Evidence for a Sub-Chandrasekhar-mass Type Ia Supernova in the Ursa Minor Dwarf Galaxy

At [Fe/H] = −1.35 dex, the most metal-rich star in the CH10 sample, COS 171, has an extraordinary chemical composition, including large deficiencies (exceeding 0.6 dex) of the [C/Fe], [Na/Fe], [Sc/Fe], [V/Fe], [Mn/Fe], [Ni/Fe], [Cu/Fe], and [Zn/Fe] ratios, as well as subsolar ratios, below −0.3 dex, for [Mg/Fe], [Ca/Fe], [Ti/Fe], [Cr/Fe], and [Co/Fe].

In the following discussion of COS 171, we consider only the UMi abundance results of CH10 in order to avoid complications from systematic measurement differences between studies.

Figure 1 shows [X/Fe] versus [Fe/H] in UMi for the sample of stars studied by CH10, shown with small red crosses, compared to the MW halo, and thick and thin disks (black symbols). It is immediately obvious that UMi shows depleted [α/Fe] ratios, with a general trend that is qualitatively consistent with the scenario of MB90, in which dwarf galaxies are predicted to show the decline in [α/Fe] at lower [Fe/H] than the MW due to reduced SFR. Since this reduction of [α/Fe] is thought to be due to the contribution of iron from SNe Ia, the UMi stars appear to show an increasing, and relatively large, SN Ia/SN II ratio. Notably, the most iron-rich star in UMi, COS 171 (shown as the large filled red circle), exhibits extraordinarily low [α/Fe] ratios compared to any MW study.

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On closer inspection, Figure 1 shows that, excluding the most metal-rich star in UMi, the [Mg/Fe] ratios in UMi are not as depleted as the [Si/Fe], [Ca/Fe], and [Ti/Fe] ratios; indeed, the [Mg/Fe] ratios appear normal compared to the MW halo (again, except for the most metal-rich UMi star). If [α/Fe] deficiencies in dwarf galaxies are supposed to be due to a reduced SFR resulting from excess SN Ia iron at low [Fe/H], as predicted by MB90, then the halo-like [Mg/Fe] in UMi stars is unexpected: naively, all [α/Fe] ratios should decline together.

The implied [Mg/Ca] enhancement, near +0.3–0.4 dex, might be explained by an overrepresentation of massive SNe II. Much larger [Mg/Ca] ratios, near +0.95 dex, have been seen in the Hercules dwarf (henceforth Her) by Koch et al. (2008). Because Mg production is made almost exclusively by massive core-collapse SN II events with progenitor masses exceeding ∼30 M_⊙ (e.g., Woosley & Weaver 1995), the high [Mg/Ca] ratios in Her indicate enhanced pollution by high-mass SN II events. Koch et al. (2008) suggested that for Her, this could result from stochastic sampling of the initial mass function (henceforth IMF) that, by chance, favored massive stars. However, the probability of randomly selecting only massive stars, above 30 M_⊙, from the IMF diminishes rapidly with the number of samplings. Such a mechanism could only occur if a small number of SN II events (fewer than 11) produced the Her chemical composition. Similarly, the enhanced [Mg/Ca] ratios in UMi may be the signature of the stochastic sampling of the SN II IMF in the chemical evolution of this dwarf galaxy.

We note that in Figure 1 the [Mg/Fe] ratio for COS 171 is markedly lower than would be extrapolated from the trend at lower [Fe/H]. Indeed, while the bulk of UMi stars show [Mg/Ca] ∼+0.3 dex, for COS 171, [Mg/Ca] = +0.0 dex. This suggests some production of Ca in the composition of COS 171.

The iron-peak elements in Figure 2 show generally good agreement with the MW stars, but severe underabundances for the most metal-rich UMi star, COS 171. In particular, the odd-numbered elements Sc, V, Mn, and Cu are neutron-rich, so their deficiency suggests a rather low neutron excess, η (or equivalently, high electron fraction, Y_e).

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It occurs to us that the excessively low [X/Fe] ratios for 10 of the 27 measured elements in COS 171, shown in Figures 1 and 2, might be largely explained by the addition of nearly pure iron to a pre-existing composition. In Figures 3 and 4, we show the UMi [X/H] versus [Fe/H] LTE abundances from CH10; some panels show a 1:1 line. It is clear from these figures that a simple shift to lower [Fe/H] by ∼0.7 dex would bring the COS 171 [X/H] ratios into approximate consistency with the more metal-poor members of the galaxy, at least for Na, Mg, Sc, Cu, Ni, Zn, Y, and Ba.

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Figures 3 and 4 suggest that COS 171 resulted from ∼0.7 dex of Fe added to the pre-existing galaxy composition. Given that the COS 171 [Fe/H] = −1.35 dex, a pre-existing composition of [Fe/H] ∼ −2.05 dex is suggested. The CH10 star with metallicity closest to our putative pre-existing composition is UMi 28104, at [Fe/H] = −2.08 dex. Because UMi 28104 has a composition similar to the more metal-poor stars in UMi, with abundance ratios fairly typical of dwarf galaxy stars in other systems (e.g., Shetrone et al. 2001), we take the chemical composition of UMi 28104 to indicate that of UMi just prior to the enrichment event that produced COS 171.

Figure 5 shows the abundance ratios of COS 171 relative to the standard, UMi 28104 (i.e., this is the difference in log abundances); we emphasize that this is not the difference in the number of atoms.

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The abundance ratios in Figure 5 not only highlight the enhanced elements in COS 171, but thanks to the similar stellar atmosphere parameters of UMi 28104, they also mitigate a number of systematic measurement errors (e.g., gf values, systematic model atmosphere errors, non-LTE effects, temperature-scale errors, etc.). However, random errors due to EW measurement and abundance scatter due to random atmosphere parameter uncertainties persist. While the abundance ratios in Figure 5 are based on the CH10 LTE abundances, the points in the figure have been corrected for differential non-LTE effects, whenever possible (see Section 2.4).

Error bars in Figure 5 were taken from the abundance dispersions given by CH10, or in the case of oxygen from the EW uncertainties, combined in quadrature with random errors arising from uncertainties in the spectroscopic stellar atmosphere parameters, as indicated by the CH10 Fe i abundances. The main difference between the ratios presented in Figure 5 compared to the CH10 LTE results is for Mn: with non-LTE corrections, the Mn enhancement in COS 171, at +0.11 dex, is only 1.2σ from zero, whereas the uncorrected CH10 result is +0.38 dex. In Figure 5, the displayed oxygen abundance ratio is not from CH10, but indicates the value found in this work (see Section 2.3) from the original CH10 spectra. Thus, we find no oxygen enhancement for COS 171 relative to UMi 28104, whereas the original CH10 results suggested an oxygen abundance for COS 171 higher by 0.31 dex.

Figure 5 shows strong enhancements of neutron-capture elements (i.e., elements heavier than zinc), increasing with increasing atomic number, which appears to be due to an r-process enrichment event that affected all UMi stars above [Fe/H] ∼ −1.9 dex. Since three such r-process rich stars do not share the unusual iron-peak composition of COS 171, we assume that the r-process enrichment event was an unrelated phenomenon.

Excluding the neutron-capture elements, Figure 5 shows clear detection of Si, Ca, Cr, and Fe enhancements in COS 171, well above the individual measurement uncertainties. Marginal detections, comparable to the estimated error bars, occur for C, Ti, V, Mn, and Ni, while O, Na, Mg, K,⁶ Sc, Co, Cu, and Zn show no evidence for enhancement.

As a check on the CH10 results, for UMi 28104 and the unusual UMi star COS 171, we have employed the CH10 equivalent widths (EWs) and atmosphere parameters to compute element abundances, using the 2014 version of the LTE spectrum synthesis program MOOG (Sneden 1973). Our abundances are in very good agreement with CH10, including the excitation temperatures derived from Fe i lines, thus supporting the unusual composition of COS 171 claimed by CH10.

The CH10 abundance of oxygen in COS 171 was based on only two lines: [O i] at 6363 Å and O i at 7771 Å, with putative EWs of 12.6 mÅ and 8.5 mÅ; for UMi 28104, only the 6363 Å line was measured, with an EW of 8.8 mÅ. These EWs are strongly affected by noise, given the 1σ EW uncertainty of ∼4 mÅ, which explains the large abundance difference derived from the two lines in COS 171.

Curiously, the [O i] line at 6300 Å, which has a larger gf value than the 6363 Å line (roughly three times stronger), was not employed by CH10.

In our comparisons of observed and predicted yields from a variety of nucleosynthesis sites, the CH10 oxygen abundance showed significant discordance with abundances of other elements, such as Mg. We therefore elected to re-analyze the original CH10 Keck/HIRES spectra of COS 171 and UMI 28104, which we downloaded from the Keck Archive.⁷ Reduction to one-dimensional spectra was performed using the program makee, and EWs were measured with the IRAF splot routine.

These spectra show that the 6363 Å [O i] and O i 7771 Å lines are, indeed, extremely noisy in COS 171 and UMi 28104. The [O i] line at 6300 Å has a significant EW and should be readily measured; however, in the CH10 UMi spectra, this line is blended with a comparable telluric O₂ intercombination (P7) line from the (2–0) b–X ${}^{1}{{\rm{\Sigma }}}_{g}^{+}$–${}^{3}{{\rm{\Sigma }}}_{g}^{-}$ electronic vibration–rotation transition. This telluric blend suggests why CH10 did not employ the [O i] 6300 Å line. In UMi 28104, the [O i]/O₂ blend at 6300 Å has a total EW of 42.8 mÅ, while for COS 171 the feature has a total EW of 35.8 mÅ. We estimated the strength of the blending telluric O₂ line from the EW of its spin doublet, located 0.78 Å redward. The two P7 spin-doublet lines have very similar, but not identical, EWs in telluric standard spectra of hot stars, and the redder of the doublet lines is unblended in the UMi stellar spectra. We computed the strength ratio of the O₂ line pair from a high S/N spectrum of a telluric standard B star, which then enabled the strength of the O₂ contamination of the [O i] 6300 Å feature to be computed from the unblended O₂ line.

For UMi 28104, the telluric-corrected [O i] 6300 Å EW is 21.8 mÅ, while for COS 171 the line is weaker, at 12.1 mÅ. Incidentally, these values suggest 6363 Å [O i] line EWs of 7 and 4 mÅ, respectively (compared to the CH10 values of 8.8 and 12.6 mÅ). Thus, the 6363 Å lines are too weak compared to the measurement uncertainty, of 1σ ∼ 4 mÅ, to allow reliable oxygen abundance measurement. For this reason, we rely only on the [O i] line at 6300 Å for oxygen abundances in the UMi stars.

Oxygen abundances were computed here from our telluric-corrected EWs for the [O i] 6300 Å line, using the spectrum synthesis program MOOG (Sneden 1973), the stellar model atmosphere grid of Kurucz,⁸ and the atmosphere parameters given in CH10. We find an [O/H] of −1.616 and −1.712 dex for UMi 28104 and COS 171, respectively, on the meteoritic solar abundance scale of Asplund et al. (2009). Curiously, COS 171 has a lower [O/H], by 0.10 dex, despite its significantly higher [Fe/H], but since this oxygen abundance difference is within the measurement uncertainty of 0.15 dex, the two stars might reasonably have the same oxygen abundance.

We also employed the CH10 spectra to check the measured EW for critical species, including potassium, for which only the K i line at 7699.0 Å was used to determine potassium abundances. We measured a K i line EW of 105 mÅ for COS 171, which is significantly smaller than the 130 mÅ in CH10. Unfortunately, we find no reasonable explanation for the difference, since the data appear to be completely inconsistent with the high published EW. However, we confirmed the CH10 K i line EW for UMi 28104, at 109 mÅ. Our K i EW measurement resulted in a decreased potassium abundance for COS 171, at ε(K) = 3.28 dex, which is within 0.01 dex of the value found for UMi 28104. Thus, there appears to have been no measurable potassium production by the progenitor event of COS 171.

Our use of star UMi 28104 as a comparison to COS 171 both accounts for the pre-existing UMi composition present in COS 171 and eliminates constant systematic effects, such as log gf scales.

One important correction enabled by taking differences between COS 171 and UMi 28014 is that these stars are both metal-poor RGB stars and both likely suffer similar non-LTE effects on the derived LTE abundances. Thus, to first order, the non-LTE effects cancel out when comparing COS 171 to UMI 28104, but because the latter is more metal-poor, by ∼0.7 dex, differential non-LTE effects are possible. In particular, non-LTE effects are typically more extreme in more metal-poor stellar atmospheres (e.g., Asplund 2005; Collet et al. 2005).

We refer the reader to Asplund (2005) for a review of non-LTE effects in stellar atmospheres, as well as computational aspects, caveats, and limitations due to the paucity of known collisional rates.

In order to evaluate the differential non-LTE abundance corrections, and thus compare the abundances here with predicted nucleosynthetic yields, we have searched the literature for non-LTE abundance corrections appropriate for the COS 171 and UMi 28104 atmosphere parameters; this includes the lines used for the abundances of each element. Unfortunately, not all lines of all elements have been investigated, and we could not find non-LTE calculations for vanadium.

Incomplete coverage of stellar atmosphere parameter space is a problem that prevents us from estimating the differential non-LTE abundance corrections between COS 171 and UMi 28104 for some elements; for example, the focus on warm dwarfs in Yan et al. (2015, 2016) prevents reliable differential non-LTE abundance corrections for copper.

In Table 1 we list non-LTE corrections for a variety of species in COS 171 and UMi 28104; when possible, we have preferred results from Bergemann⁹ and collaborators, because that group's results include more species than other studies. We make no evaluation of which source of non-LTE corrections is more reliable.

Fortunately, the non-LTE correction differences in Table 1 for most elements are less than 0.10 dex, with the exception of those derived from lines of Ti i, Mn i, and Co i. Since the yield of Mn is sensitive to the neutron excess during explosive nucleosynthesis, it is a useful element for diagnostic purposes; however, unfortunately, Mn abundances suffer from very large non-LTE corrections.

As Table 1 shows, the Fe i non-LTE abundance corrections for COS 171 are smaller than those for UMi 28104, in the same sense as a number of other species; this mitigates, to a small extent, the deviation of the non-LTE corrected [X/Fe i] ratios from the LTE values.

In Table 2, we present our final adopted LTE abundances, non-LTE corrections, and random 1σ X/Fe abundance uncertainties for COS 171 and UMi 28104. The random X/Fe abundance uncertainties were based on the reported abundance dispersions from CH10 combined in quadrature with the abundance errors due to 1σ random T_eff and microturbulent velocity uncertainties of 30 K and 0.05 km s⁻¹, respectively (random gravity and metallicity uncertainties have negligible effect so were ignored). These 1σ spectroscopic parameter uncertainties were deduced here from the 1σ uncertainties in the slope of CH10 Fe i abundance correlations with excitation potential and equivalent width, respectively.

Table 2 constitutes the abundance data for comparison with a variety of explosive stellar nucleosynthesis scenarios used in this work.

In Table 3, we compare the raw LTE and non-LTE corrected [X/Fe] ratios of a handful of diagnostic elements in COS 171 with predicted element yields for various explosive events.

For core-collapse SN II yields, we compare with the predictions of Woosley & Weaver (1995, henceforth WW95) and Kobayashi et al. (2006, henceforth K06); for pair instability supernova (PISN) predictions, at Z = 0, we compare with the results of Heger & Woosley (2002, henceforth HW02), while for Z = 0.001 PISNe, we use the result of Kozyreva et al. (2014). For predicted SN Ia yields of various masses and metallicities, we consider the Chandrasekhar-mass DDT models of Badenes et al. (2003, 2008b)¹⁰ and Yamaguchi et al. (2015), and the sub-Chandrasekhar-mass models of E. Bravo (2016, private communication; henceforth the Bravo models) introduced in Yamaguchi et al. (2015), calculated with a version of the code described in Bravo & Martínez-Pinedo (2012).¹¹ In particular, we seek predicted yields that could potentially reproduce the unusually low [Mn/Fe], [Ni/Fe], and [α/Fe] ratios seen in COS 171, as displayed in Figures 1 and 2.

From Table 3, one can immediately see that massive (e.g., ≥20 M_⊙), core-collapse SNe II fail to reproduce the COS 171 composition because of their expected large α-element yields (e.g., Si, Ca); the situation would be worse for more massive SNe II, especially for [Mg/Fe], which is overproduced in very massive SNe II (e.g., WW95, K06). Table 3 shows that massive SN II also overproduce C, V, Cr, and Mn relative to COS 171.

Low-mass SNe II, such as the 12 M_⊙ and 13 M_⊙ models of WW95 and K06, respectively, produce low enough α-elements to be consistent with COS 171, but they still significantly overproduce carbon and nickel relative to COS 171. We note that the yields for Z = 0, 10 M_⊙ SNe II predicted by Heger & Woosley (2010) indicate [Ni/Fe] ratios close to the solar value, well above the measured COS 171 value at −0.56 dex.

For PISNe, the Z = 0 HW02 260 M_⊙ [X/Fe] yields for C, Si, Ca, V, Cr, and Mn are fairly close to the low values seen in COS 171, but the predicted [Ni/Fe] ratio is too high by more than ∼0.5 dex. The 250 M_⊙, Z = 0.001 PISN model of Kozyreva et al. (2014) gives a very poor match to COS 171, and in particular cannot explain the low X/Fe values for Si, Ca, Cr, Mn, and possibly Ni.

For the DDTa Chandrasekhar-mass SN Ia model, Table 3 shows that C/Fe, Si/Fe, and Ca/Fe ratios are low enough to fit COS 171, but Cr/Fe, Mn/Fe, and Ni/Fe fail significantly.

The sub-Chandrasekhar Bravo models indicate Mn and Ni abundances low enough to match the observed COS 171 Mn/Fe and Ni/Fe ratios for almost all models presented. The 1.06 M_⊙ sub-Chandrasekhar-mass model predicts [X/Fe] suitably low for all diagnostic species listed in Table 3, except for chromium, where the measured [Cr/Fe] ratio exceeds the prediction by 1.5σ times the random measurement uncertainty.

Predicted yields for DDT models added to the UMi 28104 background composition, at two deflagration to detonation transition densities (DDTa and DDTc; e.g., Badenes et al. 2003, 2008b), and a range of metallicities are shown in Figure 6. We note that the neutron-excess increase due to the pre-explosion simmering phase (e.g., Piro & Bildsten 2008) was not included in these calculations. Thus, the large increase in neutron excess due to the pre-explosion carbon-burning simmering phase neutronization does not occur in these models. However, efficient neutron captures do occur close to the center of the WD during the early deflagration phase of the explosion, despite the relatively low initial central density near 2 × 10⁹ g/cm⁻³, and is the likely source of Mn production of these incomplete models.

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In the study of Piersanti et al. (2017), which included the simmering effect, the neutron excess at explosion for their lowest metallicity DDT models always exceeds 0.668 × 10⁻³, equivalent to a metallicity of z ∼ 0.007. Thus, the Badenes et al. (2003, 2008b) DDT model predictions with metallicity less than z ∼ 0.007 (giving the lowest predicted Mn/Fe ratios) are not expected to occur.

Generally, however, the Badenes et al. (2003, 2008b) DDT models give fair agreement with the measured non-LTE-corrected COS 171 composition. However, the important neutron-rich elements Mn and Ni are significantly overproduced, compared to COS 171, well beyond the measurement uncertainties (even when simmering effects are ignored); Cr/Fe is also poorly fit.

Badenes et al. (2003, 2008b) did not compute Na or K yields, so Figure 6 shows, with red lower limits, the [Na/Fe] and [K/Fe] ratios expected for no production in the COS 171 progenitor; here, the final [Na/Fe] and [K/Fe] ratios are due to the UMi 28104 background composition diluted with 0.7 dex of extra Fe.

A range of Chandrasekhar-mass, single-degenerate SN Ia models, investigated by Dave et al. (2017), permits some comparison with the composition of COS 171. Although Dave et al. (2017) did not publish their yields, their Figures 4 and 7 contains yield information for a few elements. In particular, their Figure 4 allows a comparison of the predicted X/Fe mass fractions for Ni, Mn, and Cr as a function of WD metallicity for all classes of models considered; also, their Figure 7 allows an approximate comparison for their standard deflagration model and their high-density, low C/O ratio deflagration to detonation model.

Surprisingly, we found that the Mn/Fe and Cr/Fe mass ratios for the zero-metallicity, high-density, gravitationally confined detonation (z = 0, GCD-HIGHDEN) model in Dave et al. (2017), Figure 4, provide a reasonable match to the measured Mn/Fe and Cr/Fe mass ratios in COS 171. However, the predicted Ni/Fe mass fractions for all models were factors of 12 to 60 greater than those measured for COS 171, with the closest match given by the GCD-HIGHDEN model. The STD-DEF and DDT-HIGHDEN-LOWC/CENTRAL models in Dave et al. (2017) compared badly with COS 171, with Mn/Fe and Ni/Fe much larger than observed, by approximately a factor of 10; however, Cr/Fe was reasonably well matched by these models.

We conclude that none of the single-degenerate models match the observed composition of COS 171; in particular, the predicted Mn/Fe and Ni/Fe ratios appear to rule out this scenario.

Interestingly, the predicted PISN element yields, added to the UMi 28104 background composition, for the 260 M_⊙, Z = 0 star of HW02 come fairly close to fitting the measured non-LTE-corrected COS 171 X/Fe ratios for most elements, except for Ni/Fe, which is too high by more than 0.5 dex. Given the comparison in Figure 7, an extrapolation of the PISN yields to slightly higher than their maximum mass seems to do even better for all elements except Ni. However, HW02 stress that the 260 M_⊙ is strictly the highest possible Z = 0 PISN mass; above this limit, pair production is unable to provide sufficient pressure, and the object collapses to a black hole.

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Furthermore, an improved fit with PISN yields cannot be obtained with nonzero metallicity PISN events, as indicated by the Z = 0.001, 250 M_⊙ model by Kozyreva et al. (2014), which fails to match the observed Si/Fe, Ca/Fe, Cr/Fe, Mn/Fe, and Ni/Fe in COS 171. Thus, currently predicted element yields from PISN events do not fit the composition of COS 171, and we reject this scenario.

Figure 8 shows excellent overlap between the predicted sub-Chandrasekhar-mass SN Ia yields added to the UMi 28104 background composition and the observed abundances in COS 171 (corrected for differential non-LTE effects). Critically, there is good overlap for the important [Mn/Fe] and [Ni/Fe] ratios, but also for Sc, Ti, V, and Co. In particular, the low [Mn/Fe] and [V/Fe] ratios seen in COS 171 are only reproduced in the lowest metallicity models.

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Figure 8 reveals that the Bravo model sub-Chandrasekhar-mass predictions give decreasing [X/Fe] yields of Si, Ca, and Cr with increasing WD mass; conversely, the [Ni/Fe] yield increases with increasing WD mass. These trends suggest that both the WD mass and metallicity may be constrained using the full array of element ratios relative to iron.

The low [Ni/Fe], [Cu/Fe], and [Zn/Fe] ratios in COS 171, while reproduced in the 0.88 M_⊙, Z = 0.00025 Bravo model, are not well-matched with higher WD masses. However, Si is best reproduced in the 0.97 M_⊙ models, and Ca, Ti, and Cr abundances in COS 171 are best matched by the 1.06 M_⊙, Z = 0.00025 models. Thus, there is some disagreement between the best matching sub-Chandrasekhar WD mass depending on which elements are considered. While errors in the adopted differential non-LTE corrections to Ca, Ti, and Cr LTE abundances might resolve the mass discrepancy, the changes required are at least 0.2 dex and need to work in the same direction, which seems unlikely. Alternatively, an increase in the Fe i non-LTE correction for UMi 28104 of 0.2 dex would reduce the progenitor mass indicated by Ca, Ti, and Cr, but this would shift all solid curves in Figure 8 down, and the implied progenitor mass from Si and Ni abundances would move to even lower values, still out of agreement with Ca, Ti, and Cr.

In the Bravo models, Cu and Zn are made in two regions: by alpha-rich freeze-out in the core and also following carbon burning close to the surface, where protons and neutrons are released that subsequently build up Cu and Zn in a series of (n, γ), (p, γ), and (n, p) reactions. Importantly, the alpha-rich freeze-out cannot occur in the 0.88 M_⊙ model because its maximum temperature is insufficient for complete Si burning, unlike the more massive WD models (where maximum temperatures are near T ∼ 6 GK). Furthermore, for the (n, γ) and (n, p) source of Cu and Zn near the surface, the controlling neutron excess is determined by the original stellar metallicity in the sub-Chandrasekhar-mass models. Therefore, the observed low abundances of Cu and Zn in COS 171 suggests both low metallicity (Z = 0.00025) and low WD mass (0.88 M_⊙).

Direct comparison of the background-subtracted COS 171 element mass ratios with predicted sub-Chandrasekhar-mass yields are presented in Figures 9 and 10 for Mn/Fe as a function of Ni/Fe and Si/Fe, respectively. These two figures show abundance differences, by number, between COS 171 and UMi 28104, compared to the Bravo model predictions. Because these mass ratios are based on true abundance differences, the measurement uncertainties lead to large uncertainties for elements with similar abundances in the two stars; this is despite the small abundance measurement uncertainties, near 0.1 dex, seen in Figure 8.

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We estimated the relative abundance difference uncertainties in Figures 9 and 10 arising from the scatter in CH10 measurements, including covariances and random excitation temperature errors, and assuming a 0.03 dex log gf scatter. Accordingly, we found 1σ uncertainties of 0.070 dex, 0.047 dex, and 0.089 dex for for Mn/Fe, Ni/Fe, and Si/Fe, respectively. Thus, the small total relative abundance uncertainties translate into the substantial mass ratio uncertainties shown in Figures 9 and 10.

In Figure 9, the low Mn/Fe mass ratio indicates a low metallicity for the COS 171 progenitor, within 1σ of the lowest metallicity in the Bravo models, at Z = 0.00025, corresponding to [Fe/H] = −1.7 dex. Thus, the COS 171 Mn/Fe mass ratio is consistent with a low-metallicity sub-Chandrasekhar-mass SN Ia and lies well below any of the DDT model predictions.

The COS 171 Ni/Fe mass ratio in Figure 9 also lies well below the DDT models, and below most of the sub-Chandrasekhar-mass model predictions, and indicates a low WD mass between 0.97 and 0.88 M_⊙. We note that for the lowest WD masses considered in the Bravo models, the maximum core temperatures are insufficient to drive the alpha-rich freeze-out, which is an important source of Ni, as well as of Cu and Zn. In the Bravo models, the reduced Ni production from the alpha-rich freeze-out is likely the reason why the predicted Ni/Fe ratio declines steeply below 0.97 M_⊙ and at low metallicity. However, at high metallicity, there is an increase in Ni/Fe, even for the 0.88 M_⊙ models; this is likely due to increased neutron excess for higher metallicity sub-Chandrasekhar-mass SNe Ia.

The importance of the alpha-rich freeze-out in the production of Ni, Cu, and Zn leads to the sensitivity of these elements to the WD progenitor mass as well as to metallicity; indeed, the measured low Ni/Fe, Cu/Fe, and Zn/Fe ratios for COS 171 suggest that the progenitor was likely low mass (a linear interpolation suggests 0.95 M_⊙), with a reduced or no alpha-rich freeze-out and very low metallicity. The low metallicity is supported by the measured low Mn/Fe and V/Fe ratios.

Figure 10 also shows that the COS 171 composition lies outside the range of Chandrasekhar-mass SNe Ia in Table 3. Linear interpolation over Si/Fe for the sub-Chandrasekhar-mass models in Figure 10 suggests a mass of 0.94 M_⊙, consistent with that indicated by the Ni/Fe ratios. Contrary to the case for Ni/Fe, however, the Si/Fe ratio increases with decreasing WD mass; this is likely due to the relatively low temperatures of the low-mass models resulting in incomplete Si burning and larger amounts of unburnt Si remaining.

We can compare the subtracted COS 171 minus UMi 28104 element mass ratios with the sub-Chandrasekhar-mass SN Ia mass ratio predictions of Shen et al. (2017), appearing in their Figures 8–11. Our subtracted Mn/Fe and Ni/Fe mass ratios for COS 171 lie close to the 0.9 M_⊙, Z = 0, result of Shen et al. (2017) in their Figure 8, but suggest a mass near 0.97 M_⊙ in their Figure 9 (both adopt a C/O mass ratio of 50/50). On the other hand, the Shen et al. (2017) predictions for Cr/Fe mass ratios, appearing in their Figure 11, barely overlaps with the measured value for COS 171, but is best matched in their models with a WD mass of 1.1 M_⊙. As mentioned previously, the Bravo model Cr/Fe mass ratio predictions suggest a match to COS 171 near 1.06 M_⊙. Thus, both sets of sub-Chandrasekhar-mass models suffer the same differences as our best estimate for the element ratios in COS 171.

We are encouraged by the agreement between the Shen et al. (2017) and Bravo model predictions for sub-Chandrasekhar-mass SN Ia element yields of Si, Mn, Fe, and Ni; of particular significance is the implied low mass of the SN Ia progenitor, which is also supported by the large deficiencies of the alpha-rich freeze-out elements Ni, Cu, and Zn.

However, the higher mass WD progenitor indicated by the Ca/Fe, Ti/Fe, and Cr/Fe ratios suggest that details of the actual SN Ia event differed slightly from the models.

It is possible that the unusual composition of COS 171, dominated by a sub-Chandrasekhar-mass SN Ia, may have been due to direct accretion of ejecta from a nearby supernova. In this scenario, COS 171 would have been the outer star in a triple system orbiting a pair of merging low-mass WDs. Assuming an envelope mass for COS 171 of 0.4 M_⊙, then at [Fe/H] = −1.35 dex, it contains 2.8 × 10⁻⁵ M_⊙ of iron, of which 6.3 × 10⁻⁶ M_⊙ was due to the pre-existing, [Fe/H] ∼−2 dex, material. If 0.5 M_⊙ of Fe was produced by the SN Ia event, then a fraction of only 4.3 × 10⁻⁵ of the SN Ia iron was captured by COS 171. If COS 171 was a main-sequence star at the time of the accretion, with roughly solar radius, and assuming that the accretion radius was equal to the physical radius, then COS 171 must have been separated from the SN Ia event by ∼76 R_⊙, roughly 0.4 au, in order to reach [Fe/H] =−1.35 dex. This distance is smaller than the radius of the RGB star phase of the WD progenitors, and so seems unlikely.

On the other hand, if COS 171 was an RGB star, of 20 R_⊙ radius, at the time of accretion, then the separation from the SN Ia event would have been approximately 7 au, which is larger than the maximum radius of the AGB phase (roughly 1.5 au) of the progenitor WDs. These separations seem small considering that the merger of two WDs would be required for the SN Ia event in an even smaller region, and must also have accommodated the previous RGB and AGB phases for both WD progenitors. Thus, if this mechanism did occur, there may well have been a reduction in the size of the COS 171 orbit prior to the accretion and supernova event. Furthermore, in the RGB accretion scenario, the SN Ia event must have occurred relatively recently. Given these constraints, we do not favor this scenario.

In order to reach the chemical composition of COS 171 via pollution of a giant molecular cloud near 10⁶ M_⊙, ejecta from approximately 100 SNe Ia are required. The difficulty with such a scenario is that with many SNe, one might expect to see an averaging of element yields from other nucleosynthesis events, in particular SNe II and Chandrasekhar-mass SNe Ia, in which case the unusual abundance ratios seen in COS 171 might not be expected. For such a scenario, a systematic modulation of the polluting supernova ejecta appears to be necessary in order to obtain the COS 171 composition, which is dominated by sub-Chandrasekhar-mass SN Ia ejecta.

To circumvent this problem, one could propose that only sub-Chandrasekhar-mass SNe Ia occurred during a late phase of chemical enrichment in UMi, perhaps from the last epoch of iron-peak enrichment by the longest-lived progenitors, which led to the SN Ia in UMi being dominated by the merger of sub-Chandrasekhar-mass WD stars.

Evidence for large-scale enrichment by low-metallicity sub-Chandrasekhar-mass SN Ia in other dwarf galaxies could be construed, qualitatively, from the deficiencies of V, Mn, Co, Ni, Cu, and Zn, relative to Fe, in the Sagittarius dwarf galaxy obtained by Hasselquist et al. (2017), Sbordone et al. (2007), and McWilliam et al. (2003); from the Ni deficiencies in LMC stars found by Van der Swaelmen et al. (2013); and from the Ni deficiencies in the Fornax dwarf galaxy by Letarte et al. (2010). However, the element deficiencies in these dwarf galaxies are much less extreme than those seen in COS 171, as if mixing with a range of supernova yields occurred in these systems, unlike in COS 171.

Detailed investigation into the less extreme deficiencies, seen elsewhere, is required before they are taken as solid evidence of sub-Chandrasekhar-mass SN Ia nucleosynthesis; they likely require dilution with element yields from other supernova types. Thus, it is possible that sub-Chandrasekhar-mass SN Ia nucleosynthesis is common among dwarf galaxies, and therefore that a sub-Chandrasekhar-mass SN Ia dominated phase might have occurred in UMi, but it is not yet proven.

In this pollution scenario, we would expect many other stars sharing the chemical composition of COS 171 to be present in UMi; such objects may yet be found among the lower luminosity UMi stars. Indeed, the frequency of stars in UMi that share the chemical composition of COS 171 would provide strong constraints on the three scenarios outlined here.

One possibility is that the iron-peak composition of COS 171 resulted from the pollution of interstellar gas by a single SN Ia event. Since individual SN Ia events typically yield approximately 0.5 M_⊙ of iron, this must be diluted with ∼9000 M_⊙ of [Fe/H] =−2 dex gas, in order to reach the COS 171 metallicity, at [Fe/H] = −1.35 dex. This amount of gas dilution corresponds to a relatively low-mass molecular cloud.

Detailed modelling of the evolution of SNR by Chevalier (1974) show that the amount of interstellar material (ISM) swept up by an SNR depends on many factors, including the energy of the explosion, the density of the ISM, the strength of the local magnetic fields, and cooling from metals and grains.

Equations describing SNR growth, in Chevalier (1974), indicate that at an ISM density of 1.0 cm⁻³ (characteristic of the warm ISM), the typical SNR shell velocity drops to the dispersion of interstellar clouds at a radius near 44 pc, indicating a swept-up mass of 10⁴ M_⊙. This is completely consistent with the detailed SNR treatment of Cioffi et al. (1988), also including metal-dependent cooling, which gives a radius of 42 pc, again with an implied swept-up mass near 10⁴ M_⊙.

A more recent calculation, by Asvarov (2014), is also consistent with these results, and estimated the largest SNR radius of 45 pc for a remnant expanding into an ISM with uniform density of 1.0 cm⁻³, over 4 × 10⁵ yr. A radius of 34 pc was found when the magnetic field pressure was increased by a factor of 4. Notably, Asvarov (2014) employed a relatively small critical velocity, at Mach 2.

These predictions are consistent with the distribution of SNR sizes in nearby galaxies, for example as found by Badenes et al. (2010), who found a sharp cutoff at a radius near 30 pc and the largest SNR radii near 60 pc.

The formation of molecular clouds out of enriched warm interstellar gas is the subject of ongoing research (e.g., see Vázquez-Semadeni et al. 2007); however, it appears that molecular clouds are short-lived objects within an ongoing equilibrium process of rapid formation by gravitational instability and equally rapid disruption by stellar feedback (e.g., Mac Low et al. 2017).

Given these considerations, it seems reasonable that as UMi ran out of gas and star formation in the galaxy drew to a close, a single, stochastic, event might have enriched 10⁴ M_⊙ of warm interstellar gas, all or part of which subsequently formed into a star-forming molecular cloud, producing the last few stars in UMi, including COS 171. Such an event might be more likely to result from a long-lived progenitor, delayed from a previous star formation epoch, such as a sub-Chandrasekhar-mass SN Ia. Given the requirement of mixing the SN Ia ejecta with ∼10⁴ M_⊙ of hydrogen in order to produce COS 171, and that this is the natural outcome for an SNR mixing into warm interstellar gas, this is our favored scenario for the origin of COS 171.

This scenario for the origin of COS 171 suggests that stochastic chemical enrichment occurred in the high-metallicity phase of UMi evolution. Recent work by Cescutti & Kobayashi (2017) compared the trend of reported [Mn/Fe] with [Fe/H] in UMi. While they found that DDT models gave the best fit for chemical evolution through homogeneous enrichment, a model of stochastic chemical enrichment, including nucleosynthesis products from at least two SN Ia types (SN Iax and sub-Chandrasekhar-mass SN Ia), gives the best fit to the observed dispersion in [Mn/Fe]. While their conclusion is completely consistent with the result found here, their fit to the dispersion requires a reliable estimate of the [Mn/Fe] measurement uncertainties. On the other hand, the highly unusual abundance ratios in COS 171, as discussed in this work, cannot reasonably be explained by measurement error.

The idea of stochastic chemical enrichment for the Carina dwarf galaxy was put forward by Venn et al. (2012) in order to explain their stellar abundance patterns. Remarkably, their most metal-rich star, Car 612, has highly unusual chemical abundance patterns and a similar [Fe/H] to UMi COS 171, near −1.3 dex, suggesting the possibility that this object also formed from the enrichment of warm ISM by a single SN Ia event.