The Origin of the Large Magellanic Cloud Globular Cluster NGC 2005

Mucciarelli et al. (2021) recently reported that the Large Magellanic Cloud (LMC) old globular cluster NGC 2005 is the unique surviving relic of a low star formation efficiency dwarf galaxy that merged into the LMC in the past. The ex situ origin of NGC 2005 was claimed from its deficient abundance of some chemical species—forming from different nucleosynthesis channels—with respect to those of five LMC old globular clusters of similar metallicities (−1.75 < [Fe/H] ⁷ < −1.69). A Fornax-like progenitor of NGC 2005 was suggested by arguing that such a dwarf spheroidal galaxy matches the peculiar chemical composition of NGC 2005. NGC 2005 is a 13.77 ± 4.90 Gyr old globular cluster (Wagner-Kaiser et al. 2017), with a overall metallicity [Fe/H] = −1.75 ± 0.10 (Suntzeff et al. 1992; Beasley et al. 2002; Mucciarelli et al. 2010), and a total mass of log(M/M_⊙) = 5.49 ± 0.16 (Mackey & Gilmore 2003).

While the proposed scenario for the formation of NGC 2005 results plausible in the context of the hierarchical assembly of galaxies according to the standard cosmological model (e.g., Moore et al. 1999), there are a couple of inferences made by Mucciarelli et al. (2021) in order to conclude on the ex situ origin of NGC 2005 that may allow another interpretation.

Precisely, this work aims to introduce them so that they can trigger further analysis. The arguments in this work imply that the Mucciarelli et al. (2021)' results would not be conclusive but greatly enrich the debate on the NGC 2005 origin. The possible in situ or ex situ formation of NGC 2005 points to the need for a better understanding of galaxy formation. Particularly, whether the LMC partly formed through the accretion of smaller galactic systems or from a purely gaseous outside-in formation scenario (Carrera et al. 2011; Piatti & Geisler 2013) is still under debate. Furthermore, the analysis of the origin of NGC 2005 can shed light on some distinctive features that an LMC-like galaxy formed as a primordial dwarf should have with respect to an LMC-like galaxy partially built from the accretion and merging of smaller subunits. In this context, it is worth studying whether there is a minimum mass budget to differentiate the above two modes of galaxy formation. As far as we are aware, there are no simulations testing whether it is possible to distinguish both modes of galaxy formation.

In this work, we gathered relevant works available in the literature about mechanisms of nucleosynthesis that take place during the early life of galaxies in order to show that there exists an alternative interpretation for the origin of NGC 2005 to that suggested by Mucciarelli et al. (2021). The present results do not discredit the possible ex situ origin of this ancient LMC globular cluster but pose the issue in a broader context. These results point to the need for detailed simulations exploring the space of similarities and differences of galaxy formation processes for different galaxy masses. In order to provide a conclusive answer about the origin of NGC 2005, further spectroscopic observation campaigns of LMC field stars are needed, as well as globular cluster formation modeling in the context of galaxy formation with higher resolution and precision of the orbital integration. Nevertheless, the present somehow qualitative arguments shed light on a more comprehensive analysis of the origin of NGC 2005.

The first piece of analysis that led us to support a possible in situ origin of NGC 2005 is a rigorous statistical treatment of the abundances used by Mucciarelli et al. (2021) to conclude on the ex situ origin. Mucciarelli et al. (2021) showed that 13 chemical abundances measured in NGC 2005 are systematically lower than the values for five LMC globular clusters (NGC 1786, 1835, 1916, 2210, 2257) with metallicities ([Fe/H]) similar to that of NGC 2005. However, if the uncertainties are taken into account, those differences change as a function of the chemical element.

Figure 1 shows a more comprehensive picture in this respect. In order to build it, we first computed the difference (Δ, absolute value) in abundance ratios between the mean abundance ratios for the aforementioned five LMC globular clusters ([X/Fe]_mean) and that of NGC 2005 ([X/Fe]_{NGC 2005}), using values kindly provided by A. Mucciarelli. We note that Mucciarelli et al. (2021) only included the values for [Si/Fe], [Ca/Fe], [Cu/Fe], and [Zn/Fe] in their Table 1, because they focused on elements with predictions of stellar yields that are representative of different nucleosynthesis channels. Particularly, they rely their analysis on the [Zn/Fe] ratio, for which they found the largest mean difference (0.68 dex).

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For completeness purposes, we included in Table 1 all the [X/Fe] ratios used in that work. Then, we added in quadrature their respective uncertainties σ[X/Fe]_mean and σ[X/Fe]_{NGC 2005}, and calculated η = Δ/$\sqrt{\sigma [{\rm{X}}/\mathrm{Fe}{]}_{\mathrm{mean}}^{2}+\sigma [{\rm{X}}/\mathrm{Fe}{]}_{\mathrm{NGC}\,2005}^{2}}$, which we plotted in Figure 1 as a function of Δ, and included them in Table 1. As can be seen, [Sc/Fe], [Co/Fe], [La/Fe], [Zn/Fe], and [Eu/Fe] ratios show differences Δ larger than 3 times the sum of their respective uncertainties, which means these chemical element abundances in NGC 2005 and the other five globular clusters are different. We note that η values < 3 do not warrant a real difference so that the conclusion on distinctive chemical patterns between NGC 2005 and the other five LMC globular clusters for [Si/Fe], [Ca/Fe], and several other chemical abundances should be taken with caution. Therefore, if only some chemical elements show real abundance differences between NGC 2005 and five LMC globular clusters, both ex situ and in situ formation scenarios are feasible.

Figure 1 shows that the 13 different chemical abundances in NGC 2005 and the other five LMC clusters would not seem to be equally distinguishable, and those differences are only exhibited for a couple of the 13 chemical species analyzed by Mucciarelli et al. (2021). The unavoidable question arises: what does the difference in these few chemical species mean? Mucciarelli et al. (2021) argued that NGC 2005 formed in a Fornax-like dwarf galaxy that was accreted onto the LMC. According to them, the Fornax-like dwarf galaxy would have left negligible consequences in the LMC in the form of relics (galaxy mass ratio < 0.01), except only NGC 2005. The different chemical abundance features would be a signature that NGC 2005 formed ex situ the LMC.

However, the global chemical pattern of NGC 2005 is not statistically peculiar compared to that of the LMC. In order to quantify this, we figured out that we measured 1000 times the abundance of each of the 13 elements of Table 1 in NGC 2005 and in the other five LMC globular clusters; then we gathered the 1000 measurements of each element, and looked at the obtained distributions. We assume, as expected, that this experimental exercise will provide normal distribution functions, so that we represented them by generating 1000 points following a Gaussian distribution for each element in NGC 2005 and in the other five LMC globular clusters. In order to do this, we used the random.normal library within Numpy ⁸ using the mean values and errors quoted in Table 1 as loc and scale parameter values, respectively (see Figure 2). Note that most of the points are concentrated within 1σ. As can be seen, there are some elements in NGC 2005 and in the five LMC globular clusters whose point distributions totally overlap (Mn, Ni); other elements with a partial overlap (e.g., Ca, V, Ba), and a few ones which look different (Sc, La). The total overlap of the point distributions for some chemical elements means that any possible measure of that element in NGC 2005 can also be obtained for the other five LMC globular clusters, or role reversal. A similar reasoning can be used for those elements with a partial or null overlap, respectively. We note that the comparison of these distributions for each element in NGC 2005 and in the five LMC globular clusters is more meaningful than the use of the respective η values (see Table 1), although the latter has the advantage of providing a quantitative measure.

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If we considered altogether the 13 element distributions of NGC 2005 and compared it with that of the five LMC globular clusters, we would obtain a measure of the level of similitude between them. We then considered the 13 chemical elements together using the 26,000 points of Figure 2; most of the points distributed within 1σ as provided by the normal distribution law. We built two tables, one for NGC 2005 and another for the five LMC globular clusters containing the respective 13,000 generated previously. Then we statistically estimated the similarity between these two tables—in a scale from 0 to 1, where 0 means totally different and 1 means totally equals—between the 13 chemical abundances in NGC 2005 (gray points in Figure 2) and the LMC (orange points in Figure 2) using different statistical methods; namely, Jaccard similarity (0.47); cosine distance (0.59); Sørensen–Dice statistic (0.64); Levenshtein, Hamming, Jaro, and Jaro–Winkler distances (0.52); Pearson correlation (0.83); Spearman correlation (0.81). We used Python language v3.8.10, ⁹ and the following packages: Numpy (Harris et al. 2020) and Scipy (Virtanen et al. 2020). ¹⁰ The Appendix shows the Python scripts used in order to applied the aforementioned statistics. The resulting similarities between both samples are given within parenthesis above, following the name of the respective method. As can be seen, the general consensus of these statistics is that the chemical abundance pattern of NGC 2005 can partially overlap that of the other five LMC globular clusters.

In order to explore such a possibility more deeply, we first thoroughly searched the literature for [X/Fe] ratios measured in the LMC. Hasselquist et al. (2021) used APOGEE abundances (Majewski et al. 2017) to uncover the chemical abundance patterns in massive Milky Way satellites, including the LMC. They carefully selected galaxy stars based on APOGEE data quality cuts and proper motions. For Si, Ca, and Ni (the only three elements overlapping those in Mucciarelli et al. 2021), they obtained the median abundances and ±1σ uncertainties listed in Table 2. When comparing these values with those of five LMC globular clusters in Table 1, we found that abundances of Ca and Ni are less than 1η and that of Si is different at 2.5η level. We assume that this result supports that both metallicity scales are similar within the quoted uncertainties, inhomogeneities and/or systematic effects, if present, being smaller. We carried out the same statistical comparison for the values of NGC 2005, and found that abundances of Si and Ni are less than 1η, but Ca is different at 1.6η. They suggest that these chemical elements in NGC 2005 and the LMC have similar abundances.

We also derived the mean values of different chemical elements of dwarf galaxies using the homogenized analysis carried out by Reichert et al. (2020), which is, as far as we are aware, the largest compilation of these quantities for this type of object. The calculated values are listed in Table 2. As can be seen, the abundance of Ni in Sagittarius is in excellent agreement with that of Hasselquist et al. (2021) so that we assumed that both results are in the same scale within the quoted uncertainties.

For the chemical elements showing η > 3 in Figure 1 (Sc, Zn, and Eu), we repeated the statistical analysis described above by comparing the values in Table 1 with those in Table 2. We found that: (1) the five LMC globular clusters have η < 3 for Sc, Zn, and Eu with respect to all the dwarfs included in Table 2, with the exception of Sc for Sagittarius and Ursa Minor; (2) NGC 2005 has only Sc abundance different from Sagittarius and Sculptor and Zn abundance different from Sagittarius. The above results show that chemical element abundances that appear to be different in NGC 2005 with respect to LMC are also found to be different, unevenly, between the LMC and other dwarfs, as well as between NGC 2005 and other dwarfs.

Note that we performed this statistical analysis based on chemical abundances derived by the different sets of analysis, i.e., we adopt chemical abundances of Mucciarelli et al. (2021) and Hasselquist et al. (2021). On the other hand, Mucciarelli et al. (2021)' chemical abundances were derived with the same analysis. This difference may introduce additional inhomogeneity and systematic effects.

We would expect that if NGC 2005 formed in a dwarf (Fornax-like) galaxy as proposed by Mucciarelli et al. (2021), their chemical abundance patterns should be similar. Mucciarelli et al. (2021) compiled from the literature abundances for Si, Ca, Cu, and Zn in Fornax (see their supplementary Figure 5). Unfortunately, none of these chemical elements are in the compilation by Reichert et al. (2020) to compare one to the other. Nevertheless, we found that Letarte et al. (2006) measured Ba, Ni, and Ti abundances for Fornax's globular clusters. When extrapolating their [X/Fe] versus [Fe/H] relationships up to [Fe/H] = −1.75, we found that the values for Ba and Ni are similar to those in Table 2, while that for Ti is somewhat different. Therefore, according to the compilation by Reichert et al. (2020), the chemical element abundances in NGC 2005 and Fornax would not seem to be clearly different. We note that it would be worth performing further measurements for more chemical elements in the LMC and other dwarfs to make a more comprehensive comparison with the values obtained for NGC 2005.

In this study, we explore whether a scenario of in situ formation of NGC 2005 is still allowed. We have shown that most elements show η between 2 and 3, meaning that the probability that the difference in chemical abundance is real is more than 95%, it cannot be considered insignificant. Although this argument would suffer from systematics in different observations, the following discussion of chemo-dynamical properties of NGC 2005 could support the in situ formation scenario.

3.1. Chemical Abundances

3.2. Kinematics

Kinematics of globular clusters let us consider an in situ origin for NGC 2005. Indeed, the kinematics of Milky Way globular clusters have been used to disentangle different accretion events (Kruijssen et al. 2019; Massari et al. 2019) since their motions have kept along their lifetimes' imprints of their origins (Piatti 2019). Similarly, Bennet et al. (2022) performed a 6D phase-space analysis from multiple independent analysis techniques of 31 LMC globular clusters using Gaia EDR3 (Gaia Collaboration et al. 2021) and Hubble Space Telescope data. They found that the system of globular clusters rotates like in a stellar disk with one-dimensional velocity dispersions of order 30 km s⁻¹, similar to that of the LMC old stellar disk population. From these results, they argued that most, if not all, LMC globular clusters formed through a single formation mechanism in the LMC disk, albeit their significant dispersion in age and metallicity, any accretion signature being absent within the involved uncertainties. Similarly to outer halo Milky Way globular clusters, which are associated with dwarf galaxy accretion events (e.g., Sagittarius, Gaia-Enceladus, Sequoia, etc.; Forbes 2020), the LMC halo globular cluster should be those with more chances to have an ex situ origin, but at present, there is no chemical signature hinting at it. Note that NGC 2005 is placed in the inner LMC disk.

Several recent studies support the in situ scenario. Shao et al. (2021) showed that accreted globular clusters in the Milky Way and Fornax are less centrally concentrated than those formed in situ. Moreover, globular clusters that escape dwarf satellites of the Milky Way are found orbiting the latter (Rostami Shirazi et al. 2022). Piatti et al. (2019) derived mean proper motions of the 15 LMC globular clusters, and from existent radial velocities, they computed their velocity vectors. They found that LMC globular clusters are distributed in two different kinematics groups, namely: those moving in the LMC disk and others in a spherical component. Since globular clusters in both kinematicstructural components share similar ages and metallicities, they concluded that their origin occurred through a fast collapse that formed a halo and disk concurrently. NGC 2005 resulted in being a disk globular cluster, while among the other five LMC clusters, three and two are in the disk and halo, respectively.

In addition to kinematics, the mass required to form globular clusters would support the in situ formation scenario. Eadie et al. (2022) estimated a minimum galaxy stellar mass required to form globular clusters of ∼10⁷ M_⊙. We found from Table 3 that only Sagittarius and Fornax could form globular clusters. Carina, Draco, and Ursa Minor do not have globular clusters (either formed in situ or ex situ). With a total galaxy stellar masses of ∼10^5.4 M_⊙ it is probable that these galaxies are primordial dwarfs, i.e., they did not form from the merger of smaller galaxies.

Table 3. Stellar Mass of Dwarf Galaxies using the Absolute M_V Magnitudes Compiled by Drlica-Wagner et al. (2020) and Interpolating them in Figure 5 of Georgiev et al. (2010)

Name	MV (mag)	log(stellar mass/M⊙)
Carina	−9.43	5.6${}_{-0.2}^{+0.3}$
Draco	−8.71	5.3${}_{-0.2}^{+0.3}$
Fornax	−13.46	7.4${}_{-0.2}^{+0.3}$
Sagittarius	−13.50	7.4${}_{-0.2}^{+0.3}$
Sextants	−8.72	5.3${}_{-0.2}^{+0.3}$
Sculptor	−10.82	6.2${}_{-0.1}^{+0.2}$
Ursa Minor	−9.03	5.4${}_{-0.2}^{+0.3}$

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We also computed the LMC mass for a lookback time of 11.5 Gyr, when all its globular clusters formed (Piatti et al. 2019), using the SFRs derived by Mazzi et al. (2021) and Massana et al. (2022). We obtained an LMC mass of ∼10⁸ M_⊙. Thus, the preenriched gas cloud out of which the LMC globular clusters formed could have been a gathering of smaller pieces, each with a particular chemical enrichment history.

Following these discussions, we anticipate that stars with chemical abundances similar to NGC 2005 would be formed if there are gas clouds with enough mass (∼10⁷ M_☉) enriched by SNe Ia larger than the other region. On the other hand, in Mucciarelli et al. (2021)' scenario, NGC 2005 would be formed around a Fornax-like dwarf galaxy and later accreted to the LMC. Our discussion suggests that NGC 2005 could be formed in situ without imposing unphysical assumptions.

The present analysis shows that the 13 chemical elements employed by Mucciarelli et al. (2021) to claim an ex situ origin of NGC 2005 are not all of the same accuracy. Consequently, they cannot be used indistinctly to support abundance differences between the [X/Fe] values derived for NGC 2005 and for five LMC globular clusters with similar metallicities. Nevertheless, the abundance differences measured for some chemical elements (>3σ) are yielded by SNe Ia. Different dwarf galaxies with studied chemical enrichment histories show abundances spread of the considered chemical elements that encompass the mean values of NGC 2005, which means that NGC 2005 could have been born in any of these galaxies, including the LMC. The five LMC globular clusters with [Fe/H] values similar to that of NGC 2005 belong to the inner disk (3) and the outer halo (2) of the LMC, and they have similar individual [X/Fe] ratios. The LMC globular clusters span a wide range of metallicities, and that range is verified from those populating the kinematically different disk and halo substructures, respectively (Piatti et al. 2019). Therefore, the presence of NGC 2005 in the inner LMC disk should not catch our attention to differentiate it from the remaining LMC globular cluster population. Recent modeling has also shown a widespread abundance of chemical species at the metalicity level of NGC 2005 can be produced by supernova explosions, as has also been probed in the LMC.

We thank the referee for the thorough reading of the manuscript and timely suggestions to improve it. We thank Alessio Mucciarelli for providing data for Table 1, and Giuseppina Battaglia for valuable comments. Y.H. is supported in part by JSPS KAKENHI grant Nos. JP21J00153, JP20K14532, JP21H04499, JP21K03614, JP22H01259, MEXT as "Program for Promoting Researches on the Supercomputer Fugaku" (Toward a unified view of the universe: from large scale structures to planets, grant No. JPMXP1020200109), JICFuS, and grants PHY 14-30152: Physics Frontier Center/JINA Center for the Evolution of the Elements (JINA-CEE) and OISE-1927130: The International Research Network for Nuclear Astrophysics (IReNA), awarded by the U.S. National Science Foundation. Numerical computations and analysis were carried out on Cray XC50 and computers at the Center for Computational Astrophysics, the National Astronomical Observatory of Japan, and the Yukawa Institute Computer Facility. This research has made use of NASA's Astrophysics Data System Bibliographic Services.

In what follows y1 and y2 represent values of the 13 element abundances in NGC 2005 and in the five LMC globular clusters, respectively (see text for details).

# Spearman correlation

• spearman = stats.spearmanr(y1,y2, axis = 0)
• print (spearman)

# Sørensen–Dice statistic

• def dice(a, b):_
• a = set(a)_
• b = set(b)
• return (2*len(_a.intersection(_b))) / (len(_a) + len(_b))
• dice = dice(y1, y2)
• print (dice)

# Jaccard similarity

• def jaccard_similarity(x,y):
• intersection_cardinality = len(set.intersection(*[set(x), set(y)]))
• union_cardinality = len(set.union(*[set(x), set(y)]))
• return intersection_cardinality/float(union_cardinality)
• jaccard = jaccard_similarity(y1,y2)
• print (jaccard)

# Cosine similarity

• def square_rooted(x):
• return round(np.sqrt(sum([a*a for a in x])),3)
• def cosine_similarity(x,y):
• numerator = sum(a*b for a,b in zip(x,y))
• denominator = square_rooted(x)*square_rooted(y)
• return round(numerator/float(denominator),3)
• cosine = cosine_similarity(y1,y2)
• print (cosine)

# Pearson correlation

• my_rho = np.corrcoef(y1,y2)
• print (my_rho)

# Levenshtein distance

• import Levenshtein as lev
• ratio = lev.ratio(y1,y2)
• jaro = lev.jaro(y1,y2)
• jw = lev.jaro_winkler(y1,y2)
• ham = lev.hamming(y1,y2)
• print (ratio, jaro, jw, ham)