Combining Astrometry and Elemental Abundances: The Case of the Candidate Pre-Gaia Halo Moving Groups G03-37, G18-39, and G21-22^*

We obtained high-resolution spectroscopy of six stars identified by Silva et al. (2012) as members of G21-22 in service mode with the Ultraviolet and Visual Echelle Spectrograph (UVES; Dekker et al. 2000) and the 8.2 m Unit 2 (UT2, Kueyen) telescope of the Very Large Telescope (VLT) at Cerro Paranal, Chile, between the months of 2012 October and 2013 March. A standard dichroic setting (DIC 1) was used to provide a wavelength (incomplete) coverage of 3280–6800 Å. The slit width was set to 06, giving a nominal resolving power of R ≈ 65,000, and the Poisson signal-to-noise ratio (S/N) of the spectra is ≈100 near 6500 Å. The data were reduced through the observatory's standard pipeline processing using the REFLEX environment (Freudling et al. 2013) within the European Southern Observatory Common Pipeline Library and were taken directly from the ESO Science Archive. Representative samples of the spectra are shown in Figure 3.

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We derived stellar parameters and abundances of up to 13 elements—Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Ni, and Ba—via an equivalent width (EW) analysis assuming local thermodynamic equilibrium (LTE) line formation for each star. Starting with the spectral lines analyzed by Villanova & Geisler (2011) and Sakari et al. (2019), we constructed our linelist with those falling in the wavelength coverage of our VLT/UVES spectra. The transition probabilities ($\mathrm{log}{gf}$) were checked against atomic parameters based on recent accurate laboratory data provided by the Wisconsin atomic physics program (e.g., Yousefi & Bernath 2018; Lawler et al. 2019). The laboratory data were accessed via the Python tool Linemake, ⁷ developed by Vinicius Placco (Placco et al. 2021). In all cases of discrepancy, the laboratory transition probabilities were adopted. The linelist is provided in Table 2.

Table 2. Linelist and Equivalent Widths for Putative Members of G21-22

	λ	χ	$\mathrm{log}{gf}$	Equivalent Widths
Species	(Å)	(eV)		G02-38	G82-42	G108-48	G119-64	G161-73	HIP 36878
Na i	5682.63	2.10	−0.70	⋯	⋯	19.8	⋯	11.0	21.9
	5688.21	2.10	−0.45	⋯	24.6	33.3	10.1	19.2	31.5
	6160.75	2.10	−1.26	⋯	⋯	6.9	⋯	⋯	⋯
Mg i	5528.41	4.34	−0.62	⋯	169.3	⋯	80.8	121.2	⋯
	5711.09	4.34	−1.83	32.1	58.5	⋯	15.8	35.3	65.7
	6318.72	5.10	−1.73	⋯	⋯	9.3	⋯	⋯	⋯
	6319.24	5.10	−1.95	7.4	⋯	5.5	⋯	⋯	⋯
Al i	6696.02	3.14	−1.35	⋯	⋯	7.2	⋯	⋯	3.7
Si i	5684.52	4.93	−1.65	9.3	14.0	13.9	⋯	12.0	⋯
	5701.10	4.93	−2.05	⋯	⋯	⋯	⋯	⋯	9.2

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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EWs of each line were measured using the Python tool pyEW, ⁸ developed by Monika Adamów. The code attempts to fit each spectral line from a user-provided linelist with Gaussian, multiple Gaussian (combined), and Voigt profiles, and provides the best fit as the one that minimizes the least-squares errors in the fit to the observed line. All lines were inspected visually to ensure the goodness of each fit. The EWs of each measured line are included in Table 2.

To derive stellar parameters and abundances, we made use of our newly developed Python code, SPAE (Stellar Parameters, Abundances, and Errors ⁹ ), that uses a state-of-the-art Bayesian method to self-consistently propagate uncertainties from the stellar atmosphere solutions in calculating individual abundances. SPAE employs the LTE plane-parallel spectral analysis code MOOG ¹⁰ (MOOGSILENT version; Sneden 1973) and Kurucz (2011) model atmosphere grids ¹¹ to derive the abundances of elements included in a user-provided linelist. We note that in the following and throughout the paper, we distinguish [Fe/H]_m, the metallicity of a star relative to the Sun, and [Fe/H], the Fe abundance of a star relative to the solar Fe abundance. ¹² The former is used as an input for a model atmosphere; the latter is an output of MOOG.

Starting with an (adjustable) initial parameter grid step defined by an effective temperature (T_eff), surface gravity ($\mathrm{log}g$), metallicity ([Fe/H]_m), and microturbulent velocity (ξ), the code interpolates the Kurucz grids to produce a model atmosphere, and then passes the model and linelist to MOOG to derive the abundances. The resulting Fe i and Fe ii abundances are read by SPAE and used to construct the likelihood function, ${ \mathcal L }$, which is defined by the minimization of the differences in the derived [Fe i/H] and [Fe ii/H] abundances and the model metallicity, [Fe/H]_m:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{ln}{{ \mathcal L }}_{\mathrm{Fe}\,{\rm\small{I}}} & = & -{N}_{\mathrm{Fe}\,{\rm\small{I}}}\times \mathrm{ln}{\sigma }_{\mathrm{Fe}}\\ & & +\ \sum -\frac{{\left([\mathrm{Fe}\,{\rm\small{I}}/{\rm{H}}]-{\left[\mathrm{Fe}/{\rm{H}}\right]}_{{\rm{m}}}\right)}^{2}}{2{\sigma }_{\mathrm{Fe}}^{2}}\end{array}\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{ln}{{ \mathcal L }}_{\mathrm{Fe}\,{\rm\small{II}}} & = & -{N}_{\mathrm{Fe}\,{\rm\small{II}}}\times \mathrm{ln}{\sigma }_{\mathrm{Fe}}\\ & & +\ \sum -\frac{{\left([\mathrm{Fe}\,{\rm\small{II}}/{\rm{H}}]-{\left[\mathrm{Fe}/{\rm{H}}\right]}_{{\rm{m}}}\right)}^{2}}{2{\sigma }_{\mathrm{Fe}}^{2}},\end{array}\end{eqnarray} \tag{ 2 }$$

where σ_Fe is the standard deviation of the combined line-by-line abundances of [Fe i/H] and [Fe ii/H], and N_{Fe I} and N_{Fe II} are the number of Fe i and Fe ii lines, respectively. The log of the likelihood function is then the sum of the two separate log-likelihoods in Equations (1) and (2):

$$\begin{eqnarray*}&&\mathrm{ln}{ \mathcal L }=\mathrm{ln}{{ \mathcal L }}_{\mathrm{Fe}\,{\rm\small{I}}}+\mathrm{ln}{{ \mathcal L }}_{\mathrm{Fe}\,{\rm\small{II}}}.\end{eqnarray*}$$

The parameter space is sampled using emcee (Foreman-Mackey et al. 2013), a Python implementation of an affine-invariant ensemble sampler MCMC algorithm (Goodman & Weare 2010). We adopted a four-dimensional—T_eff, $\mathrm{log}g$, [Fe/H]_m, and ξ—flat prior probability distribution constrained by the available Kurucz model atmosphere grids. The ensemble solution (posterior probability distribution) is generated by initializing 40 walkers in an N ball around Solar values (T_eff = 5777 K, $\mathrm{log}g$ = 4.44, [Fe/H]_m = 0.01, ξ =1.38 km s⁻¹), then iterating 1000 steps, resulting in 4 × 10⁴ separate combinations of parameters that are used to produce model atmospheres that are passed onto MOOG to derive abundances.

The derived T_eff, $\mathrm{log}g$, [Fe/H]_m, ξ, elemental abundances, and their uncertainties are taken as the median and 1σ confidence intervals of the ensemble solutions, after accounting for burn in (iterations to convergence, typically 200–300) and any walkers with low acceptance fractions (<0.40). We calculated autocorrelation lengths with built-in functions in emcee, and they were found to be ≲100 for each star. Note that [Fe/H]_m is determined by considering both Fe i and Fe ii, as defined by ${ \mathcal L }$. The parameters, along with the final number of iterations included in the ensemble solutions, are given for each star in Table 3.

Table 3. Stellar Parameters for the Putative G21-22 Members

	G02-38	G82-42	G108-48	G119-64	G161-73	HIP 36878
Teff (K)	${5818}_{-\,42}^{+43}$	${5413}_{-\,43}^{+42}$	${5212}_{-\,47}^{+46}$	6149 ± 50	${5981}_{-\,33}^{+36}$	${5333}_{-\,34}^{+32}$
$\mathrm{log}g$ (cgs)	4.48 ± 0.08	4.61 ± 0.08	${4.77}_{-\,0.10}^{+0.11}$	${4.06}_{-\,0.13}^{+0.12}$	${3.97}_{-\,0.09}^{+0.08}$	4.55 ± 0.05
ξ (km s−1)	1.27 ± 0.08	${0.65}_{-\,0.18}^{+0.13}$	${0.78}_{-\,0.21}^{+0.18}$	1.54 ± 0.06	1.45 ± 0.05	${0.49}_{-\,0.18}^{+0.13}$
[Fe/H]m	−1.41 ± 0.03	−1.17 ± 0.04	−1.07 ± 0.04	−1.56 ± 0.04	−1.07 ± 0.03	−1.13 ± 0.03
Iterations a	26,600	30,420	31,200	28,000	30,000	34,000

Note.

^a Number of iterations included in ensemble solution after accounting for burn in and solutions with low acceptance fractions. Our walkers have typical autocorrelation lengths of ≲100, meaning the number of independent samples is somewhat lower than that shown.

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In addition to the stellar parameters and metallicity, the abundances of the other elements measured are derived with each iteration of the MCMC, resulting in ensemble solutions for each element. In Table 4, the medians and 1σ confidence intervals of the ensemble solutions for each element are shown, with the abundances given relative to the solar values of Asplund et al. (2009). ¹³

The implementation in SPAE of the likelihood function ${ \mathcal L }$ is a departure from the typical method used to spectroscopically derive stellar parameters and abundances. The more typical method, excitation and ionization balance of Fe i and Fe ii, entails requiring the line-by-line Fe i abundances to be independent of excitation potential (χ) and EW, and requiring the mean [Fe/H] abundances as derived from Fe i and Fe ii lines to be the same. The uncertainties are then typically determined by altering the stellar parameters to achieve 1σ deviations in the correlations between χ, EW, and the Fe i abundances (e.g., Schuler et al. 2011).

While ionization balance is intrinsic to ${ \mathcal L }$, excitation balance is not. Therefore, the ability to check the excitation balance of the median solution, as well as identifying any solution(s) in the ensemble that achieve excitation balance, has been built into SPAE. This allows the user to verify that the solution(s) obtained using the typical method is contained in the posterior distribution and determine its (their) statistical significance relative to the distribution.

As an example, in Figure 4 we show the plots of ${\mathrm{log}}_{10}N$(Fe i) as a function of χ and reduced equivalent width (${\mathrm{log}}_{10}\mathrm{RW}$) for the median solution for G161-73. A linear least-squares fit is applied to each relation. For χ, the r value (correlation coefficient) is r = −0.037 and the corresponding p value (Wald test with t distribution) is p = 0.663, and for ${\mathrm{log}}_{10}\mathrm{RW}$, r = −0.009 and p = 0.916. While the statistical significance of r is marginal for ${\mathrm{log}}_{10}\mathrm{RW}$, the p value for χ indicates that the data are not consistent with the null hypothesis of having a slope of zero and thus formally do not satisfy excitation balance; the criteria for which we have adopted to be ∣r∣ < 0.01 and p > 0.90. However, of the 30,000 iterations included in the ensemble solution for G161-73, 17 of them do satisfy excitation balance. In Figure 5 we show the correlation plots for the solution satisfying excitation balance at the highest confidence level for G161-73. With r = −0.000 and p = 0.998 for χ, and r = −0.003 and p = 0.973 for ${\mathrm{log}}_{10}\mathrm{RW}$, this solution is consistent with both relations having a slope of zero. The differences in T_eff, $\mathrm{log}g$, [Fe/H]_m, and ξ between this solution and the median solution are −9 K, −0.07 dex, −0.01 dex, and 0.02 km s⁻¹, respectively.

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The position of this solution is indicated by the blue lines in Figure 6, which summarizes the ensemble solution for the stellar parameters of G161-72 as determined by SPAE. All four parameters are within 1σ of those of the median solution, indicating that SPAE is able to converge on the correct solution for this star. A direct comparison of the SPAE solutions to the solutions satisfying excitation balance at the highest confidence level for each star is shown in Figure 7.

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The mean of the stellar parameters of the solutions satisfying excitation balance for each star is provided in Table 5; standard deviations and the number of solutions are also given. The standard deviations demonstrate that although numerous solutions satisfy excitation balance for each star, those solutions occupy a tight parameter space, as would be expected. A major advantage of SPAE is that these solutions are contained in the generated ensemble solution and therefore taken into account in the final stellar parameter and abundance uncertainties. Indeed, the 1σ confidence intervals of the ensemble solutions are a true measure of the uncertainty in the parameters and abundances as derived with our data.

Table 5. Excitation Balance Stellar Parameters of Putative G21-22 Stars ^a

	G02-38	G82-42	G108-48	G119-64	G161-73	HIP 36878
Teff (K)	5804.0 ± 1.8	5415.4 ± 3.8	5197.4 ± 3.9	6130.3 ± 1.3	5970.4 ± 2.4	5333.2 ± 3.9
$\mathrm{log}g$ (cgs)	4.467 ± 0.009	4.652 ± 0.007	4.728 ± 0.005	4.029 ± 0.008	3.903 ± 0.005	4.557 ± 0.003
ξ (km s−1)	1.187 ± 0.006	0.552 ± 0.017	0.794 ± 0.016	1.469 ± 0.005	1.469 ± 0.004	0.487 ± 0.023
[Fe/H]m	−1.402 ± 0.006	−1.161 ± 0.010	−1.075 ± 0.010	−1.560 ± 0.007	−1.077 ± 0.007	−1.129 ± 0.008
Solutions b	20	10	14	7	17	24

Notes.

^a The stellar parameters included herein are the means of parameters of the solutions satisfying excitation balance as defined in the text. The quoted uncertainties are the standard deviations of the means. ^b Number of solutions satisfying excitation balance.

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While we used SPAE to analyze the majority of the elements we discuss in this work, we took a separate approach to deriving the abundances of the predominately r-process element Eu. We derived Eu abundances using spectrum synthesis of the Eu ii lines at 4129.7 and 4205.0 Å. Other lines typically used for Eu abundances, such as λ 3724, λ 3819, λ 6437, and λ 6645, were not detected in our spectra. Synthetic spectra were fit to the observed spectra using the synth driver of MOOG, along with a stellar model characterized by the parameters and metallicities from SPAE. Linelists for the 4205 and 4130 Å regions were assembled using Linemake, which includes the atomic data for the Eu ii lines from Lawler et al. (2001); we adopted isotopic ratios of 47.8% and 52.2% for ¹⁵²Eu and ¹⁵³Eu, respectively, also from Lawler et al. (2001).

The linelist was further adjusted by changing slightly the transition probabilities and wavelengths of a handful of lines in the λ 4130 and λ 4205 regions to fit a high-quality solar spectrum (Schuler et al. 2015) obtained with the W.M. Keck Observatory and High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994). None of the atomic parameters of the Eu lines were altered during this process.

Examples of the synthetic fits to the Eu lines are shown in Figure 8. These lines are found in the bluer wavelength regions of our spectra and thus are characterized by lower S/N compared to the redder regions where the rest of the metal lines are measured. The effect of the lower S/N on the Eu lines themselves can be seen in Figure 8. Nonetheless, we measured consistent [Eu/Fe] abundances from each line for each star. The derived [Eu/Fe] abundances are given in Table 6. We adopted a conservative abundance uncertainty of ±0.10 dex for each star.

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By comparing the kinematic properties of the G21-22 stars to the models of Meza et al. (2005), Silva et al. (2012) suggest that the stars may be related to the tidal debris of the long hypothesized ω Cen accretion event (Freeman 1993) or some other accreted dwarf galaxy. Schuster et al. (2019) offer an alternate explanation, implying the stars formed in situ in the Galaxy and are now trapped in orbital resonances created by the Galactic bar (see also Amarante et al. 2020).

In a search for metal-rich Gaia-Enceladus stars, Zhao & Chen (2021) compare the maximum height above or below the Galactic plane (${z}_{\max }$) to the mean Galactic distance (R_m = R_apo + R_peri/2, where R_apo is the apocenter distance and R_peri is the pericenter distance) for a sample of stars that includes the star G21-22, after which the putative G21-22 moving group was named. The features of the resulting Zhao & Chen (2021) plot (their Figure 7) are similar to those found by Amarante et al. (2020), who compare ${z}_{\max }$ to R_apo (their Figure B1).

Amarante et al. (2020) use newly derived stellar halo and thick-disk fractions, and new stellar kinematics with the Galaxia population synthesis model (Sharma et al. 2011), to conclude that this ${z}_{\max }$–R_apo relation is a natural consequence of resonant effects. However, Haywood et al. (2018) examine the blue and red sequences of the Gaia HR diagram Gaia Collaboration et al. (2018a) and find a similar relation for ${z}_{\max }$–${R}_{{\rm{R}}2{\rm{D}},\max }$ (the apocenter distance projected on the Galactic plane) and, based on this and other dynamical and orbital properties, conclude the blue sequence stars are possible relics of a significant accretion event experienced by the Galaxy.

We attempted to determine the origins of the G21-22 stars by comparing their stellar properties to other stars in the Milky Way halo in kinematic and chemical space. While it is generally accepted that at least part of the halo has been populated by accretion events (e.g., Helmi 2020), some recent studies suggest that it was built entirely by accretion (Helmi et al. 2017; Naidu et al. 2020). This raises the possibility that the G21-22 stars can be associated to one or more of these structures, each of which occupies a characteristic region in integrals of motion, particularly E–L_z (Naidu et al. 2020).

Naidu et al. (2020) derived their integrals of motion using the same Galactic model as we did (see Section 2). Using these authors' results as a guide, we can eliminate Sagittarius, Sequoia, Helmi stream, and Thamnos as progenitors of the six G21-22 stars based on their positions in the E–L_z and V_ϕ –V_r planes. There is no overlap between these structures and the stars.

The kinematic properties of the stars are consistent with the lower density regions of the high-α disk and in situ halo component of Naidu et al. (2020), but they do not meet the metalicity cutoff set by these authors to distinguish it from the metal-weak thick disk (MWTD), which is taken to be the metal-poor extension of the high-α disk. Conversely, two of the G21-22 stars fall in the [α/Fe] ¹⁴ –[Fe/H] selection box set for the MWTD, but as we show in Figure 1, the stars are clearly part of the halo and are not consistent with the MWTD in any of the kinematic spaces.

This leaves Gaia-Enceladus, which has been tied to greater than 50% of the Galactic halo (Mackereth et al. 2019), as the possible progenitor. Indeed, the six G21-22 stars are consistent with Gaia-Enceladus in four key diagnostics presented by Naidu et al. (2020): they have eccentricities e ≥ 0.77 (see Table A2), which is larger than the cutoff value of e = 0.7, and they overlap with Gaia-Enceladus stars in the E–L_z, V_ϕ –V_r, and [α/Fe]–[Fe/H] spaces. Moreover, these stars' metallicities ([Fe/H]) are within about 1σ of the mean metallicty of the structure, depending on the value considered (e.g., Matsuno et al. 2019; Vincenzo et al. 2019; Naidu et al. 2020).

To investigate the six G21-22 stars in chemical space, their abundances are plotted with those of general halo populations and ω Cen in Figures 9–12. The general halo population includes stars observed by APOGEE and deemed by Hayes et al. (2018) to have likely been accreted by the Milky Way early in its history (labeled the low-Mg population, LMg) and to have formed in situ, possibly as part of the thick disk (labeled the high-Mg population, HMg). The remaining halo stars are found in Venn et al. (2004), Reddy et al. (2006), Nissen & Schuster (2010), Ishigaki et al. (2012, 2013), and Roederer et al. (2014). Abundances of ω Cen stars are from Johnson & Pilachowski (2010).

The abundances of ω Cen, LMg, and HMg occupy distinct regions of the abundance plots, although there is some overlap between LMg and both ω Cen (at low [Fe/H]) and HMg (at high [Fe/H]) for some elements. The G21-22 stars follow the general halo trend, which spans across the ω Cen, LMg, and HMg stars, and cannot be definitively assigned to any of the three. The abundances of the two more metal-poor stars—G02-38 and G119-64—are consistent with those of ω Cen, raising the possibility that they are part of the cluster's tidal debris, as suggested by Silva et al. (2012). However, L_z of these stars are inconsistent with the recently discovered Fimbulthul stream, which has been identified as the tidal stream of ω Cen (Ibata et al. 2019a, 2019b), arguing against an association with the cluster.

The four more metal-rich stars, G82-42, G108-48, G161-73, and HIP 36878, have abundances generally consistent with those of both the LMg and HMg groups. However, given that the kinematics of all six stars are consistent with Gaia-Enceladus and much of the general halo is composed of stars from Gaia-Enceladus, possibly even the LMg stars, we suggest it as the more likely progenitor of the G21-22 stars. If this is indeed the case, the abundances presented here will add to the nascent list of abundances derived for Gaia-Enceladus stars.