$. To get a better estimate of the likely age distribution of RC stars, we follow Girardi (2016) and compute the RC age distribution for representative SFHs of Sagittarius. We do this for two assumptions of the SFH: (i) the Sgr dSph has a constant SFH, and (ii) the SFH follows the observed SFH from the CMD analysis of de Boer et al. (2015). The de Boer et al. (2015) SFH shows a declining SFR with time but is constructed from the tail of the Sgr dSph, so it is likely missing the most metal-rich and young stars—biasing the star formation to early times. Inclusion of the younger populations in the CMD analysis might produce an SFH more closely represented by a constant SFH. We therefore consider these two cases as plausible bounds on the likely true SFH of Sgr. For the constant SFH case we find that the RC stars are predominantly (∼51%) younger than 2.2 Gyr, thus being more likely to belong to the YMR subpopulation than to the IMR (10%). For case (ii), we obtain that anywhere from 10% to 70% of RC stars are younger than 2.2 Gyr, with probabilities of less than 10% for the IMR. Taking these two cases into consideration, we consider it most likely that the majority of the RC stars are associated with the YMR subpopulation, and we consider them as part of that population in our further analysis.

Comparing the metallicity and age information presented in the CMDs in Figure 6, we observe that in the TO region in the CMD+age we distinguish three well-separated subpopulations with different age ranges. The faintest stars have ages over 9 Gyr. This subpopulation belongs to the metal-poor regime in the CMD+metallicity. The middle subgiant branch population has ages of ∼3–9 Gyr, while the brightest stars have ages younger than 3 Gyr. These last two populations belong to the metal-rich regime in the CMD+metallicity. From the CMD+metallicity figure, some small difference in metallicity (∼0.3 dex) is also visible between these two younger populations.

In the CMD+metallicity the metal-poor RGB is well defined by stars with metallicity below [Fe/H] = −0.8, displaying a wide range toward [Fe/H] = −2.5, corresponding to an intrinsic iron spread of ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}=0.24$ dex. In addition, we observe that the stars in the BP region between $18.5\leqslant I\leqslant 20.5$ and $0.1\leqslant V-I\leqslant 0.5$ show a wide range in metallicity (from −2.0 to 0.5). We discuss this further in Section 5.3.

From the CMDs and the AMR (Figure 7), we can decipher the SFH of the Sgr dSph NSC. It appears to be extended from 0.5 to 14 Gyr, showing a clear metallicity enrichment toward younger stars.

We present a CMD comparing the three subpopulations in Figure 8. In both panels the subpopulations are represented as follows: YMR in red, IMR in orange, and OMP in blue. In the top panel we can see how the different populations fall in different positions in the CMD; this is easier to see in the zoom-in of the TO region shown in the bottom panel.

Zoom In Zoom Out Reset image size

Our findings are in good agreement with the characteristics of three (of four) subpopulations obtained with isochrone fitting by Siegel et al. (2007), and later also by Mucciarelli et al. (2017). From their fitting of the CMD, Siegel et al. (2007) suggest the presence of four populations: (i) the old metal-poor population, with ages of 13 Gyr and [Fe/H] = −1.8; (ii) the intermediate-age metal-rich population, with ages between 4 and 6 Gyr and [Fe/H] = −0.6; (iii) the YMR population with 2.3 Gyr and [Fe/H] = −0.1; and (iv) the very young, very metal-rich population with [Fe/H] = 0.6 and ages 0.1–0.8 Gyr. We do not detect any stars belonging to their fourth population.

We do find a higher mean metallicity for the metal-rich regime population compared to Carretta et al. (2010a) and Mucciarelli et al. (2017). This may be due to several factors. First, we separate the metal-rich stars into two subpopulations, with the YMR having significantly higher mean metallicity than the IMR; the latter, older stars have metallicity closer to previous measurements. Second, our spatial coverage is confined to much smaller radii in comparison to Carretta et al. (2010a) and Mucciarelli et al. (2017), which cover out to a larger radius. Third, the resolution of our data allows us to extract more stars from the most crowded central regions. Fourth, on average, our metallicity estimates are slightly higher. We obtain a mean Δ[Fe/H] of 0.15 ± 0.03 dex when comparing with Carretta et al. (2010a), and 0.05 ± 0.02 dex when comparing with Mucciarelli et al. (2017). The differences in the measurements might be caused by the method used and/or spectral resolution (see Appendix B).

In Table 1 we include a summary of all the estimated parameters for the subpopulations.

We now analyze the spatial distribution of the three subpopulations in the Sgr dSph NSC defined in the previous section. In Figure 9 we present the cumulative radial distribution for the three subpopulations: YMR (red), IMR (orange), and OMP (blue). We consider all the member stars extracted with S/N ≥ 10. In order to fairly compare the three subpopulations' distribution in terms of completeness, we also constrain the sample to magnitudes I ≤ 20.5 mag.

Zoom In Zoom Out Reset image size

In Figure 9 we observe that the YMR subpopulation is the most centrally concentrated of the three in this NSC. The second-highest central density is shown by the OMP subpopulation, which is the dominant one in stellar number with over 2000 stars. Finally, the lowest central concentration is shown by the IMR subpopulation. Comparing the distribution of these subpopulations with a uniform distribution (magenta dashed line), we observe that the stars in the IMR subpopulation are the least centrally concentrated in the most central 40''. However, they are still not uniformly distributed; as we observed in Figure 9, the distribution shows that the stars in the IMR subpopulation are still significantly centrally peaked. This difference in the spatial distribution between the subpopulations suggests different origins. We discuss this in detail in Section 5.

It is important to consider that, due to extreme central crowding and the limitations of our spatial resolution, we are not able to extract all the stars that actually reside in this NSC. Improved spatial resolution is needed to more accurately derive the spatial distribution of the different stellar populations.

Using the coordinate information of the stars and the data FOV, we fit a two-dimensional Plummer profile (Plummer 1911) to each of the subpopulations, optimizing the best profile using an MCMC algorithm (Goodman & Weare 2010; Foreman-Mackey et al. 2013). We set the centroid, ellipticity, position angle (PA), and half-light radius as free parameters, thus obtaining the best estimates for each stellar subpopulation.

The estimated parameters are summarized in Table 1. The likelihoods for the YMR and OMP populations converge and give good estimates for the centroid, ellipticity, and PA. However, for the IMR it does not converge owing to the less centrally concentrated distribution that this subpopulation shows (see Section 4.2).

We find that the stars in the metal-poor regime show a large spread in age, ${\sigma }_{\mathrm{age}}=0.9\,\mathrm{Gyr}$, and iron content, ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}=0.24$, a higher spread in comparison with the literature (${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}\,=0.186$; Carretta et al. 2010b; Willman & Strader 2012). Large iron spreads in GCs can be explained by a scenario in which two GCs merge (Bekki & Tsujimoto 2016; Gavagnin et al. 2016; Khoperskov et al. 2018, and references therein).

Gavagnin et al. (2016), using N-body simulations, studied the structural and kinematic signatures in the remnants of GC mergers with a sample of progenitors of different densities and masses. They pointed out that if two GCs were formed in the same dwarf galaxy (or molecular cloud) and display a low relative velocity, they could merge, making the merging scenario more likely in dwarf galaxies. They actually mention the Sgr dSph as a good candidate for this scenario to happen. Bellazzini et al. (2008) found that the velocity dispersion profile is close to flat, with values of ∼10 km s⁻¹ in the innermost $80\buildrel{\,\prime}\over{.}$

Bekki & Tsujimoto (2016) used numerical simulations to suggest that GC mergers explain the existence of complexity in high-mass GCs, with multiple stellar populations and a large spread in metallicity, what the authors called "anomalous" GCs. Performing several tests, Bekki & Tsujimoto (2016) found that the merger between GCs with masses greater than 3 × 10⁵ M_⊙ will occur inevitably in the host dwarf galaxy, with a mass in the range of ${M}_{\mathrm{dh}}=3\times {10}^{9}$–3 × 10¹⁰ M_⊙. This is due to stronger dynamical friction effects on the GCs compared to the field stars in those shallow, low-dispersion galaxies. The authors mention that if the clusters are massive enough, the timescale for the merger is just a few gigayears, and it occurs before the total disruption of the dwarf galaxy due to the Galactic tidal field. They find that with a merger of at least two GCs it would be possible to observe GCs with an internal metallicity spread. In the case of the Sgr dSph, the progenitor dark halo mass before infall to the Milky Way has been estimated with a lower limit of 6 × 10¹⁰ M_⊙ by Gibbons et al. (2017), in good agreement with Mucciarelli et al. (2017). The mass estimated for M54 is (1.41 ± 0.02) × ${10}^{6}$ M_⊙ (Baumgardt & Hilker 2018), consistent with mergers of GCs of 10⁵ M_⊙.

The merger scenario might explain the high mass and the large iron and age spreads in the OMP subpopulation. The mass of the Sgr dSph progenitor would be conducive for the GCs to merge. From simulations, the infall of a massive GC to the center of the Sgr dSph due to dynamical friction effects has been estimated to have occurred ∼5–9 Gyr ago (Bellazzini et al. 2006, 2008). The infall time is at most 3 Gyr (Bellazzini et al. 2008) for a cluster with M54's mass. The spread in age and metallicity of the oldest, metal-poor stars is consistent with the scenario where multiple GCs were driven to the center of the Sgr dSph and merged, thus building up the metal-poor component of the NSC.

From the metallicity and age characterization of our stellar sample we distinguish two subpopulations in the metal-rich regime. We are able to separate them using the AMR and CMD position of the stars. We observe that the youngest population—YMR—has the highest central density in the Sgr dSph NSC. The high metallicity, young age, and spatial distribution suggest that the formation of the YMR subpopulation formed in situ starting ∼3 Gyr ago.

Additional evidence for in situ formation of the YMR population is that it appears more flattened than the OMP population. We measure an ellipticity of 0.31 ± 0.10 for the YMR component, while the OMP population has an ellipticity of 0.16 ± 0.06 (Table 1). Centrally concentrated and sometimes flattened young subcomponents are commonly found in other NSCs in both early- and late-type galaxies (Seth et al. 2006; Carson et al. 2015; Feldmeier-Krause et al. 2015; Nguyen et al. 2017); given the young age of these populations, in situ formation is strongly favored, with the flattening suggestive of formation in a star-forming gas disk. We note that the difference in ellipticity between the YMR and OMP subpopulations is small, given the measurement uncertainties. However, this difference becomes meaningful when we combine the ellipticity with the kinematics. In a second paper we will present the kinematic characterization of the subpopulations, adding a new diagnostic to address this issue.

These young, flattened populations can survive despite being embedded in an older, hotter population. Mastrobuono-Battisti & Perets (2013, 2016) modeled the evolution of stellar disks in dense stellar clusters using N-body simulations, finding that even after several gigayears (around the Milky Way GC's age) the stars are still not fully mixed. Thus, both generations of stars show different distributions. They observed that the second population is concentrated at the center after 12 Gyr with no relaxed spherical shape. The amount of rotation is also evidence for this model, where the second generation of stars is found to rotate faster than the first one. From our kinematic analysis, we found that the YMR subpopulation rotates faster than the OMP. We will present the evidence on this matter in our upcoming paper on this NSC's kinematics.

To form the youngest metal-rich subpopulation, enriched gas is needed; however, no neutral gas has been detected in this galaxy. Using simulations, Tepper-García & Bland-Hawthorn (2018) found that the Sgr dSph might have lost all its gas after the second encounter with the Galactic disk. They found that two pericentric passages happened ∼2.8 and ∼1.3 Gyr ago. The first produced a gas loss of 30%–50%, while the second would be responsible for the stripping of all the residual gas. The timescales of both encounters are consistent with the latest bursts of star formation seen in Figure 7 and were suggested based solely on the photometry by Siegel et al. (2007). This suggests that the YMR population may have formed by gas being driven into the nucleus during encounters with the Milky Way, supporting the in situ formation of this population.

The in situ formation of a new generation of stars could alternatively be explained for a massive NSC with a deep enough potential well to collect the enriched gas ejected from metal-rich and high-mass stars at larger radii that cools and sinks to the center (Bailey 1980). This seems plausible given the characteristics of the stars in the IMR subpopulation and the relatively small fraction of YMR stars in comparison with the OMP.

A different situation is observed for the IMR population in comparison to the YMR. These stars seem to be less centrally concentrated in the field, with a wide spread in ages from 3 to 8 Gyr. These findings suggest that the star formation in the Sgr dSph during this period was not particularly concentrated in the nucleus. The metallicity range of these stars is consistent with those found for stars close to the center of the galaxy (Hasselquist et al. 2017). In addition, comparing the IMR sample of our AMR (Figure 7) with the one presented by de Boer et al. (2015) for the Sagittarius bright stream, we see a good agreement in both age (4–14 Gyr) and metallicity (−2.5 < [Fe/H] < −0.1), thus supporting our good recovery of the underlying chemical evolution of the host galaxy.

The spatial distribution of these two subpopulations—YMR and IMR—has also been reported by Mucciarelli et al. (2017). Using a sample of 109 stars with [Fe/H] ≥ −1.0 and a magnitude limit of ${I}_{\mathrm{mag}}=18$, the authors observed a shift in the metallicity peak in the metal-rich population at different projected distances from its center. At $0\buildrel{\,\prime}\over{.} 0\lt R\lt 2\buildrel{\,\prime}\over{.} 5$ the peak is at [Fe/H] = −0.38, changing to [Fe/H] = −0.45 at 25 < R < 50, noticing a metallicity gradient for this population. In addition, the authors present the cumulative radial distribution of the two young populations, where they found that the youngest subpopulation is more centrally concentrated than the intermediate-age population. With this finding they suggest that the youngest population is the dominant population in the Sgr dSph NSC, with the intermediate-age one becoming more important at larger radii. Since our observations reach out to $\sim 2\buildrel{\,\prime}\over{.}$0 from the center of this NSC, we are not able to see a change in the peak at larger radii. However, we also see this behavior between the two youngest metal-rich subpopulations.

Our spectroscopic sample also includes stars in the BP region, which could be populated by YMR stars of [Fe/H] = 0.6 and 0.1–0.8 Gyr (Siegel et al. 2007) or blue straggler stars (BSSs). However, we measure a wide range of metallicities for these stars, suggesting that they are BSSs instead of young stars, which would be expected to display a more homogeneous metallicity, e.g., as observed in the YMR subpopulation. Mucciarelli et al. (2017) found that the cumulative radial distributions of the BP and the intermediate-age metal-rich stars were not distinguishable. Since this is a less dense environment in comparison to the center of the NSC, these BSSs could be the product of mass transfer between binaries as has been found in other dSphs (e.g., Mapelli et al. 2007, 2009; Momany et al. 2007).

As discussed in this section, the stars from the IMR subpopulation seem to have properties consistent with those at larger radii in the galaxy. This population shows a central concentration, shallower than the other two. With the current information we are not able to tell if the stars in the inner regions are actually dynamically bound to the NSC (with the YMR and OMP) or if they are part of the main body of the host galaxy.

From this work and previous studies of the populations in the Sgr dSph NSC, we can put together the story of this NSC. It starts with two or more massive GCs that eventually merge at the center of the Sgr dSph, forming a massive nucleus consisting of old and metal-poor stars with a large metallicity spread. The two encounters of the Sgr dSph with the Galactic disk occurred ∼2.8 and ∼1.3 Gyr ago (Tepper-García & Bland-Hawthorn 2018) and could have triggered two new episodes of star formation before the total stripping of the gas, creating in the first the YMR subpopulation. This results in a complex multipopulation NSC.

This NSC is on its way to becoming a stripped nucleus considering the ongoing strong interaction between its host—the Sgr dSph—and the Milky Way. In fact, Bellazzini et al. (2008) suggested that this nucleus will probably end up as a compact remnant with two populations: old metal-poor and young metal-rich, with no signatures of the progenitor galaxy. This puts the Sgr dSph NSC in close company with the most massive cluster in the Milky Way, ω Cen, which has long been considered a potential stripped nucleus (e.g., Lee et al. 1999; Carretta et al. 2010b). ω Cen presents a centrally concentrated disk-like component (van de Ven et al. 2006, see their Figures 19 and 20), very similar to the YMR subpopulation we detect in the Sgr dSph NSC. The age spread in ω Cen (at least 2 Gyr; Hilker et al. 2004; Villanova et al. 2014), similar to the spread we see in the OMP, suggests the merging of GCs early on in the nucleus of a progenitor galaxy (e.g., Bekki & Tsujimoto 2016). Unlike ω Cen, the stripping around the Sgr dSph NSC is ongoing, and thus we have the opportunity to understand the role mergers and stripping have played in creating the cluster we see today.

Given all the evidence we have presented in this paper, our suggestion to the community is to revert to the original naming and use "M54" in the same manner as it was given to the object upon its discovery by Charles Messier in 1778. The evidence consistently suggests that M54 is not a normal metal-poor GC but a complex NSC.