Evidence for an Aspherical Population III Supernova Explosion Inferred from the Hyper-metal-poor Star HE 1327–2326^∗

In our abundance analysis of HE 1327−2326, we use an effective temperature of ${T}_{\mathrm{eff}}$ = 6180 ± 80 K, derived from color-effective temperature relations using broadband UBVRI photometry (Frebel et al. 2005), a surface gravity of $\mathrm{log}g=3.7\pm 0.2$ and a microturbulent velocity of ${\xi }_{t}=1.7$ ${\rm{km}}\,{{\rm{s}}}^{-1}$ based on previous studies (Korn et al. 2009; Ezzeddine & Frebel 2018). The Gaia second data release DR2 (Gaia Collaboration et al. 2018) produced ${T}_{\mathrm{eff}}=5915\pm 300$ K and $\mathrm{log}g=3.40\pm 0.3$ based on photometric colors and parallax, respectively. We use both sets of stellar parameters to determine the [Zn/Fe] abundance ratio of HE 1327−2326. We employ a standard model atmosphere (Castelli & Kurucz 2004) with an input model metallicity of [Fe/H] = −5.0 and α-enhancement [α/Fe] = 0.4 throughout.

We measure an equivalent width of 43.4 ± 12.7 mÅ for the Zn i line at 2138.57 Å, by convolving the COS line-spread functions (Ghavamian et al. 2009) with Gaussian profiles following Roederer et al. (2016). We determine uncertainties in the equivalent width and Zn abundance measurements by altering the continuum placement and the FWHM of the spectral line by ±1σ, and recording the corresponding changes. We assess a detection significance of 3.4σ by dividing the equivalent width of the line by its uncertainty. We then calculate the abundance of Zn using the equivalent width curve-of-growth method using the local thermodynamic equilibrium (LTE) radiative transfer code MOOG updated to include proper scattering treatment (Sneden 1973; Sobeck et al. 2011), and with custom analysis tools (Casey 2014). The abundances are determined relative to the solar values from Asplund et al. (2009).

Using ${T}_{\mathrm{eff}}=6180$ K and $\mathrm{log}g=3.7$ (Frebel et al. 2008), we determine a Zn abundance of [Zn/H] = −4.40 ± 0.25 using the 1D, LTE framework. The conditions of line formation in metal-poor stars are known to deviate from the assumptions of LTE and 1D model atmospheres (Thévenin & Idiart 1999; Takeda et al. 2005; Mashonkina et al. 2011; Bergemann et al. 2012). Abundances from lines of minority species, such as neutral Zn i and Fe i, are often prone to larger non-local thermodynamic equilibrium (NLTE) effects in the atmospheres of low-metallicity stars than from lines of the corresponding dominant ionized species. Investigations of possible NLTE effects for abundances of commonly used optical Zn i lines over a range of stellar parameters showed that NLTE abundance corrections, defined by the differences between the NLTE and LTE abundances using the same observed equivalent widths, are actually not significant and ≤0.2 dex (Takeda et al. 2005). Even though the departures from LTE have not been calculated explicitly for any UV Zn i lines, it could be shown by Roederer & Barklem (2018) that ionization equilibrium in LTE can be reached in metal-poor stars with −3.0 < [Fe/H] < −1.0 (within 0.1 dex) using optical (e.g., Zn i λ4810) and UV (e.g., Zn ii λ2062) lines. Departures from LTE for Zn were indeed insignificant, even at [Fe/H] = −3.0. Following these results, we assume that our LTE Zn abundance, as derived from the UV line, would be compatible with values obtained from any optical lines, if ever detected.

For Fe, however, strong NLTE effects have been well documented (e.g., Asplund 2005, and references therein). We thus adopt the 1D, NLTE Fe abundance of [Fe/H] = −5.20 in HE 1327−2326, inferred from 10 Fe i optical lines as determined in Ezzeddine & Frebel (2018). This Fe abundance for HE 1327−2326 is based on detailed investigations of possible 3D and NLTE effects on both Fe i and Fe ii lines in the optical and UV. We then obtained a zinc to iron abundance ratio of [Zn/Fe] = 0.80 ± 0.25. For completeness, we note that any potential NLTE correction to the Zn i abundance (should they exist) would be positive, and would thus only further increase the [Zn/Fe] ratio (Takeda et al. 2005).

We also investigate the [Zn/Fe] abundance ratio using Gaia DR2 stellar parameters, which yield slightly lower 1D, LTE Zn and 1D, NLTE Fe abundances of [Zn/H] = −4.70 and [Fe/H] = −5.40, respectively. This 1D, NLTE abundance of Fe was determined following the same setup used in Ezzeddine et al. (2017). Compared to our other value, the [Zn/Fe] decreases only slightly, to 0.70 ± 0.25. This shows that the [Zn/Fe] ratio in HE 1327−2326 is robustly enhanced, irrespective of the choice of stellar parameters.

To establish the overall [X/Fe] abundance pattern of HE 1327−2326, we adopt [Zn/Fe] = 0.80 ± 0.25, in addition to the UV Si i abundance from Ezzeddine & Frebel (2018), as well as the optical abundances for 11 elements and upper limits for 5 others (Sc, V, Cr, Mn and Co) from Frebel et al. (2008). All elemental abundances used are listed in Table 1. We use this pattern to compare to the theoretical SNe nucleosynthesis yields of various models.

Table 1.  Chemical Abundances of 13 Elements Determined from the UV and Optical Spectra of HE 1327−2326

El	Nnlines	$\mathrm{log}\epsilon (X)$	$\sigma \mathrm{log}\epsilon (X)$	[X/H]	[X/Fe]
C (CH)	syn.	6.21a	0.10	−2.22	3.49
N (NH)...	syn.	6.10a	0.20	−1.73	3.98
O (OH) ...	syn.	6.12a	0.20	−2.57	3.14
Na i...	2	2.99	0.04	−3.25	2.46
Mg i...	4	3.54	0.02	−4.06	1.65
Al i...	1	1.90	0.03	−4.55	1.16
Si ib...	1	2.80	0.27	−4.71	1.28
Ca ii...	4	1.34	0.15	−5.00	0.71
Ti ii...	15	−0.09	0.17	−5.04	0.67
Fe ic...	10	1.79	0.15	−5.71	⋯
Fe id...	10	2.30	0.11	−5.20	⋯
Fe ii...	4	1.51	0.26	−5.99	⋯
Ni i...	4	0.73	0.20	−5.49	0.33
Zn i...	1	+0.16	0.25	−4.40	0.80
Sr ii...	2	−1.76	0.06	−4.63	1.08
Sc ii...	⋯	<−1.68	⋯	<−4.83	<0.88
Mn i...	⋯	<0.53	⋯	<−4.90	<0.81
Co i...	⋯	<0.58	⋯	<−4.41	<1.30

Notes. Upper limits for Sc, Mn, and Co are also included.

^a3D values adopted from Frebel et al. (2008). ^bAdopted from Ezzeddine & Frebel (2018). ^cLTE abundance from Frebel et al. (2008). ^dNLTE abundance adopted from Ezzeddine & Frebel (2018).

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Previous studies have commonly compared abundance patterns of individual UMP stars, such as that of HE 1327−2326, to the yields of faint MF quasi-spherical Pop III SNe (Umeda & Nomoto 2002; Christlieb et al. 2004; Frebel et al. 2005; Iwamoto et al. 2005; Keller et al. 2014; Bessell et al. 2015; Placco et al. 2016; Nordlander et al. 2017). As discussed in Section 1, such spherical explosions underproduce iron-peak elements (such as Co, Cr, or Zn) (Tominaga 2009; Grimmett et al. 2018; Hirai et al. 2018; Tsujimoto & Nishimura 2018). Due to a lack of iron-peak abundances, the comparisons of the data with these model results usually remained unconstrained in the that region. With available Zn abundances, however, new constraints can be obtained.

We perform statistical fitting tests following Placco et al. (2016), to compare the determined abundance pattern of HE 1327−2326 (including Zn) to 16,800 theoretical yields¹⁴ of quasi-spherical MF SNe models, computed with different explosion parameters (e.g., progenitor mass, explosion energies, mixing parameters). To account for uncertainties in our fitting results, we simulate 10,000 different abundances for each observed element used in the fit, which follow a normal distribution centered around the measured abundance (taken as the mean). We then randomly sample the abundance distributions for all elements and generate 10,000 artificial abundance patterns for HE 1327−2326, to compare the yields. Our results, shown in Figure 3, demonstrate that indeed none of the mixing-fallback supernova models can match the Zn abundance (relative to Fe) in HE 1327−2326. Overall, 82% of the simulated abundance patterns of HE 1327−2326 can be fit best (although not satisfactorily) with a 27 M_⊙ progenitor exploding with 0.3 × 10⁵¹ erg. Of the simulated abundance patterns, 18% are also reproduced by a 27 M_⊙ progenitor, but with a slightly higher explosion energy of 0.6 × 10⁵¹ erg. The remaining few abundance patterns (≪1%) are fit best with 20.5 M_⊙ and 27 M_⊙ progenitors with 0.3 × 10⁵¹ erg and 0.9 × 10⁵¹ erg, respectively.

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Building on these results, we can statistically rule out faint quasi-spherical SNe as the source of metals in HE 1327−2326, as no superposition of yields would produce enough Zn relative to the lighter elements. Enrichment by multiple events can also more broadly be eliminated following the theoretical mono-enrichment classification scheme suggested by Hartwig et al. (2018), in which stars with −6.0 < [Fe/H] < −4.0 and [Mg/C] < −1.0 have a strong likelihood of being enriched by a single SNe event. This applies well to HE 1327−2326 with [Fe/H] = −5.2 and [Mg/C] = −1.84. Overall, this shows that the progenitor of HE 1327−2326, and possibly those of other UMP stars with similar abundance patterns, did not explode (quasi-)spherically.

We compare the abundance pattern of HE 1327−2326 to the yields of density-modified MF models with different masses and explosion energies, thus mimicking aspherical SNe with bipolar outflows. Specific details on the explosion models and yield calculations are described in Tominaga et al. (2007b). We find that the yields of a 25 M_⊙ first star progenitor exploding with an aspherical SNe, with a high explosion energy of E = 5 × 10⁵¹ erg, best matches the entire abundance pattern of HE 1327−2326, including zinc. We show this result with the black solid line in Figure 4. Our best-fit model has an initial mass cut of M_cut = 1.64 M_⊙, outer boundary mixing region mass of M_mix = 5. 65 M_⊙, and ejection factor of f = 0.0002. To specifically increase the zinc yield of an MF SNe model, the explosion mechanism was modified such that the matter density is artificially reduced, to mimic a high-entropy explosion environment, which is required for increased explosive nucleosynthesis (Maeda & Nomoto 2003; Tominaga et al. 2007a, 2007b; Grimmett et al. 2018). In this modified framework, elements formed in the deepest layers during the explosion, such as zinc, are (at least partially) mixed upward and then ejected. This occurs alongside the release of only small amounts of iron (most iron falls back onto the nascent black hole) and large amounts of, e.g., carbon made in the layers farther out. The density-modified MF model thus parameterizes what would physically be an aspherical SNe with bipolar outflows or jets (see panel (b) of Figure 12 in Tominaga et al. 2007b), with the ejection factor f in the 1D model being equivalent to the fraction of the solid angle of the region where the ejected mass elements in the Si-burning layer are located in the 2D model (i.e., f = 1 in the spherical model). The necessary high-entropy environment would occur along the rotation axis. Tominaga (2009) showed that the abundance patterns of the yields of the 2D aspherical bipolar explosion are reproduced by the density-modified MF model. Unfortunately, more realistic 3D explosion models of metal-free stars are not available yet to further investigate this behavior.

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We also explore other geometries using the same progenitor mass of 25 M_⊙ including two quasi-spherical MF SNe models with low (E = 1 × 10⁵¹ erg; teal solid line in panel (a) of Figure 4) and high (E = 5 × 10⁵¹ erg; magenta solid line in panel (a) of Figure 4) explosion energies. Two spherical SNe models with and without enhanced [C/Fe] ratios were also explored, corresponding to, respectively, the gold and blue solid lines in panel (b) of Figure 4. The explosion parameters M_cut, M_mix, and f used for each of these models are listed in Table 2. Both quasi-spherical MF models with E = 1 × 10⁵¹ erg and E = 5 × 10⁵¹ erg are not able to produce the [Zn/Fe] > 0 ratio. Simultaneously, they also underreproduce the [Sc/Fe] and [Ti/Fe] ratios compared to the aspherical model. The explosive nucleosynthesis in the density-modified, high-entropy aspherical model enhances the α-rich freezeout, thus enhancing the [Sc/Fe] and [Ti/Fe] ratios usually determined in EMP stars with [Fe/H] < −3 (Tominaga et al. 2007b). Given that the determined [Ti/Fe] = 0.67 ratio in HE 1327−2326 is enhanced, an aspherical explosion model is thus clearly favored.

We note that spherical models could principally also produce a high-entropy environment, and hence a solar [Zn/Fe] ratio if the explosion energy were large enough, e.g., E = 5 × 10⁵¹ erg (see panel (b) of Figure 4; Nomoto et al. 2013). However, such an energetic explosion would be highly inconsistent with the significant fallback required to produce the low Fe abundances observed in UMP stars, including HE 1327−2326. This explains why the spherical models are unlikely contenders for the explosion mechanisms of the HE 1327−2326 progenitor, and perhaps even for other first stars.

Overall, the explosion of the massive Pop III star progenitor of HE 1327−2326 is thus more energetic than previously thought (i.e., a hypernova), in line with more recent studies, such as Grimmett et al. 2018. Interestingly, previous work has suggested that only faint MF-first SNe would seed carbon-enhanced metal-poor (CEMP) stars such as HE 1327−2326, because their host minihalos would be disrupted by any larger energy input (Cooke & Madau 2014). Our results provide an alternative explanation, as high-energy aspherical SNe explosions could also produce high [C/Fe] ratios.

It has been proposed that aspherical SNe are driven by (fast) rotating progenitors with possibly strong magnetic fields (Maeda & Nomoto 2003; Meynet et al. 2006; Ekström et al. 2008). This is in line with theoretical predictions that the first stars were heavily rotating (Meynet et al. 2006; Stacy et al. 2011; Tsujimoto & Nishimura 2018). Indeed, the progenitors of HE 1327−2326 and those of other second-generation stars have already been shown to be fast-rotating based on their large relative nitrogen abundance ratios, e.g., [N/Fe] = 3.98 in HE 1327−2326, [N/Fe] = 2.57 in HE 0107−5240 (Christlieb et al. 2004), and [N/Fe] = 3.46 in SD 1313−0019 (Frebel et al. 2015).

Stellar surface nitrogen abundances become enhanced due to internal mixing caused by rotation (Meynet et al. 2006; Choplin et al. 2017), rather than being produced during their explosion (see Figure 4). Additionally, Maeder et al. (2015) and Choplin et al. (2018) have proposed that a fast-rotating Pop III star progenitor could be responsible for the enhanced [Sr/Fe] = 1.08 determined for HE 1327−2326 and other EMP stars with [Sr/Fe] > 0.5. They showed that fast rotation in a low-metallicity, massive star can set off a strong mixing between the H- and He-burning zones, which triggers the synthesis of Sr and other light neutron-capture elements made in the s-process.

Introducing rotation of Pop III stars into the standard neutrino-driven paradigm of core-collapse supernovae has independently been shown to lead to bipolar (jet-like) SNe (Fryer & Heger 2000; Burrows et al. 2004). Finally, rotation has also been implemented into early universe and first-stars cosmological simulations (Greif et al. 2010; Stacy et al. 2011) to investigate the ab initio formation of the first stars. Moreover, Tsujimoto & Nishimura (2018) recently predicted through their galactic chemical evolution calculations that magneto-rotational driven explosions could indeed be the dominant source of enhanced [Zn/Fe] abundance ratios in the Milky Way satellite dwarf galaxy stars with −4 < [Fe/H] < −1.

Fröhlich et al. (2006a) and Pruet et al. (2006) proposed that increasing the entropy by increasing the electron mole fractions Y_e in a faint quasi-spherical SNe model to values >0.5 would mimic a νp-process in the neutrino-driven winds emerging from the proto-neutron star of the Pop III progenitor. This could enhance the production of [Sr/Fe] as well as the iron-peak elements [Sc,Co,Zn/Fe] ratios, as is observed in UMP stars.

Fröhlich et al. (2006b), however, showed that such a scenario only leads to the production of Zn of up to [Zn/Fe] = 0, which remains inconsistent with observational results of [Zn/Fe] ≳ 0.5, as determined for EMP stars and HE 1327−2326. Tominaga et al. (2007b) confirmed these results by introducing neutrino-transport into their MF SNe models of Pop III stars by artificially increasing Y_e in the complete Si-burning region where Zn is produced. They showed that increasing Y_e to >0.5 could indeed enhance the production of [Sc/Fe] > 0.3, as is observed in EMP stars, but could not simultaneously produce the enhanced [Zn/Fe] > 0 as well as [Co/Fe] > 0.

This suggests that the νp-process is not responsible for the enhanced Zn production in HE 1327−2326 and other EMP stars. Instead, the entire abundance pattern of HE 1327−2326 can be produced by rotation-driven, high-energy (E = × 10⁻⁵¹ erg) aspherical SNe with bipolar jets, as described in Sections 4.2 and 4.3. Nevertheless, the νp-process could contribute to an increased [Sr/Fe] ratio, as has been determined for HE 1327−2326 and other UMP stars.