[α/Fe] ABUNDANCES OF FOUR OUTER M31 HALO STARS

G12 identified over 1600 M31 halo stars as part of the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey. They used a combination of five diagnostics to calculate the relative likelihood of membership in the M31 halo versus a foreground MW population (Gilbert et al. 2006). These diagnostics utilize photometric and spectroscopic measurements: the star's radial velocity, its position in a (V − I, I) color–magnitude diagram (CMD), its magnitude in the narrowband DDO51 filter, the strength of the Na i absorption line at 8190 Å, the difference between photometric and calcium triplet (CaT)-based metallicities. Stars are designated as M31 stars if it is more probable they are red giant branch (RGB) stars at the distance of M31 than MW foreground stars. Stars are designated as having a high likelihood of M31 membership if it is three times more likely that they are M31 RGB stars rather than MW stars. In Section 2.3, we additionally assess whether the stars are M31 halo or M31 dwarf satellite members.

To measure metallicities and alpha abundances, we obtained higher S/N spectra of halo stars from the sample described in Section 2.1. The targets were selected due to their relative proximity to various M31 satellites studied by V14, enabling us to observe them using the multi-object masks designed for the satellite targets.

The Keck/DEIMOS spectra span the wavelength range 6300 < λ < 9100 Å and have a resolving power of λ/Δλ ∼ 6000. The data reduction for the additional spectra follows that of the G12 sample, and was performed with a modified version of the spec2d/DEEP pipeline (Cooper et al. 2012; Newman et al. 2013) adapted to stellar spectra (Simon & Geha 2007; Kalirai et al. 2010).

Including the new observations, we identified 10 likely M31 halo stars with sufficient S/N (≳ 15 Å⁻¹) for chemical abundance analysis. Four of these candidates have a high likelihood of being M31 halo stars (Section 2.1). The other six stars are marginally identified as M31 halo stars. The likelihood distributions of MW foreground stars and M31 halo stars overlap, and the number of MW foreground stars in the sample is large at the distances from M31's center considered here (Figure 3 of G12). Therefore, we expect contamination from MW foreground stars among the stars that are marginally identified as M31 stars. For these reasons, we restrict our sample to the four high likelihood M31 members.

The four stars in our sample are located at projected distances from M31's center of R_proj ∼70–140 kpc. At these distances, the contribution from an in-situ halo component is expected to be negligible. Instead, the halo should be dominated by metal-poor stars belonging to an accreted component (Zolotov et al. 2012).

Due to the proximity of the sample stars to various M31 satellites, we check whether our stars could be members of the nearby satellites. In the top panels of Figure 1, we plot the relative location in position-velocity space between each program halo star and the nearest satellite. The plots also include other high-likelihood halo stars (G12) as well as satellite stars (Ho et al. 2012; Tollerud et al. 2012). The halo stars fall far from the locus of satellite stars. Given the small velocity difference but large projected separation of the sample stars near And III, we cannot rule out a past connection to that satellite. However, the stars cannot presently be bound to And III because they lie at twice the projected tidal radius. In the bottom panels, we show CMDs for the same data as in the top row. Due to the similar line-of-sight distances to M31 and the satellites, CMDs are not a good discriminant of halo versus satellite membership.

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To find the best-fitting synthetic model, we use wavelength regions sensitive to Fe or alpha elements (here Mg, Si, Ca, and Ti) and minimize the χ² flux difference between the spectrum and the grid models. The synthetic grid samples a wide range of T_eff, log g, [Fe/H], and [α/Fe]. After measuring the best-fitting abundances, we apply a correction factor to [α/Fe] derived by V14 so that [α/Fe] better represents an unweighted average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe].

Due to the large distance to M31, our spectra have relatively low S/N. Using synthetic spectra, V14 confirmed that our method can measure both alpha-solar (∼+0.0) and alpha-rich (∼+0.4) values in luminous RGB stars using S/N ≳ 15 Å⁻¹ spectra with more than 93% completeness (see Figure 3 of V14).

In V14, we fixed log g from the best color and magnitude fit to isochrones shifted to the line-of-sight distance, D_LOS, of each galaxy. For field halo stars, D_LOS is loosely constrained by the assumption that the stars lie within the M31 stellar halo. To test the change of abundance with assumed distance, we perform the abundance analysis independently for nine assumed distances, ranging between $D_{{\rm {\rm M31}}} \pm \Delta$D (see lower panels of Figure 1). $D_{{\rm {\rm M31}}}$ is the distance to M31 (779 kpc; Conn et al. 2012), and ΔD is the line-of-sight distance between M31 and the outskirts of the stellar halo at the projected distance to each star from M31. We assume a spherical stellar halo⁷ with radius R_halo = 175 kpc, equal to the projected distance to M31 of the most distant halo stars securely identified by G12.

We show the results of this test in Figure 2. The top panels show the variation in T_eff and log g with assumed D_LOS. For larger D_LOS, T_eff tends to increase (slightly) while log g decreases. The lack of significant variation in T_eff is due to the primary dependence of T_eff on color and not on luminosity. The variation in log g is due to the star occupying a higher-luminosity position in the CMD for larger assumed D_LOS. For the yellow star, stellar parameters are only shown for D_LOS ⩽ $D_{{\rm {\rm M31}}}$; for larger D_LOS, the star lies above all isochrones, and would instead have to be considered a TP-AGB star. The number of TP-AGB stars is highly model dependent, but observations with large AGB samples suggest that for low metallicity systems, the fraction of TP-AGB relative to RGB stars is less than a few percent (Girardi et al. 2010). Thus, we suggest that it is improbable that this star is a TP-AGB member.

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The bottom two panels show how changes in D_LOS translate to changes in [Fe/H] and [α/Fe]. All abundance measurements vary by less than ∼0.15 dex, a change equal or smaller than all 1σ measurement uncertainties. We note that due to the centrally concentrated M31 halo it is most likely that each star will have a line-of-sight distance similar to that of M31.

Another source of uncertainty is stellar age, since stellar parameters are measured using a grid of 12 Gyr isochrones. We test for the dependence on isochrone age by using younger, 4 Gyr isochrones. The changes in [Fe/H] and [α/Fe] are −0.02 and −0.06 dex, respectively, lower than our minimum measurement uncertainties. Given the lack of significant change in abundances, we assume D_LOS = D_M31, and use only 12 Gyr old isochrones for the analysis below.

To draw conclusions from our small sample, we determine the sample average [α/Fe] ratio in two ways. First, we measure the unweighted average and its uncertainty taking into account the small sample size from the Student-t distribution. We obtain 〈[α/Fe]〉 = +0.20 ± 0.20. An inverse-variance weighted mean yields 〈[α/Fe]〉 = +0.28 ± 0.12, but Monte Carlo tests by V14 suggest that this weighting could bias the average high by ∼ + 0.05–0.10 due to a modest anti-correlation between [α/Fe] and its uncertainty. Second, we recalculate 〈[α/Fe]〉 by weighting our measurements by their expected fractional contribution to the halo from Gilbert et al.'s (2014) metallicity distribution function (MDF), shown in Figure 4. We use the thicker histogram, corresponding to stars at the same projected distances from M31 as our stars. We draw 10,000 realizations of [Fe/H] and [α/Fe] from each of our four stars using their best-fit values and individual errors. Each realization is thus a sample of four ([Fe/H], [α/Fe]) pairs. We reorder the pairs by [Fe/H] and calculate weights for each [α/Fe] value as the area under the normalized MDF bounded by the midpoint between the [Fe/H] value of each of our data points and the previous/next value. We truncate the MDF to the range of [Fe/H] abundances of our stars. From the 10,000 realizations, we measure 〈[α/Fe]〉 = +0.19 ± 0.14, in agreement with the simple average.

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We next compare [α/Fe] between the MW and M31 halos. For the MW, we use the homogeneous sample by Ishigaki et al. (2012), who classify stars as inner or outer halo stars kinematically. We select all 68 stars with reported measurements of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe] to calculate [α/Fe] consistently with our own definition of [α/Fe] (see Section 3.1). The MW points are also plotted in Figure 3. We calculate 〈[α/Fe]〉 for both MW inner and outer halo subsamples, finding unweighted averages of 〈[α/Fe]〉 = +0.23 in both cases. Thus, our average [α/Fe] value for M31's outer halo stars (〈[α/Fe]〉 = 0.20 ± 0.20) is consistent with the MW value within the uncertainties (in the same range of metallicities).

The lower [α/Fe] ratios in MW surviving satellites relative to MW halo stars (e.g., Venn et al. 2004; Kirby et al. 2011) have been used to infer that MW halo progenitors had short-lived and rapid star formation histories relative to the surviving satellites (Robertson et al. 2005). Using our sample and V14, we compare in Figure 5 the alpha abundances between the halo and the four present-day M31 satellites with the largest samples (And V, And VII, And II, and NGC 185). The satellites range in luminosity from 7 × 10⁵ L_☉ (And V) to 1.8 × 10⁸ L_☉ (NGC 185). Thus, they sample a wide range of the satellite luminosity function except for the faint end.

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The average [Fe/H] of our halo sample is most similar to those of the less luminous And V and And VII, whereas And II and NGC 185 are more metal-rich. Our small sample size precludes strong statistical comparisons between halo and satellite abundances, but we make a first attempt by comparing 〈[α/Fe]〉. V14 measured average [α/Fe] ratios of 0.12 ± 0.09, 0.30 ± 0.09, 0.03 ± 0.09, and 0.12 ± 0.09 for And V, And VII, And II, and NGC 185, respectively. Thus, none of the satellites have an 〈[α/Fe]〉 value discrepant by more than 1σ from the halo value calculated in Section 4.1, 〈[α/Fe]〉 = +0.20 ± 0.20. The comparison between the halo and satellites must thus be revisited with larger samples.