ELECTRON-CAPTURE SUPERNOVAE AS SOURCES OF ⁶⁰Fe

The origin of the radionuclide ⁶⁰Fe (halflife of 2.62 Myr; Rugel et al. 2009) has been extensively discussed in connection to gamma-ray astronomy (an overview of the subject can be obtained from Diehl et al. 2011). The 1173 keV and 1332 keV emission from ⁶⁰Fe decay has been confirmed by the space-based telescopes RHESSI (Smith et al. 2004) and INTEGRAL/SPI (Harris et al. 2005), indicating ongoing nucleosynthesis of ⁶⁰Fe in the Milky Way (for recent reviews, see Prantzos 2010; Diehl 2013). The sources of ⁶⁰Fe have generally been associated with massive stars and subsequent core-collapse supernovae (CCSNe), in which successive neutron captures on Fe isotopes create ⁶⁰Fe (Timmes et al. 1995; Huss et al. 2009). However, recent CCSN nucleosynthesis calculations (Rauscher et al. 2002; Limongi & Chieffi 2006; Woosley & Heger 2007) predict the ratio of ⁶⁰Fe to ²⁶Al (halflife of 0.717 Myr) being several times greater than the line flux ratio inferred from the INTEGRAL/SPI experiment, ⁶⁰Fe/²⁶Al =0.148 ± 0.06 (Wang et al. 2007). Prantzos (2004) suggested that the discrepancy could be alleviated if the dominant ²⁶Al contributors were Wolf–Rayet star winds that did not eject ⁶⁰Fe.

A detection of live ⁶⁰Fe in the deep ocean crust on the Earth has also been recently reported (Knie et al. 2004; Fitoussi et al. 2008), which may be a sign of ⁶⁰Fe injection from a nearby supernova (SN) into the heliosphere a few Myr ago (Fields et al. 2005, 2008). The origin of live ⁶⁰Fe in the early solar system has been continuously discussed since its discovery in primitive meteorites (Tachibana & Huss 2003; Mostefaoui et al. 2005; Bizzarro et al. 2007). The initial ratio at the solar birth, ⁶⁰Fe/⁵⁶Fe ∼ 6 × 10⁻⁷ (e.g., Mishra et al. 2010), appeared to be higher than the interstellar medium (ISM) value, ∼3 × 10⁻⁷ (Huss et al. 2009; Tang & Dauphas 2012).³ This fact led to an idea that one or several nearby SNe had injected freshly synthesized ⁶⁰Fe into the early solar system (Wasserburg et al. 1998; Boss & Keiser 2013). A recent meteorite study suggests, however, an initial ratio of ⁶⁰Fe/⁵⁶Fe ∼ 1 × 10⁻⁸ (see also Moynier et al. 2011; Telus et al. 2012), which is 30 times lower than the ISM value. If this is true, the live ⁶⁰Fe might have been simply inherited from the ISM to the molecular cloud that made the solar system after a certain decay interval (∼15 Myr; Tang & Dauphas 2012). This assumption, however, needs a mechanism to avoid ⁶⁰Fe coming from CCSNe during that period of time (see, e.g., Gounelle & Meynet 2012). Vasileiadis et al. (2013) suggested that the low ⁶⁰Fe/⁵⁶Fe ratios were not representative of the proto-solar values.

It should be noted that ⁶⁰Fe production in CCSN models is subject to uncertainties in several reaction rates (Woosley & Heger 2007; Tur et al. 2010) as well as in the treatment of mass loss, convection, explosion energy, and initial metallicity in stellar models (Limongi & Chieffi 2006; Woosley & Heger 2007). The calculated ⁶⁰Fe yields should thus be taken with caution. A possible solution to the aforementioned conflicts with observations would thus be that CCSNe actually produced little ⁶⁰Fe and other sources with longer stellar lifetimes supplied the Galactic ⁶⁰Fe. Such sources could be asymptotic-giant-branch (AGB, with a C-O core; Wasserburg et al. 2006) or super-AGB (SAGB, with an O-Ne-Mg core; Lugaro et al. 2012) stars, and high-density thermonuclear SNe (SNe Ia; Woosley 1997).

In this Letter, we report that electron-capture SNe (ECSNe; Nomoto 1987; Kitaura et al. 2006; Wanajo et al. 2009), a sub-class of CCSNe⁴ arising from SAGB stars, can be additional sources of ⁶⁰Fe in the Milky Way. We adopt our recent nucleosynthesis results of Wanajo et al. (2013) and show that ⁶⁰Fe is produced in appreciable amounts in the neutron-rich and low-entropy ejecta.

We employ the nucleosynthesis results of Wanajo et al. (2013), which are briefly summarized below. The nucleosynthesis analysis made use of 2000 representative tracer particles, by which the thermodynamic histories of ejecta chunks were followed in our two-dimensional hydrodynamic calculation of an ECSN (Janka et al. 2008; Wanajo et al. 2011). Our ECSN model predicts the core-ejecta mass of 1.14 × 10⁻² M_☉ with electron fractions (number of protons per nucleon) of Y_e ≈ 0.40–0.55 and entropies of s ≈ 13–25 k_B nucleon⁻¹ (k_B is the Boltzmann constant; see Figure 1 in Wanajo et al. 2013).⁵ Post-processing nucleosynthesis calculations with an up-to-date reaction network code (with the reaction library REACLIB version 2.0; Cyburt et al. 2010) predict interesting production of light trans-iron elements (and presumably weak r-process elements; Wanajo et al. 2011), whose astrophysical origin has not been fully resolved (see, e.g., Wanajo 2013). A neutron-rich isotope, ⁴⁸Ca, whose origin remains a long-standing mystery of nucleosynthesis (Meyer et al. 1996; Woosley 1997), is also found to be made in the neutron-rich ejecta with Y_e ≈ 0.40–0.42 and s ≈ 13–15 k_B nucleon⁻¹.

In addition to their "unchanged" ECSN model, Wanajo et al. (2013) also explored models in which the densities were increased by multiplying a constant scaling factor f for all the tracer particles ("ρ × f"). This effectively decreased the entropy by the same factor. It was found that increasing the densities by factors of 1.3 or 2 (f = 1.3 or 2, corresponding to a reduction by a factor of 1.3 or 2 in entropy) leads to a remarkable enhancement of the ⁴⁸Ca abundance. This is a consequence of the fact that a reduction of the entropy turns the nucleosynthesis condition from α-rich QSE (nuclear quasi-equilibrium) to α-poor QSE. In the latter condition, an upward-A shift of the heavy abundances in the QSE cluster is suppressed owing to the paucity of light particles (neutrons, protons, and α's). As a result, ⁴⁸Ca at the low-A tip of the QSE cluster survives. In this Letter, we also analyze these low-entropy models.

The final mass fractions of ⁶⁰Fe are shown in Figure 1 (top) as functions of Y_e along with those for other astrophysically important radionuclides, ²⁶Al, ⁴¹Ca, ⁴⁴Ti, ⁵³Mn, and ⁵⁶Ni. Among these species only ⁶⁰Fe forms in the most neutron-rich investigated conditions with Y_e ≈ 0.40–0.45, which is somewhat isolated from Y_e ≈ 0.46–0.55 in which the others are produced. These isotopes are made in NSE (nuclear statistical equilibrium) and QSE, and, in part, by α and proton captures after the QSE freezeout. The smaller core-ejecta mass of an ECSN results in several 10 times smaller amounts of these isotopes (first line in Table 1) than in CCSNe (fourth and fifth lines in Table 1, in which the abundances taken from Rauscher et al. 2002; Brown & Woosley 2013, are mass-averaged by the stellar initial mass function, IMF; see Section 4).

Zoom In Zoom Out Reset image size

Despite the small core-ejecta mass, we find a similar amount of ⁶⁰Fe for ECSNe comparable to that for CCSNe. This is due to appreciable production of ⁶⁰Fe in QSE with neutron-rich conditions for Y_e ∼ Y_{e, nuc} = 26/60 = 0.433 (characterizing the structure of ⁶⁰Fe), which is absent in CCSN ejecta. In fact, ⁶⁰Fe is the most tightly bound isotope in the range Y_{e, nuc} < 0.438. The mass fraction X(⁶⁰Fe), however, peaks at Y_e = 0.428, which is slightly below 0.433 (red dots in Figure 1, bottom). This is due to the presence of a more tightly bound isotope ⁶⁴Ni with Y_{e, nuc} = 0.438.

Figure 2 elucidates the nuclear evolutions for two representative tracer particles with Y_e = 0.433 (a) and 0.428 (b). The entropies are s = 14.9 k_B nucleon⁻¹ and 13.6 k_B nucleon⁻¹, respectively. The expansion timescales, defined as the e-folding times of the temperature drop below 0.5 MeV, are τ_exp = 63.8 ms and 61.8 ms, respectively. The abundances (number per nucleon, Y ≡ X/A) of α, ⁶⁰Fe, and heavy nuclei ("h," A > 4) are drawn as functions of descending temperature. Also shown are the abundances of heavy nuclei with A < 60 ("hl") and with A > 60 ("hh"). We find that the heavy abundance, Y_h, approaches a constant value around 6 GK. This is a freezeout from NSE, defined here when the timescale of heavy abundance formation, $\tau _\mathrm{h} \equiv Y_\mathrm{h}/\dot{Y_\mathrm{h}}$, exceeds τ_exp.

Zoom In Zoom Out Reset image size

We realize an upward-A shift of the heavy abundances after the NSE freezeout from decreasing Y_hl and increasing Y_hh in Figures 2(a) and (b). This is a result of the α-rich freezeout from NSE (Woosley & Hoffman 1992) followed by QSE (Meyer et al. 1998), recognized by Y_α/Y_h = 2.57 and 2.33 at the NSE freezeout for the Y_e = 0.433 and 0.428 cases, respectively. We define the QSE freezeout when the timescale of the abundance formation for A > 60, $\tau _\mathrm{hh} \equiv Y_\mathrm{hh}/\dot{Y}_\mathrm{hh}$, exceeds τ_exp. QSE freezes out typically around 4 GK (Meyer et al. 1998) and the upward-A shift of the heavy abundances ceases.

We find in Figures 2(a) and (b) that the ⁶⁰Fe abundances for Y_e = 0.433 and Y_e = 0.428, respectively, decrease and increase during the QSE phase. Figures 2(e) and (f) clarify the reason, illustrating the nuclear abundances at the NSE freezeout, at the QSE freezeout, and at the end of calculation for each tracer particle. We find that, at the NSE freezeout, ⁶⁰Fe belongs to the lighter group of the NSE cluster.

For the Y_e = 0.433 case (Figures 2(a) and (e)), a drastic upward-A shift of the heavy abundances takes place during the QSE phase. As a result, a part of the ⁶⁰Fe abundance is taken by the heavier group, in particular by ⁶⁴Ni. For the Y_e = 0.428 case (Figures 2(b) and (f)), the upward-A shift is smaller as a result of the smaller Y_α/Y_h at the NSE freezeout. More importantly, the Y_e is appreciably smaller than the Y_{e, nuc} of ⁶⁴Ni, making ⁶⁰Fe the most tightly bound isotope in this condition. As a result, ⁶⁰Fe keeps increasing in the QSE cluster and even after the QSE freezeout.

In summary, ⁶⁰Fe forms in NSE and further increases or decreases in QSE depending on the neutron-richness as well as the available number of α's during the QSE phase. The latter condition is closely related to entropy. In the following, we thus inspect the ECSN models in which densities are multiplied by a scaling factor f for all the tracer particles.

Figure 1 (bottom) shows the final mass fractions of ⁶⁰Fe for the unchanged model (f = 1) and those with f = 1.3, 2.0, 10, 1/1.3, and 1/2.0. We find a strong sensitivity of the ⁶⁰Fe production to entropy. The nuclear evolutions for f = 2.0 are presented in Figure 2(c) for Y_e = 0.433 and in Figure 2(d) for 0.428. The Y_α/Y_h ratios at the NSE freezeout are 1.46 and 1.33, respectively, being only slightly greater than unity, as a result of reduced entropies by about a factor of two. As a result, an upward-A shift of the abundances is restricted by a small number of light particles. ⁶⁰Fe thus survives and increases during the QSE phase, being maximal around Y_{e, nuc} = 0.433 (Figure 1, bottom).

The resulting ejecta masses of radionuclides for f = 1.3 and 2.0 are presented in Table 1 (second and third lines). ⁶⁰Fe is appreciably produced in the low-entropy models. A decrease of only about 30% in entropy doubles the ejecta mass of ⁶⁰Fe, being comparable to that for CCSNe. About a factor of two decrease in entropy leads to about four times greater ⁶⁰Fe amount, being already close to that for the extreme, f = 10 case (1.40 × 10⁻⁴ M_☉; not presented in Table 1). The ejecta mass of M_ej(⁶⁰Fe) ∼ 1 × 10⁻⁴ M_☉ can thus be taken to be the upper limit for ECSNe.

The contribution of ECSNe to the Galactic ⁶⁰Fe depends on the mass window leading to SNe from the stellar SAGB mass range (Nomoto 1987; Siess 2007; Poelarends et al. 2008). From their stellar evolution models, Poelarends et al. (2008) obtained the initial mass range for SAGB stars to be 7.5–9.25 M_☉ in the solar metallicity case. Assuming that all this range leads to the SN channel, the fraction of ECSNe relative to all SN events (ECSNe + CCSNe) becomes f_ECSN = 0.253 by adopting the Salpeter IMF ($\propto M_\mathrm{star}^{-2.35}$) with the upper-end of 120 M_☉.⁶ This can be regarded as the absolute upper limit of f_ECSN in the local universe with the metallicity near the solar value.

We further evaluate the upper limit on f_ECSN based on our result. For the unchanged model, the most overproduced isotope relative to the solar value is ⁸⁶Kr (Table 2, first line). Given that ⁸⁶Kr in the Milky Way was exclusively made by ECSNe, we have (Wanajo et al. 2011),

$$\begin{eqnarray} &&\frac{f_\mathrm{ECSN}}{1-f_\mathrm{ECSN}} = \frac{X_\odot (^{86}\mathrm{Kr})/X_\odot (^{16}\mathrm{O})}{M_\mathrm{ECSN}(^{86}\mathrm{Kr})/M_\mathrm{CCSN}(^{16}\mathrm{O})}, \end{eqnarray} \tag{ 1 }$$

where X_☉(⁸⁶Kr) = 2.39 × 10⁻⁸ and X_☉(¹⁶O) = 6.60 × 10⁻³ are the mass fractions of these isotopes in the solar system (Lodders 2003). M_ECSN(⁸⁶Kr) = 6.23 × 10⁻⁵ M_☉ is the ⁸⁶Kr mass for the unchanged ECSN model. M_CCSN(¹⁶O) = 1.63 M_☉ is the IMF-averaged ¹⁶O mass per CCSN event, in which the yields are taken from Brown & Woosley (2013, their Table 1).⁷ With these values, we get f_ECSN = 0.0854 for the unchanged model. For the low-entropy models with f = 1.3 and 2.0, Equation (1) gives f_ECSN = 0.165 and 0.240, respectively, by replacing ⁸⁶Kr with the most overproduced isotopes, ⁷⁴Se and ⁴⁸Ca.

Taking the IMF-averaged ⁶⁰Fe mass, M_CCSN(⁶⁰Fe) = 8.31 × 10⁻⁵ M_☉ with the CCSN yields in Brown & Woosley (2013), the fractions of the Galactic ⁶⁰Fe from ECSNe (relative to that from all SN events) become f_60Fe = 0.0391, 0.155, and 0.332 for the unchanged, f = 1.3, and f = 2.0 cases, respectively. This indicates that ECSNe supply about 4%–30% of live ⁶⁰Fe in the Milky Way. It should be noted that the ratio from the CCSN yields, ⁶⁰Fe/²⁶Al = 0.661, is already more than four times greater than the observational flux ratio of 0.148 (Wang et al. 2007). A contribution from ECSNe would thus enlarge the discrepancy. As noted in Section 1, however, ⁶⁰Fe production in CCSNe is subject to uncertainties in several reaction rates as well as in astrophysical modeling of stellar evolution. Contributions from ECSNe could therefore be greater than the above estimate. As an extreme case, we provide the ratios of ⁶⁰Fe/²⁶Al with no ⁶⁰Fe (but ²⁶Al) contribution from CCSNe (i.e., f_60Fe = 1) in Table 2 (last column). We find that the low-entropy model with f = 1.3 gives the value that is roughly consistent with the gamma-ray observation.

If the Galactic ⁶⁰Fe were exclusively produced by ECSNe, their longer progenitor lifetimes (>15 Myr) could give rise to different distributions between ²⁶Al and ⁶⁰Fe. On the one hand, the ²⁶Al distribution appears to be clumpy as evidenced by the INTEGRAL/SPI mission (Diehl 2013). Some of this clumpiness is associated with regions hosting many young, massive stars such as the Cygnus region. On the other hand, ⁶⁰Fe may not be associated with such young stellar regions and thus be distributed more diffusely. Although the Cygnus region marginally appears within the INTEGRAL sensitivity for ⁶⁰Fe, no signal of its decay has been found (Martin et al. 2010). This could be due to the age of the Cygnus complex being much younger than the lifetimes of ECSN progenitors.

The signatures of ⁶⁰Fe production in ECSNe might have been imprinted also in primitive meteorites or in the deep ocean crust. ECSNe produce appreciable ⁴⁸Ca (also ⁵⁰Ti and ⁵⁴Cr; Wanajo et al. 2013) that cannot be made by CCSNe. Its association with excess ⁶⁰Fe could thus be a sign of the ECSN origin. In fact, such a correlation in meteorites was reported by Chen et al. (2011). Note, however, that both ⁶⁰Fe and ⁴⁸Ca could also originate from a rare class of high density SNe Ia (Woosley 1997). Our ECSN model, however, produces almost all light trans-iron nuclei up to Z = 40 (Figure 5 in Wanajo et al. 2013) and presumably weak r-process nuclei up to Z = 50 (Figure 5 in Wanajo et al. 2011). The latter can also be created in the subsequent neutrino-driven outflows (Wanajo 2013). The weak r-process products should include a few radionuclides with lifetimes comparable to that of ⁶⁰Fe, such as ⁹³Zr (1.53 Myr), ⁹⁹Tc (0.211 Myr), and ¹⁰⁷Pd (6.5 Myr). Therefore, it will be crucial to find correlations also with these trans-iron species that are not made by SNe Ia.

We examined the production of ⁶⁰Fe in ECSNe in connection to the nucleosynthetic results of Wanajo et al. (2013). The models were based on the two-dimensional core-collapse simulation (Janka et al. 2008; Wanajo et al. 2011) of an 8.8 M_☉ SAGB star (Nomoto 1987). In addition to the unchanged ECSN model, we adopted the low-entropy models of Wanajo et al. (2013), in which densities were multiplied by a factor f. We found appreciable ⁶⁰Fe production during the NSE and subsequent QSE phases in the neutron-rich ejecta with Y_e ∼ 0.43. The amount of ⁶⁰Fe is highly dependent on entropy; lower entropy models (f = 1.3 and 2.0) make more ⁶⁰Fe.

The unchanged ECSN model predicted ∼4% contribution of ECSNe (relative to all SN events) to the Galactic ⁶⁰Fe. This fraction could increase to ∼30% (for f = 2.0) if the low-entropy models were adopted. If this were the case, the Galactic flux ratio of ⁶⁰Fe/²⁶Al = 0.148 (Wang et al. 2007) would be explained without ⁶⁰Fe contributions from CCSNe. If the Galactic ⁶⁰Fe were dominantly supplied from ECSNe (i.e., the CCSN yields were severely overestimated), ⁶⁰Fe would be more diffusely distributed than ²⁶Al without showing clear associations with young stellar regions such as the Cygnus complex. This should be confirmed by future gamma-ray line surveys.

Our ECSN models co-produce the neutron-rich isotope ⁴⁸Ca (Wanajo et al. 2013), light trans-iron elements, and possibly weak r-process elements (Wanajo et al. 2011; Wanajo 2013), accompanied by several radionuclides with million-year lifetimes (e.g., ⁹³Zr, ⁹⁹Tc, and ¹⁰⁷Pd). Correlations between ⁶⁰Fe and these isotopes in primitive meteorites (Chen et al. 2011) or in the deep ocean crust on the Earth (Knie et al. 2004; Fitoussi et al. 2008) will be an invaluable evidence of ⁶⁰Fe production in ECSNe.

Finally, it should be cautioned that further improvements of hydrodynamical models (e.g., three-dimensional, high-resolution, and general-relativistic treatment) will be needed before drawing more firm conclusions. Studies of ⁶⁰Fe production by a mini s-process during the SAGB stage (Lugaro et al. 2012) prior to ECSN explosions are also important to evaluate the net ⁶⁰Fe ejecta from such stars.

S.W. was supported by the JSPS Grants-in-Aid for Scientific Research (23224004). At Garching, support by Deutsche Forschungsgemeinschaft through grants SFB/TR7 and EXC-153 is acknowledged.