Elemental Abundances in M31: Gradients in the Giant Stellar Stream^*

All spectroscopic fields, except a13 and And I, ⁹ were observed for a minimum of 5 hr with the 600 line mm⁻¹ or 1200 line mm⁻¹ grating for the case of low- and moderate-resolution spectroscopy, respectively. These configurations result in spectra with an FWHM spectral resolution of 2.8 Å (R ∼ 3000) and 1.2 Å (R ∼ 6000). Additionally, each deep (5+ hr) field was designed from previous shallow (∼1 hr) DEIMOS observations from the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey (Guhathakurta et al. 2006; Kalirai et al. 2006; Gilbert et al. 2007, 2009) in order to maximize the yield of spectroscopically confirmed M31 RGB stars. Data for fields a13 and And I were obtained as part of the SPLASH survey, where a handful of stars have spectra with fortuitously high signal-to-noise ratios (S/Ns) such that measuring abundances is feasible. The spectra were reduced using a modified version of the spec2d pipeline (Cooper et al. 2012; Newman et al. 2013 for the original pipeline; Simon & Geha 2007; Kirby et al. 2020 for modifications specific to stellar point sources). Table 1 provides a summary of the properties for each spectroscopic field containing kinematically identifiable substructure.

Table 1. Properties of Substructure in Spectroscopic Fields

Field	rproj	Comp.	μ	σ	f	〈[Fe/H]〉	〈[α/Fe]〉	NM31	N[α/Fe]	Ref.
	(kpc)		(km s−1)	(km s−1)
f207	17	GSS	−529.4	24.5	0.33	−0.87${}_{-0.10}^{+0.09}$	+0.44${}_{-0.05}^{+0.04}$	108	21	1, 2
		KCC	−427.3	21.0	0.32	−0.79 ± 0.07	+0.54 ± 0.06	⋯	⋯	⋯
S	22	GSS	−489.0	26.1	0.49	−1.02${}_{-0.14}^{+0.15}$	+0.38${}_{-0.19}^{+0.17}$	87	20	3
		KCC	−371.6	17.6	0.22	−0.71 ± 0.11	+0.35${}_{-0.09}^{+0.08}$	⋯	⋯	⋯
a3	33	GSS	−444.6	15.7	0.56	−1.11${}_{-0.13}^{+0.12}$	+0.34${}_{-0.09}^{+0.08}$	75	21	1, 4
And I	45	GSS	−383.3	32.4	0.56	−1.49${}_{-0.02}^{+0.10}$	−0.19${}_{-0.05}^{+0.21}$	38	3	1, 5
a13	58	GSS	−301.6	29.2	0.62	−2.50${}_{-0.54}^{+0.40}$	+0.71${}_{-0.34}^{+0.19}$	31	3	1, 6, 7
H	12	SE Shelf	−295.4	65.8	0.56	−1.30${}_{-0.12}^{+0.13}$	+0.53${}_{-0.10}^{+0.08}$	104	16	3
f123	18	SE Shelf	−279.9	11.0	0.32	−0.71 ± 0.07	+0.41${}_{-0.05}^{+0.04}$	74	49	1, 4

Note.–The columns of the table refer to spectroscopic field name; projected radius from M31's galactic center; substructure component; the median heliocentric velocity (μ), dispersion (σ), and fractional contribution (f) of the velocity model for a given component (Section 2.2); average [Fe/H] and [α/Fe] for a given component (Section 2.3), weighted by the inverse variance of the measurement uncertainty and substructure probability; number of spectroscopically confirmed RGB members (excluding dwarf galaxy members for And I; Section 2.2); and number of RGB stars with successful [Fe/H] and [α/Fe] measurements. References: (1) Gilbert et al. (2018), (2) Gilbert et al. (2019), (3) Escala et al. (2020a), (4) Escala et al. (2020b), (5) Gilbert et al. (2020), (6) J. Wojno et al., 2021, in preparation, (7) this work.

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Radial velocities were measured via cross-correlation with templates using the procedures described in Simon & Geha (2007) and Kirby et al. (2015). The statistical uncertainty is calculated from Monte Carlo trials in which a given observed spectrum is perturbed according to its standard error, whereas the systematic uncertainty is calculated via repeat velocity measurements of the same stars. We adopted a systematic velocity term of 1.49 km s⁻¹ for 1200 line mm⁻¹ grating spectra (Kirby et al. 2015) and 5.6 km s⁻¹ for 600 line mm⁻¹ grating spectra (Collins et al. 2011).

Using a combination of heliocentric radial velocity, color–magnitude diagram (CMD) position, Na i λ λ8190 equivalent widths, and photometric and calcium triplet–based metallicity estimates, we assigned a probability of belonging to M31 to each star with a successful velocity measurement. We utilized the Bayesian inference method of Escala et al. (2020b) to determine membership for all stars except those in the 17, 45, and 58 kpc fields, for which we used the maximum likelihood–based technique of Gilbert et al. (2006). For the 45 kpc field, we additionally required that M31 RGB candidates had [Fe/H]_phot > −0.95 in order to separate M31 halo stars from stars belonging to the And I dwarf spheroidal galaxy. Gilbert et al. (2009, 2020) demonstrated that this additional photometric metallicity criterion clearly demarcates the two populations, regardless of velocity or apparent proximity to the dwarf galaxy.

As discussed by Escala et al. (2020b), the Bayesian inference and maximum likelihood–based methods of M31 membership determination produce generally consistent results, where Escala et al.'s classification of stars as M31 members is slightly more conservative. In general, we consider stars to be M31 RGB stars if they are more likely to belong to M31 than to the MW foreground. The membership criterion for the 45 and 58 kpc fields is more stringent, requiring that stars are at least three times more likely to belong to M31 than to the MW, owing to the increased likelihood of contamination by MW foreground dwarfs in M31's sparse outer halo.

Figure 2 shows the heliocentric radial velocity distribution of RGB stars in each spectroscopic field containing substructure (Table 1), where stars with velocities consistent with that of kinematically cold components have a higher probability of belonging to substructure (p_sub; Gilbert et al. 2019; Escala et al. 2020a, 2020b). Figure 2 also shows Gaussian mixture models of the velocity distribution for each field, where each model contains both halo and substructure components. We adopted the 50th percentile values of the marginalized posterior probability distributions from Escala et al. (2020a) to model the substructure components in the 12 and 22 kpc fields, whereas all other component models (including halo components) are from Gilbert et al. (2018). The substructure probability for a star with a given radial velocity is thus the odds ratio of the Bayes factor under the assumption of the substructure versus halo models.

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Chemical abundance ([Fe/H] and [α/Fe]) and stellar parameter measurements (T_eff) were obtained from spectral synthesis of low- and medium-resolution stellar spectroscopy for individual RGB stars in each field. In summary, each observed spectrum is compared to a grid of synthetic spectra using Levenberg–Marquardt minimization to identify the best-fit stellar parameters and abundances. Throughout this procedure, the spectroscopic effective temperature (T_eff) is loosely constrained by photometry, whereas the surface gravity ($\mathrm{log}g$) is fixed to its photometric value, assuming a distance modulus of (m − M) = 24.63 ± 0.2 (Clementini et al. 2011) for M31. Measurements of [Fe/H] and [α/Fe] obtained for identical stars from low- and medium-resolution spectra (Section 2.1) are generally consistent within the uncertainties (Escala et al. 2020a). Systematic uncertainties on the abundance measurements are added in quadrature to the random component of the uncertainty from the fitting procedure. We adopted systematic error terms of 0.130 (0.101) and 0.107 (0.084) for [Fe/H] and [α/Fe] measurements, respectively, obtained from 600 (1200) line mm⁻¹ spectra (Gilbert et al. 2019; Escala et al. 2020a). We refer the reader to Escala et al. (2019, 2020a) and Kirby et al. (2008, 2009) for detailed descriptions of the low- and medium-resolution spectral synthesis techniques.

Figure 3 shows [α/Fe] versus [Fe/H] for RGB stars in spectroscopic fields targeting the GSS and SE shelf in M31's stellar halo (Gilbert et al. 2019, 2020; Escala et al. 2020a, 2020b; J. Wojno et al., 2021, in preparation), where each star is color coded by its probability of belonging to the given substructure component(s) present in each field. These final samples consist of M31 RGB stars with reliable stellar parameter and abundance measurements that do not show clear evidence of strong TiO absorption in their spectra. Such TiO stars are omitted from the final sample because we did not model absorption from the molecule when generating our grid of synthetic spectra. Furthermore, the size of a potential validation sample of TiO stars that could be used to evaluate the accuracy of these abundance measurements is currently limited. In order to select the final sample of unpublished measurements in the 58 kpc field, we employed our standard criteria (δ[Fe/H] < 0.4, δ[α/Fe] < 0.4 and well-constrained χ² contours in each fitted parameter). The only exception is that we used a color cut ((V − I)₀ < 2) to exclude possible TiO stars from our final sample in this field, where we have shown that the majority of TiO stars have colors redder than this threshold (e.g., Escala et al. 2020a). Table 1 summarizes the chemical abundance properties of the GSS and SE shelf as probed at the locations of our spectroscopic fields.

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In order to explore chemical abundance trends in the GSS over a larger projected area, we expanded our analysis of gradients to include six M31 RGB stars with measurements of [Fe/H] and [α/Fe] (Gilbert et al. 2020; J. Wojno et al., 2021, in preparation; Table 1) present in spectroscopic fields beyond 40 projected kpc that are known to probe the GSS. Figures 4 and 5 show the gradients measured between 17 and 58 projected kpc, which include the outer-halo GSS stars, compared to our fiducial gradients measured between 17 and 33 projected kpc. Including the outer-halo GSS stars results in [Fe/H] and [α/Fe] gradients with respect to r_proj and the GSS-aligned coordinates that are marginally consistent (within 1.6σ) with the parameters in Table 2. Although the sign of the transverse [α/Fe] gradient changes from negative to positive upon inclusion of the outer GSS stars, each case is consistent with a flat [α/Fe] gradient within the 1σ uncertainties. Thus, the incorporation of GSS stars beyond 40 kpc suggests that the declining trends of [Fe/H] with respect to projected distance across the GSS and projected distance along the GSS continue out to the farthest positions probed by our data.

Additionally, we note that there is no statistically significant difference in the gradient slopes between including and excluding the KCC when measuring the gradients between 17 and 58 kpc, where this feature is not present in the line-of-sight velocity distributions (Figure 2) of the 45 and 58 kpc fields. The gradient intercepts maintain marginal consistency (within (1–2)σ) regardless of inclusion of the KCC, where the most notable change occurs in the normalization of the transverse [Fe/H] gradient. In summary, larger samples spanning the GSS in the outer halo are necessary to confirm the identified trends from spectral synthesis–based abundance measurements. We explore whether such trends with [Fe/H] persist in [Fe/H]_phot measurements of probable GSS stars within our set of spectroscopic fields (Table 1) in Section 3.2.

We further investigated spatial trends in the metallicity distribution of the GSS by repeating the above analysis using measurements of [Fe/H]_phot for all 270 (339) spectroscopically identified RGB stars excluding (including) the outer-halo GSS fields. We measured [Fe/H]_phot by interpolating the color and magnitude of each star on a grid of 9 Gyr PARSEC isochrones (Marigo et al. 2017) with [α/Fe] = 0 as described by Escala et al. (2020a). Figure 6 shows the spatial [Fe/H]_phot gradients fit between 17–33 kpc and 17–58 kpc compared against [Fe/H]_phot measurements for the final abundance sample (Section 2.3) and for all spectroscopically identified RGB member stars (Section 2.2) across fields spanning the GSS (Table 1). The abundance sample excludes TiO stars, which have high [Fe/H]_phot, and includes only stars that have reliable [Fe/H] and [α/Fe] measurements (Section 2.3). The latter sample includes all RGB members regardless of whether they show spectral TiO signatures or have successful [Fe/H] and [α/Fe] measurements.

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We chose to examine the [Fe/H]_phot distribution of all RGB stars along the line of sight to the GSS, as opposed to solely RGB stars in the abundance sample, given that the former sample is larger and less subject to bias against stars with high [Fe/H]_phot. The spatial [Fe/H]_phot trends are qualitatively the same between all member stars and the abundance sample. The most notable difference is that the gradient intercepts are more metal-poor for the abundance sample, which omits TiO stars. We treated the GSS and KCC as the same substructure component, where disregarding the KCC as a contributor to the substructure probability does not result in a significant difference (≳1σ) in the inferred gradients with projected radius and along the GSS core when measured out to 33 or 58 kpc.

As shown in Figure 6, considering only the inner GSS sample yields marginally positive [Fe/H]_phot gradients with respect to projected radius and projected distance along and across the GSS. However, when including RGB stars in the outer GSS, the [Fe/H]_phot gradients become marginally negative. This suggests that the photometric metallicity along the GSS increases out to ∼30–40 projected kpc before decreasing at larger distances. Furthermore, the photometry predicts a minor asymmetry in the metallicity distribution across the GSS core, where the eastern edge of the GSS appears to have higher [Fe/H]_phot than both the core at n ∼ 1 kpc and the extended western envelope.

The trends gathered from photometry are at odds with those derived from our spectral synthesis–based metallicity measurements (e.g., Figure 4), which show consistently negative [Fe/H] gradients along and across the GSS. Given that the [Fe/H]_phot gradients measured from the abundance sample show the same qualitative behavior as the sample of RGB members and the photometric and spectroscopic [Fe/H] measurements are positively correlated, it is unlikely that biases incurred by selection effects (Section 3.5.1) such as the omission of TiO stars can explain this discrepancy. The probable culprit is the disproportionately metal-rich disparity (0.60 ± 0.11 for the abundance sample) between [Fe/H]_phot and [Fe/H] measurements in the 33 kpc GSS field compared with other fields. A possible explanation is that the necessary assumptions of constant stellar age and α enhancement to determine CMD-based metallicity estimates are particularly inappropriate for the stellar populations probed in this spectroscopic field. In order to minimize this disparity, we would need to assume both older and α-enhanced isochrones when measuring [Fe/H]_phot for this field. Adopting t = 14 Gyr and [α/Fe] = +0.3, ¹⁰ as opposed to t = 9 Gyr and [α/Fe] = 0, reduces the difference between [Fe/H]_phot and [Fe/H] by ∼0.3 to ∼0.2–0.4 dex. We emphasize that using different values for the stellar age and α enhancement will not necessarily resolve this metallicity discrepancy, given that the assumption of mono-age and mono-[α/Fe] stellar populations is unrealistic for GSS stars with a range of stellar ages (Brown et al. 2006; Tanaka et al. 2010) and [α/Fe] (Gilbert et al. 2019; Escala et al. 2020a).

We refer the interested reader to Escala et al. (2020b) for a detailed discussion of the systematics between spectral synthesis– and CMD-based metallicity measurements in the context of M31's stellar halo. We compare the spatial metallicity trends implied by both the spectroscopic and photometric metallicity measurements to those from the literature in Section 4.1.

In Section 3, we measured [Fe/H] gradients out to 33 and 58 kpc as a function of projected M31-centric radius (r_proj), projected GSS-aligned distance (m), and projected absolute distance orthogonal to the GSS (∣n∣). The statistical consistency of the radial and m gradients (Table 2) prompts the question of whether the observed radial gradients are primarily driven by the gradients along or across the GSS. The former (latter) case would indicate that there is little to no intrinsic transverse (aligned) [Fe/H] gradient but rather that the observed transverse (aligned) gradient is an apparent consequence of an intrinsic GSS-aligned (GSS-transverse) gradient combined with the particular spatial sampling of the spectroscopic fields (Figure 1). Thus, we utilized 5 × 10⁴ pairs of transformed parameters sampled from the posterior probability distribution of our gradient model (Section 3) to infer the expected behavior of an apparent transverse [Fe/H] gradient in the GSS by assuming that only an intrinsic aligned gradient is present.

For each slope-intercept pair drawn from the aligned gradient model, we calculated the predicted [Fe/H] value at the observed GSS-aligned coordinate of each RGB star and then assigned this value to the corresponding transverse coordinate. Figure 7 shows the 68% confidence intervals for the [Fe/H] values predicted from the aligned coordinates alone (green envelopes) compared to the "true" [Fe/H] values inferred from the transverse coordinates (gray envelopes). Within both 33 and 58 projected kpc, the GSS-aligned position appears to predict [Fe/H] at a given transverse position, although it is less immediately clear in the 58 kpc case. This indicates that the observed radial gradient in our data is most likely driven by the gradient either along or across the GSS in the inner halo, and tentatively the outer halo, with the caveat that larger samples in the outer halo are required to distinguish between these two trends.

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Motivated by the multiple lines of evidence for an association between the SE shelf and GSS (Gilbert et al. 2007; Escala et al. 2020a), we compared their chemical abundances, defining the sample for each feature from all stars in fields where it is present (Table 1). We computed 〈[Fe/H]〉 and 〈[α/Fe]〉 for the GSS and SE shelf via 10⁴ bootstrap resamplings of their abundance distributions, weighting by substructure probability and the inverse variance of the measurement uncertainty. Table 3 presents the 50th percentiles of the resulting distributions (and the associated uncertainties from the 16th and 84th percentiles), where we included halo stars in the 45 and 58 kpc fields in our calculations (Section 3.1). In summary, the mean chemical properties of the GSS and SE shelf agree within 1σ, regardless of whether we include or exclude the KCC. There is tentative evidence that the SE shelf is both more metal-rich and α enhanced than the GSS and furthermore that the KCC is more metal-rich than the GSS alone, but larger sample sizes are required to confirm these possibilities.

Table 3. Chemical Properties of the GSS and SE Shelf (17–58 kpc)

Comp.	〈[Fe/H]〉	σ([Fe/H])	〈[α/Fe]〉	σ([α/Fe])
GSS+KCC	−0.96 ± 0.06	0.44 ± 0.05	0.40 ± 0.05	0.31 ± 0.03
GSS	−1.03 ± 0.07	0.47 ± 0.05	0.39 ± 0.06	0.34 ± 0.04
SE Shelf	−0.89${}_{-0.08}^{+0.07}$	${0.47}_{-0.05}^{+0.04}$	${0.45}_{-0.05}^{+0.04}$	0.29 ± 0.05

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Figure 8 shows the [Fe/H] and [α/Fe] distribution functions for the GSS, both including and excluding the KCC, and the SE shelf. We constructed the histograms from all [Fe/H] and [α/Fe] measurements in spectroscopic fields known to contain a given feature (Table 1), where we utilized substructure probability (Section 2.2) and the inverse variance of the measurement uncertainty as weights. In order to evaluate whether the [Fe/H] and [α/Fe] distributions are statistically consistent between the GSS and SE shelf, we generated a distribution of p-values using the k-sample Anderson–Darling test. First, we selected all stars that are likely associated with a given feature (p_sub > 0.5). We then perturbed the [Fe/H] and [α/Fe] measurements of these stars by 10⁴ random draws from their Gaussian uncertainties and computed the test statistic between the GSS (including the KCC) and SE shelf for each iteration. We found that we could not reject the null hypothesis that [Fe/H] and [α/Fe] for the GSS and SE shelf are drawn from the same distribution at or below a 10% significance level within the 1σ confidence intervals. This is the case even when adopting a more stringent threshold for substructure membership (p_sub > 0.75) or when excluding the KCC as a contributor to the GSS substructure probability.

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Based on current measurements, it is therefore feasible for the SE shelf to originate from the same progenitor as the GSS. This is consistent with the finding by Gilbert et al. (2007) that the [Fe/H]_phot distributions of M31 RGB stars kinematically associated with the GSS and SE shelf agree when correcting for contamination by the dynamically hot stellar halo, thereby bolstering support for the chemical similarity of the GSS and SE shelf. However, we acknowledge that this apparent similarity between the GSS and SE shelf may be complicated by the presence of spatial [Fe/H] gradients in the GSS, which originate in its progenitor (Section 4.2). Such large-scale [Fe/H] gradients in the GSS may therefore prohibit the existence of a clear [Fe/H] signature for debris related to the merger event, making it more difficult to definitively associate substructure such as the SE shelf with the GSS.

3.5.1. Sample Selection

3.5.2. Definition of GSS-Aligned Axes

3.5.3. Distance Variations along the GSS

Early spectroscopic studies of individual RGB stars in the GSS at 22 and 33 projected kpc revealed a photometric metallicity difference of 0.09 dex (Guhathakurta et al. 2006; Kalirai et al. 2006), supporting the possibility of metallicity variations in the stream as seen from photometry alone (Ferguson et al. 2002; Ibata et al. 2007; hereafter I07). Using a large sample of photometric metallicities of spectroscopically confirmed GSS stars, Gilbert et al. (2009; hereafter G09) corroborated I07's core versus envelope metallicity dichotomy (top left panel of Figure 9) by finding that GSS stars located at 17, 22, and 33 projected kpc near the core were more metal-rich by ∼0.10 (0.53 ± 0.13) dex than GSS stars located at 45 (58) projected kpc (without line-of-sight distance corrections). Gilbert et al. concluded that their defined GSS core has an identical metallicity distribution to the 45 kpc field and is significantly more metal-rich than the envelope as represented by the 58 kpc field.

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The G09 fields are nearly identical to those utilized in this work and target the same stellar populations. Indeed, with regard to [Fe/H]_phot measurements, we find a difference of −0.10 ± 0.05 (0.56 ± 0.15) dex, ¹³ such that the G09 core fields are nearly as metal-rich as the 45 kpc field (more metal-rich than the 58 kpc field). From our spectral synthesis–based metallicity measurements, we find that the G09 core fields are more metal-rich than the 45 (58) kpc fields by 0.63 ± 0.10 (1.62 ± 0.48) dex, which at face value suggests a steeper decline in metallicity between the GSS core and envelope. The difference between the trends predicted by the photometric and spectroscopic metallicities cannot be accounted for by field-to-field variations in estimates of the [Fe/H] bias resulting primarily from the omission of red TiO stars (Section 3.5.1; Figure 9), which modifies the [Fe/H] difference between the core and 45 (58) kpc fields to 0.26 ± 0.10 (0.57 ± 0.48) dex. However, when comparing results from various studies on spatial metallicity variations in the GSS, it is important to acknowledge varying definitions of the stream's core. For example, the G09 fields that define the GSS core are not spatially colocated with the core from I07 (top panels of Figure 9), where the region spanned by the former (latter) covers ∼17–33 (48–66) projected kpc. Thus, the [Fe/H]_phot difference examined by I07 primarily reflects orthogonal metallicity variations beyond 40 kpc in the GSS (bottom right panel of Figure 9), whereas the spatial distribution of the G09 fields presents a more complex picture.

Figure 9 provides a view of metallicity variations in the GSS on equivalent spatial footing, as a function of projected radius, GSS-aligned distance, and GSS-transverse distance, while also placing our spectral synthesis–based [Fe/H] measurements in the context of the literature (Ibata et al. 2007; Conn et al. 2016; Cohen et al. 2018). We substituted G09's [Fe/H]_phot measurements with those from this work (Section 3.2) for a similar set of spectroscopic fields (Table 1) for the sake of homogeneity. We transformed the M31-centric coordinates of the imaging fields from Conn et al. (2016; hereafter C16) and Cohen et al. (2018; hereafter C18) and the area spanned by I07's core and envelope regions into the GSS-aligned coordinate system of Fardal et al. (2006, 2013) for direct comparison with our results.

First, we summarize the methodology and main results of the relevant photometric studies. C16 derived azimuthally averaged RGB metallicities spanning 70 projected kpc along the GSS by modeling PAndAS CMDs as a combination of weighted isochrones and an MW foreground contamination model (Martin et al. 2013). C18 obtained CMD-based metallicities for individual RGB candidates in pencil-beam Hubble Space Telescope/Advanced Camera for Surveys fields from Project AMIGA (Lehner et al. 2020) and Brown et al. (2006) targeting the GSS at 21, 52, and 80 projected kpc. Neither C16 nor C18 correct for contamination of the GSS by M31's kinematically hot stellar halo, although they show that the influence of M31's halo on their results within 50 kpc should not be significant. Both studies found evidence for an increase in [Fe/H]_phot with projected distance along the GSS out to ∼45–50 kpc, after which the behavior of [Fe/H]_phot with GSS-aligned distance becomes less certain owing to heavy MW contamination. ¹⁴ Thus, it is currently unclear whether CMD-based metallicites predict a plateau or a decline in the GSS-aligned gradient beyond ∼50 kpc. As for GSS-transverse distance, the range spanned by the C16 and C18 data is limited to that of the I07 core region, where the net [Fe/H]_phot trend seems to be at most marginally positive.

Our [Fe/H]_phot measurements broadly agree with C16 and C18 between ∼0 and 10 kpc across the GSS and within ∼45 kpc along the GSS (Figure 9). However, our results diverge beyond this latter point, where we find an ∼0.60–0.90 dex lower average metallicity at ∼50 kpc. Potential reasons for this difference could be (1) unaccounted-for contamination in the PAndAS/Hubble Space Telescope data by red MW dwarf stars with high inferred [Fe/H]_phot or (2) issues regarding sample selection and the associated Poisson noise in the sparse outer regions of the GSS. Although neither C16 nor C18 provide constraints in the I07 envelope region, the combination of these measurements with those from this work (and equivalently G09) appear to suggest that the "edge" of the photometrically metal-rich core occurs between ∼20 and 25 kpc across the GSS (see also C18). However, we have shown that it is unclear whether the core-envelope dichotomy visible from photometric metallicities clearly extends to spectroscopic metallicities based on currently available data (Section 3.3), where we cannot distinguish between an intrinsic gradient along or across the GSS.

Figure 9 also demonstrates that the [Fe/H] measurements show an apparent decline with projected distance along the GSS that is inconsistent with the qualitative trends predicted by [Fe/H]_phot measurements in this work, C16, and C18. If the radial [Fe/H] gradient of the stream is intrinsic to the GSS-transverse distance (and not the GSS-aligned distance; Section 3.3), some of this inconsistency could result from our pencil-beam spectroscopic fields at 33, 45, and 58 projected kpc probing metallicity variations between the core and the envelope rather than those between the inner and outer GSS. However, this cannot entirely explain the discrepancy between trends deduced from CMD-based and spectral synthesis–based metallicities, given that it persists for the fields at 17 and 22 projected kpc near the GSS core. Thus, at least some of this discrepancy is likely fundamental to the measurement metholodogies (Section 3.2), where this interpretation is supported by the general similarity between [Fe/H]_phot gradients from various studies. As we have previously discussed (Section 3.1, 3.3), additional spectroscopy in the outer GSS is required to provide improved constraints on the stream's spatial abundance patterns.

Both major and minor merger models for the formation of the GSS broadly reproduce the observed morphological and kinematical features of the stream and its associated shells (Fardal et al. 2006, 2007, 2008, 2013; Mori & Rich 2008; Kirihara et al. 2014; Sadoun et al. 2014; Kirihara et al. 2017; Miki et al. 2016 for minor mergers; Hammer et al. 2010, 2018; Bhattacharya et al. 2019, 2021; D'Souza & Bell 2018 for major mergers). Among minor merger models, rotating, disky progenitors better match the observed asymmetric structure of the GSS than spheroidal counterparts (Fardal et al. 2008, 2013; Kirihara et al. 2017), although neither class of progenitor models can currently account for the existence of the KCC (Gilbert et al. 2019) or the disturbed nature of M31's disk (e.g., Quirk & Patel 2020; Dorman et al. 2015; Bernard et al. 2015; Williams et al. 2015). To first order, major merger models explored thus far can simultaneously explain M31's disk and halo properties, although this does not necessarily disqualify a minor merger from being responsible for the GSS's formation.

Thus, it is currently unknown whether the GSS progenitor had a stellar mass of (1−5) × 10⁹ M_⊙, or ∼ 10¹⁰ M_⊙, as, respectively, predicted by minor and major merger models (see above references). Current observational constraints on the stellar mass of the GSS progenitor from chemical abundance measurements place it between that of the LMC and M32 ((1−5) × 10⁹ M_⊙; Gilbert et al. 2019) when correcting for potential sources of observational bias (Section 3.5.1), which is consistent with predictions of minor merger models for the formation of the GSS. However, Gilbert et al. caution that this cannot be interpreted as direct evidence in favor of a minor merger scenario without knowledge of where the GSS stars originate from in the progenitor, if the progenitor possessed a metallicity gradient. Along with prior studies (Section 4.1), this work has shown that this situation is indeed the case given the observed presence of spatial metallicity gradients in the GSS.

Simulations of minor and major merger scenarios for the formation of the GSS that track stellar metallicity ubiquitously predict the existence of strong gradients in the progenitor in order to approximately match observations (Fardal et al. 2008; Mori & Rich 2008; Miki et al. 2016; Kirihara et al. 2017; D'Souza & Bell 2018; Hammer et al. 2018). Nonetheless, they differ in the details regarding the exact magnitude of the gradient (but less so in its direction; cf. Miki et al. 2016) and the original location in the progenitor of GSS core stars. For example, some simulations posit that the GSS core is constituted by stars originating near the metal-rich center of the progenitor (Fardal et al. 2008; Miki et al. 2016; Kirihara et al. 2017), whereas others postulate that the stream debris comes from more metal-poor regions corresponding to a larger radial range within or on the outskirts of the progenitor (Mori & Rich 2008; D'Souza & Bell 2018; Hammer et al. 2018). Thus, an understanding of how the distribution of GSS-related tidal debris on the sky maps to galactocentric radius in the progenitor is crucial for reconstructing the progenitor's metallicity gradient—and subsequently its average metallicity and inferred stellar mass—from available observational data.

Although the lack of a consensus on the original location of GSS stars in the progenitor limits our ability to directly constrain its metallicity gradient, comparisons between current model predictions and data are informative for identifying potential areas of disagreement. Figure 10 shows CMD-based ([Fe/H]_phot) and spectral synthesis–based ([Fe/H]) metallicity measurements for the GSS in our spectroscopic fields (Table 1) as a function of projected radius and azimuthal angle (defined such that 0° is east and the GSS core is located at ∼ 65°) alongside trends from the models of Kirihara et al. (2017). Their model assumes a minor merger with a GSS progenitor described by a rotating thick disk with a stellar mass of 7.3 × 10⁸ M_⊙, a central value of 〈[Fe/H]〉 = −0.5, and a gradient of Δ[Fe/H] = −0.5 in units of disk scale length (where R_d = 1.1 kpc). Kirihara et al. investigated the metallicity patterns in their simulated GSS analog, which resulted from the initial gradient in the progenitor, predicting that the strongest metallicity variations were azimuthal and located at large projected radii (48–62 kpc). Furthermore, stronger gradients in their model translated to more pronounced metallicity differences between the GSS core and envelope, and metallicity differences along the stream were most prominent in its innermost regions.

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Although the above scenario could be qualitatively consistent with our measurements, Figure 10 clearly illustrates that this model is not able to provide a quantitative match. Considering only our fields within 33 kpc, the predicted trends are generally too metal-rich for the [Fe/H] measurements, even when taking into account [Fe/H] bias terms (Section 3.5.1), although it is more similar to the equivalent [Fe/H]_phot measurements. Additionally, the observed azimuthal behavior of [Fe/H] is more complicated than can be accounted for by the model. Although the former discrepancy could be minimized by assuming a more metal-poor center for the progenitor, a similar effect could presumably be achieved if the GSS core originates from further out in the progenitor's disk than is the case in this model. Additionally considering fields out to 58 kpc highlights the fact that the observed radial metallicity gradient may be much steeper than that predicted by this model, which could indicate a need for a stronger initial gradient in the progenitor.

Given that few GSS formation models that track stellar metallicity take the additional step of quantifying the predicted abundance ratios (Fardal et al. 2008; Miki et al. 2016; Kirihara et al. 2017), it is unclear whether they can generally reproduce sufficiently strong gradients in comparison to our spectroscopic and photometric metallicity measurements. From a statistical sample of major merger scenarios for M31's formation, D'Souza & Bell (2018) found that tidal debris from GSS progenitor analogs exhibited metallicity variations as large as 1 dex but did not further quantify such results. ¹⁵ Furthermore, although this class of simulations demonstrate core-envelope dichotomies (Fardal et al. 2008; Mori & Rich 2008; Kirihara et al. 2017; D'Souza & Bell 2018), they do not generally predict observed gradients along the stream, as may exist in our data. This is excepting the models of Miki et al. (2016), which produced negative radial gradients of approximately −0.01 dex kpc⁻¹ (compared to −0.018 ± 0.003 dex kpc⁻¹; Table 2). In the case of Fardal et al. (2008), the initial gradient in the progenitor is calibrated to the results of Ibata et al. (2007), as opposed to being set by the relationship between its stellar mass and metallicity. In general, current GSS formation models appear to be capable of generating the morphological structure of the stream and its associated shells despite assuming a wide range of mass and metallicity properties for the progenitor (e.g., Hammer et al. 2018), therefore limiting the predictive power of any given modeled metallicity gradient for the GSS.

Additional studies that perform detailed modeling of the GSS metallicity distribution and careful comparisons to observations are therefore needed. In particular, models that also track α elements will be instructive. The lack of significant spatial [α/Fe] gradients in the GSS (Section 3) suggests that its progenitor may have been uniformly α enhanced or that its [α/Fe] variations are below the detectable threshold set by our typical measurement uncertainty (i.e., ≲0.3). The presence of spatial [α/Fe] variations in Local Group dwarf galaxies, such as MW dwarf spheroidal satellite galaxies and the Magellanic Clouds (e.g., Kirby et al. 2011; Nidever et al. 2020), has generally not been quantified, thus largely precluding comparisons of observational expectations for [α/Fe] gradients to the GSS. The exceptions include chemical abundance studies of M31 satellite dwarf galaxies (Vargas et al. 2014b), where no strong evidence for significant [α/Fe] gradients was found, and Sgr (Hayes et al. 2020). Hayes et al. measured an [α/Fe] gradient of (0.1 − 1.2) × 10⁻³ dex deg⁻¹ (or 0.06−0.15 dex in absolute difference) between the Sgr core and Sgr streams—in addition to weaker internal [α/Fe] gradients in the streams—that they interpreted as reflecting Sgr's [Fe/H] gradient combined with the characteristic anticorrelation between [α/Fe] and [Fe/H] in dwarf galaxies (e.g., Shetrone et al. 2001; Venn et al. 2004; Kirby et al. 2011). Given that the GSS possesses a significant [Fe/H] gradient (Table 2) and shows evidence for a decline in [α/Fe] with [Fe/H] in some spectroscopic fields (Section 3.5.1), the GSS could therefore feasibly exhibit [α/Fe] variations of ≲0.3 dex.

Regardless of whether an [α/Fe] gradient exists in the GSS, its high average α enhancement (+0.40 ± 0.05; Table 3) can provide constraints on the nature of the GSS progenitor and thus formation scenarios for the stream. From the first [α/Fe] measurements of individual RGB stars in the GSS, Gilbert et al. (2019) concluded that the GSS progenitor must have formed stars efficiently enough to enrich to high metallicity ([Fe/H] ∼ −0.9) before experiencing a precipitous decline in its star formation rate such that the yields of Type Ia supernovae dominated over those of core-collapse supernovae. Indeed, the GSS progenitor must have had more efficient star formation than that of the present-day massive dwarf galaxies of the Local Group (Hasselquist et al. 2017; Mucciarelli et al. 2017 for Sgr; Pompéia et al. 2008; Lapenna et al. 2012; Van der Swaelmen et al. 2013; Nidever et al. 2020 for the Magellanic Clouds) or even the dominant progenitor of the MW's stellar halo (Gaia-Enceladus-Sausage; Haywood et al. 2018; Helmi et al. 2018; Naidu et al. 2020), which have 〈[α/Fe]〉 ≲ +0.2 dex. The observed average α enhancement of the GSS—and by extension, its progenitor—is therefore unusual compared to expectations of its stellar mass from dynamical modeling in a minor merger scenario (M_⋆ ∼ (1−5) × 10⁹ M_⊙).

Even a scenario in which a massive progenitor dwarf galaxy (M_⋆ ∼ 10⁹ M_⊙) is accreted sufficiently early to truncate its star formation history on the high [α/Fe] plateau (e.g., Johnston et al. 2008; Lee et al. 2015) is unlikely to explain the observed 〈[α/Fe]〉 of the GSS. Minor merger models for the GSS place its first pericentric passage and accompanying formation of the stream at ≲ 1 Gyr ago (Fardal et al. 2006, 2007, 2008, 2013; Mori & Rich 2008; Kirihara et al. 2014; Miki et al. 2016), where the cosmologically motivated models of Sadoun et al. (2014) time the initial accretion of the progenitor at ∼3 Gyr ago. In addition, the most recent star formation in the GSS occured ∼4 Gyr ago, where the GSS has a typical stellar age of ∼8 Gyr (Brown et al. 2006). Thus, a lower-mass progenitor would have produced lower 〈[α/Fe]〉 than is observed in the GSS: the progenitor's star formation would have quenched via interaction with M31's ionized circumgalactic medium (Lehner et al. 2020) only within the last few gigayears, providing sufficient time for Type Ia supernovae to deplete [α/Fe] with respect to [Fe/H]. The extended star formation history of the GSS similarly constrains the scenario of a high-mass progenitor (M_⋆ ∼ 10¹⁰ M_⊙), although the interaction between M31 and the progenitor can begin as early as ≳5–10 Gyr ago in this case (D'Souza & Bell 2018; Hammer et al. 2018).

The most significant difference between a major versus minor merger scenario for the average α enhancement of the GSS is therefore not the accretion time of the event but rather the ability of the progenitor to sustain efficient star formation—and high 〈[α/Fe]〉—over many gigayears such that the progenitor could simultaneously enrich to high [Fe/H] (up to at least −0.96 dex; Table 3). Simulations have shown that massive, star-forming MW-like galaxies (M_⋆ ∼ 10^(9.7−10.7) M_⊙) can produce [α/Fe] ∼ +0.4 dex at [Fe/H] ∼ −1 dex (Mackereth et al. 2018; Naiman et al. 2018; Gebek & Matthee 2021), in broad agreement with the abundance ratios observed in the GSS. On the observational front, Gallazzi et al. (2021) recently presented the first measurements of [α/Fe] in star-forming, massive galaxies (M_⋆ ∼ 10^(9.5−11.5) M_⊙) beyond the Local Group using >110,000 z = 0 galaxies in SDSS DR7 (Abazajian et al. 2009), confirming that the positive correlation between [α/Fe] and stellar mass observed for quiescent massive galaxies (e.g., Thomas et al. 2005; Gallazzi et al. 2006; Conroy et al. 2014; Segers et al. 2016) extends to these systems. However, Gallazzi et al. found that star-forming massive galaxies tend to have lower star-formation-history-integrated [α/Fe] at a given stellar mass, with a mean value of [α/Fe] ∼ +0.15 dex at M_⋆ ∼ 10^10.5 M_⊙ and 1σ upper limits of ∼+0.3 dex. Assuming that the average α enhancement of the GSS is representative of the progenitor, ¹⁶ the GSS progenitor would be within ≲1.5σ of this relation in a major merger scenario (with the caveat that the progenitor halted star formation at z ∼ 0.4, although it was star forming at the time of accretion). We therefore conclude that a massive GSS progenitor (M_⋆ ∼ 10¹⁰ M_⊙) provides a more natural framework for explaining the high α enhancement and metallicity gradient of the GSS.