PUSHing Core-collapse Supernovae to Explosions in Spherical Symmetry. IV. Explodability, Remnant Properties, and Nucleosynthesis Yields of Low-metallicity Stars^*

In this study, we explore pre-explosion models of two different metallicities: low metallicity (Z = 10⁻⁴ Z_⊙, "u-series") and zero metallicity (Z = 0, "z-series") from Woosley et al. (2002). These models are based on the stellar evolution code KEPLER and represent nonrotating single stars. We investigate all models of the z-series from 11 to 40 M_⊙ ZAMS mass, increasing in steps of 1 M_⊙. From the u-series, we investigate the corresponding pre-explosion models of the same mass and six additional models between 45 and 70 M_⊙. A list of all pre-explosion models used in this study is given in Table 1. We use the same naming convention as in our previous papers: each model is labeled by its ZAMS mass and the letter "u" or "z," indicating which series it belongs to (see also Table 1). We compare our results for the u- and z-series to those of the two previously investigated series of pre-explosion models with solar metallicity: the "s-series" (Woosley et al. 2002) and the "w-series" (Woosley & Heger 2007), as presented in Papers II and III.

As in our previous studies, we make use of the compactness, introduced in O'Connor & Ott (2011) and given by

$$\begin{eqnarray}&&{\xi }_{M}=\displaystyle \frac{M/{M}_{\odot }}{R(M)/100\,\mathrm{km}},\end{eqnarray} \tag{ 1 }$$

where we use M = 2.0 M_⊙ for the mass enclosed by the radius R(M) in our investigations. In Figure 1 we show the compactness for the low- and zero-metallicity pre-explosion models used in this study and the solar-metallicity models used in our previous studies, which illustrates the nonmonotonic relationship between compactness and ZAMS mass. This is due to a complex interplay of different burning shells and the efficiency of semiconvection and overshooting (Sukhbold & Woosley 2014; Sukhbold et al. 2018). Furthermore, at zero metallicity hydrogen burning proceeds initially solely via the p–p chains, which do not produce enough energy to prevent the star from contracting during H burning. Once the temperature is high enough, the triple-alpha reaction switches on and H burning continues as in low-metallicity stars but at higher temperature. The total mass at collapse, however, follows a monotonic relationship with the ZAMS mass for these low/zero-metallicity pre-explosions models. Stellar winds, which cause mass loss from the stellar surface, are metallicity dependent and can significantly influence the stellar evolution (Chiosi & Maeder 1986). The mass-loss rate scales with the initial metallicity of the stellar model, such that zero-metallicity stars experience virtually no mass loss during their evolution. In Figure 2, we show the internal structure of the pre-explosion models used in this work. We define the Fe core as the layers with Y_e < 0.495, the carbon–oxygen (CO) core mass as the enclosed mass with X_He ≤ 0.2, i.e., up to the beginning of the He shell, and the He core mass as the mass regions with X_H ≤ 0.2, i.e., up to the beginning of the H shell. For ZAMS masses up to ∼27 M_⊙, the CO core masses are very similar for all four series of pre-explosion models and increase monotonically with ZAMS mass. Above 27 M_⊙, the CO core mass continues to increase monotonically for the u- and z-series. For the s- and w-series (at solar metallicity), mass loss can be strong enough that even the outermost layers of the CO core can be stripped (see Figures 3 and 4 in Paper II).

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We use the same setup as in Papers II and III to simulate and investigate the collapse, bounce, and post-bounce phases of all models in Table 1. The hydrodynamic simulations are performed with the general relativistic, adaptive-grid code Agile, which is coupled to neutrino transport. We use the IDSA scheme (Liebendörfer et al. 2009) for the electron-flavor neutrino transport and the advanced spectral leakage scheme (ASL) for heavy-flavor neutrino transport (Perego et al. 2016). For matter in nuclear statistical equilibrium (NSE) conditions we use the finite-temperature, nuclear equation of state (EOS) HS(DD2) (Hempel & Schaffner-Bielich 2010). Matter in the non-NSE regime is described by an ideal gas EOS coupled with an approximate alpha-network. We trigger explosions in spherical symmetry using the PUSH method (Perego et al. 2015). PUSH is a physically motivated, effective method that mimics in one-dimensional simulations the additional neutrino heating caused by accretion and convection present in multidimensional simulations. This is achieved via the parameterized heating term ${Q}_{\mathrm{push}}^{+}$(t, r), which deposits a fraction of the heavy-flavor neutrino energy behind the shock (see Equation (4) in Paper I). This heating term depends on the spectral energy flux for a single heavy lepton neutrino flavor and includes both a spatial term (which ensures that heating only takes place where electron neutrinos also heat) and a temporal term ${ \mathcal G }(t)$, which contains the two free parameters of the method, ${k}_{\mathrm{push}}$ and ${t}_{\mathrm{rise}}$.

We follow Paper II and use the there-presented standard calibration of the PUSH method, which is in good agreement with observations. This calibration uses t_rise = 400 ms and a parabolic dependence of ${k}_{\mathrm{push}}$ on the compactness ξ: ${k}_{\mathrm{push}}(\xi )=a{\xi }^{2}+b\xi +c$, where the calibrated parameters are a = −23.99, b = 13.22, and c = 2.5, and ξ denotes the compactness at bounce. For the standard calibration we use ξ_2.0, i.e., the compactness evaluated at M = 2.0 M_⊙. To investigate the dependence of the explodability and remnant properties on the PUSH calibration, we also study the "second calibration" from Paper II,⁶ which is based on the compactness value ξ_1.75 instead of ξ_2.0. Hence, the "second calibration" depends more strongly on the iron-core mass, resulting in a setup more prone to BH formation.

We include matter of the pre-explosion model from the center to the He layer, corresponding to a radial coordinate of ∼10¹⁰ cm. For the pre-explosion models above ∼30 M_⊙ that collapse to BHs, we include ∼10 M_⊙. The hydrodynamic simulations are run for a total time of 5 s. The outcome of a run for a given model corresponds to one of the following three options: (i) a successful explosion if the explosion energy at the end of the simulation is saturated and positive, (ii) the formation of a BH if the central density exceeds ∼10¹⁵ g cm⁻³ during the 5 s simulation time, or (iii) a failed explosion if the explosion energy is negative at the final simulation time for which PUSH no longer is active. We calculate the explosion energy as in Paper I, where we defined it as the sum of thermal, kinetic, and gravitational energy integrated from the mass cut to the stellar surface (see also Equations (14)–(16) in Paper I).

The detailed nucleosynthesis of our CCSN simulations is calculated in a post-processing approach using the nuclear reaction network CFNET (Fröhlich et al. 2006a), as in Paper III. We follow 2902 isotopes, including free neutrons, protons, and isotopes on both sides of the valley of β-stability, up to ²¹¹Eu. For the reaction rates we use the reaction rate library REACLIB (Cyburt et al. 2010), which is based on experimentally known rates wherever available, and theoretical predictions for n-, p-, and α-capture reactions from Rauscher & Thielemann (2000). For the weak interactions, we include electron and positron capture rates from Langanke & Martínez-Pinedo (2001), β^± decays from the nuclear database NuDat2⁷ and from Möller et al. (1995), and also neutrino/antineutrino captures on free nucleons.

We divide the ejecta into mass elements (called "tracers") of 10⁻³ M_⊙ each. For every tracer, the thermodynamic history is known from the beginning of the hydrodynamical simulation until the final simulation time of 5.0 s. Following Papers II and III, only tracers that reach a peak temperature ≥1.75 GK are processed with the nuclear reaction network. For tracers that are heated to ≥10 GK, we start the nucleosynthesis calculations when the temperature starts dropping below that value. We assume an NSE abundance distribution for the initial abundances at 10 GK. For the other tracers that never reach 10 GK, we start the nucleosynthesis calculations at the beginning of the hydrodynamic simulation and follow the full thermodynamic history of the tracer. In both cases, we use the electron fraction from the hydrodynamic simulation as the initial value and evolve the electron fraction in the nuclear reaction network consistent with the nuclear reactions occurring. The extrapolation of the trajectories of the tracers beyond the end of the hydrodynamic simulations is given by

$$\begin{eqnarray}&&r(t)={r}_{\mathrm{final}}+{{tv}}_{\mathrm{final}},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\rho (t)={\rho }_{\mathrm{final}}{\left(\displaystyle \frac{t}{{t}_{\mathrm{final}}}\right)}^{-3},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&T(t)=T[{s}_{\mathrm{final}},\rho (t),{Y}_{e}(t)],\end{eqnarray} \tag{ 4 }$$

where r is the radial position, v the radial velocity, ρ the density, T the temperature, s the entropy per baryon, and Y_e the electron fraction of the tracer. The subscript "final" indicates the end time of the hydrodynamical simulation. To calculate the extrapolated temperature, we use the EOS of Timmes & Swesty (2000). The end point of the nucleosynthesis calculations is set when the temperature falls below 0.05 GK.

In this section we present and discuss the explosion properties of our simulations for the u-series and z-series. An overview of the explosion properties and predicted remnant properties for all pre-explosion models of this study is given in Figure 3. We show the explosion energy, the explosion time, the ejected ⁵⁶Ni mass, the total ejecta, and the baryonic remnant mass (top to bottom) for the u-series (left column) and the z-series (right column) for the standard calibration.

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We obtain explosion energies from ∼0.2 to 1.6 B. The lowest explosion energies are obtained for the lowest ZAMS mass progenitors (≤12 M_⊙), as well as for the heaviest ZAMS mass progenitors that still explode for both series. In addition, we find very low explosion energies for a few models with ZAMS masses that are located directly next to a region of BH formation (almost-failing SNe; see Section 3.3). The highest explosion energies are obtained for pre-explosion models around ∼15 M_⊙ ZAMS mass for the u-series and around ∼17 M_⊙ for the z-series. This corresponds to the slight shift of the peak compactness values to higher ZAMS masses for the u-series when compared to the z-series.

The obtained ejected ⁵⁶Ni masses range from ∼0.025 to 0.14 M_⊙. Below 20 M_⊙ ZAMS mass, the highest and lowest values of the ejected ⁵⁶Ni coincide with the highest and lowest explosion energies, respectively. Above 20 M_⊙, the almost-failing models do not follow this trend. Instead, they eject the largest amount of ⁵⁶Ni at the lowest explosion energies in delayed explosions. This aspect is discussed in more detail in Section 3.3.

The total ejecta mass increases with ZAMS mass below ∼20 M_⊙ for all exploding models. Above ∼20 M_⊙ ZAMS mass, the total ejecta mass continues to increase with increasing ZAMS mass for models at low/zero initial metallicity, while at solar metallicity the total ejecta mass decreases with increasing ZAMS mass above ∼20 M_⊙. This is because at low metallicity massive stars experience almost no mass loss during their evolution, and as a result they collapse with their initial mass, while at solar metallicity mass loss is quite strong, which reduces the total stellar mass significantly.

For the exploding models, we obtain gravitational NS masses from ∼1.3 to 1.8 M_⊙. Overall, the u-series is more prone to BH formation than the z-series, consistent with the results of O'Connor & Ott (2011). Also in agreement with their results, we find that low-metallicity stars above ∼30 M_⊙ robustly form BHs. These low-metallicity sets were studied by Pejcha & Thompson (2015) as well. While they also find successful explosions interwoven with BH formation, their detailed predictions differ from ours. In particular, one of their parameterizations predicts a larger fraction of BHs compared to our standard calibration, including BHs below 20 M_⊙ ZAMS mass, for both progenitor sets. Their second parameterization is more optimistic and predicts explosions below 20 M_⊙; however, it also finds many exploding models above 30 M_⊙, in contrast with our results. In the u-series, BH formation starts to occur at lower ZAMS masses than in the z-series. Exploding models beyond 20 M_⊙ ZAMS mass also have lower explosion energies in the u-series than their counterparts in the z-series. As we have speculated in Paper II—based on the higher compactness and larger stellar masses at collapse—the low-metallicity models indeed do not lead to successful explosion above ∼30 M_⊙ and therefore constitute a potential origin of the BHs seen by LIGO/VIRGO (see also Section 6).

In Figure 4, we give a summary of the final outcomes of the "standard calibration" and of the "second calibration" for both samples of pre-explosion models presented in this paper and the two samples at solar metallicity discussed in Paper II. In agreement with our previous work, we see that the second calibration results in a lower explodability and leads to a larger fraction of BHs, which is of particular interest for the resulting birth-mass distributions of NSs and BHs discussed in Section 6. Additionally, the low- and zero-metallicity series have a continuous region of BH formation above certain values of ZAMS mass for both calibrations. The one outlier to this in the z-series is a model with very low explosion energy and that almost fails to explode (see also Section 3.3).

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In this section, we examine the outcomes of our simulations in terms of the compactness ξ_2.0 at bounce and discuss emerging trends. The explosion energy, the baryonic remnant mass, and the explosion time for both series of pre-explosion models are shown in Figure 5. For all three quantities we find similar trends to those for the samples at solar metallicity presented already in Paper II.

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For the explosion energy as a function of the compactness we find two trends within our models. Below compactness values of ξ_2.0 ∼ 0.3 the explosion energy increases roughly linearly with compactness (${k}_{\mathrm{push}}$ increases with compactness up to ξ_2.0 ∼ 0.3; see Figure 8 in Paper II). Above compactness ξ_2.0 ≳ 0.3, we observe a bifurcation into two branches of explosion energies. In one branch (consisting mostly of filled symbols), the explosion energies decrease with compactness, slightly following the decrease in ${k}_{\mathrm{push}}$ for ξ_2.0 ≳ 0.3 of our calibration. In the other branch (consisting of open symbols) continues the increasing relation between compactness and explosion energy from ξ_2.0 < 0.3. The two branches of explosion energy correspond to the pre-explosion models with similar compactness but distinct ZAMS masses. In Figure 1 we see that there are two regions of ZAMS masses, separated by a peak in compactness around ∼25 M_⊙, which have similar values of compactness. These models, however, differ in their total mass at collapse and also in the mass of the CO core (see Figure 2). These differences lift the degeneracy in compactness and explain the two branches of explosion energies. In Figure 5 we use open markers for models to the left of the peak in compactness and filled markers for models to the right of the peak to emphasize this point. Furthermore, the models in the lower explosion energy branch have higher pre-explosion model mass and an overall flatter density profile with on average higher densities above an enclosed mass of ∼1.25 M_⊙. Therefore, in these models more mass needs to be unbound in the course of the explosion and the shock front needs to pass through denser infalling matter.

We find a strong correlation between the NS mass and the compactness. Models with a higher compactness experience higher mass accretion rates and therefore accrete more matter onto the PNS before they ultimately explode. In our framework, the models with the highest compactness values do not explode and instead collapse to BHs. This sets an upper mass limit for the NSs that are formed in CCSNe. The explosion times somewhat reflect our choice of calibration and as such are not a true prediction from our models. The models with the lowest and the highest compactness values have lower values of ${k}_{\mathrm{push}}$ and hence take longer to explode than the models with intermediate compactness values where ${k}_{\mathrm{push}}$ reaches the largest values. There the explosion times become comparable to the set value of ${t}_{\mathrm{rise}}$.

As we have seen in Section 3.1, there are some models with low explosion energies around 0.3 B and relatively high masses of ejected ⁵⁶Ni around 0.1 M_⊙. From Figure 3 we immediately find that these are the u24, u30, and z31 models, which have very low explosion energies and large values of ejected ⁵⁶Ni mass, coupled with very delayed explosion times and among the highest remnant masses in the investigated samples. All three models have high compactness values (ξ_2.0 ∼ 0.6) and are right next to regions of BH formation. In our calibration of PUSH, a high compactness value implies a small ${k}_{\mathrm{push}}$ value, and hence only a little extra heating is provided, which results in delayed explosions (or no explosion). A reduction of ${k}_{\mathrm{push}}$ by a small amount leads to the failing of the explosion of these models, and an increase of ${k}_{\mathrm{push}}$ would result in earlier explosions with increased explosion energies. For delayed explosions, the mass accretion onto the freshly formed PNS extends to later times. This leads to higher luminosities of the electron neutrinos and antineutrinos during this extended accretion. As a consequence, the neutrino heating from electron neutrinos and antineutrinos is enhanced at later times. This is illustrated with Figure 6, which shows the contributions from electron neutrinos/antineutrinos (dE_IDSA/dt) and from PUSH (dE_push/dt), as well as the total heating rate dE_tot/dt for z31 (blue) and z30 (green). In the almost-failing models such as u24, u30, and z31 this extended heating leads to very marginal and delayed explosions (t_expl ≳ 0.5 s). A delayed explosion time also means that some of the energy is deposited in layers that will be accreted later onto the PNS, which further reduces the final explosion energy. As long as the mass accretion and hence the high neutrino luminosities persist, the material above the PNS is being heated to temperatures ≳6 GK, sufficient for the synthesis of ⁵⁶Ni. In models with delayed explosions, this is ∼0.1 M_⊙ of material (a similar amount of ⁵⁶Ni is synthesized in models with more canonical explosion energies around 1 B). In spherically symmetric models the accretion onto the PNS effectively shuts off when the explosion sets in irrevocably. In models with short explosion times, the accretion onto the PNS turns off early, allowing less material to be neutrino heated to temperatures high enough for the synthesis of ⁵⁶Ni. In models that ultimately fail to explode, similar (or larger) amounts of mass are neutrino heated above 6 GK; however, all of this material eventually accretes on the central compact object.

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Based on the low explosion energies, the delayed explosion times, and the fact that these models are directly next to BH-forming regions, we argue that they could easily experience sufficient fallback to transition into the failed SN branch of neutrino-driven SNe. We will discuss the effect the assumed collapse of the critical models has on the resulting distribution of the NS birth mass and BH birth mass in Section 6. Due to the large amount of synthesized ⁵⁶Ni, the weakly exploding CCSNe could result in comparably bright events.

Here we want to examine the yields of all models for trends with ZAMS mass and compactness of the pre-explosion models. As seen in Figure 3, we do not find a monotonic behavior of ejected ⁵⁶Ni as a function of the ZAMS mass. However, we find a correlation of the symmetric (N = Z) isotopes ⁵⁶Ni and ⁴⁴Ti with compactness ξ_2.0, as seen in the first and fourth panels of Figure 9. The correlation is similar for the u-series and z-series presented in this paper to that for the s-series and w-series presented in Paper III. When combining the results from all four sets of pre-explosion models, it becomes visible that the correlation has some width to it, which indicates that an exact one-to-one connection between compactness and ⁵⁶Ni ejecta may not exist. Some of our models with the highest yields of ejected ⁴⁴Ti are the almost-failing models with low explosion energy and high ⁵⁶Ni yields discussed in Section 3.3. The asymmetric nickel isotopes ⁵⁷Ni and ⁵⁸Ni behave differently. The yields of these asymmetric isotopes strongly depend on small changes in the local Y_e, with lower values of Y_e favoring higher production of ^57,58Ni (see second and third panels of Figure 9). The color-coding in Figure 9 denotes the electron fraction of the layers where each isotope is made. In Paper III, we found two (or more) branches of yields that independently correlate with compactness for the pre-explosion model sets at solar metallicity. The u-series and the z-series predominantly populate the branch with lower yields of the asymmetric ^57,58Ni isotopes. For almost all models of the z-series, the final mass cut lies in layers with Y_e ∼ 0.5, either in the Si layer but outside of the region with Y_e < 0.5 or in the O-rich layer. The only exception is z15.0, where the mass cut is located in the inner parts of the Si-rich layer, where the pre-explosion Y_e is lower (Y_e ∼ 0.498). This allows for the ejection of slightly neutron-rich material where asymmetric isotopes such as ^57,58Ni can be synthesized. In the u-series, only u11.0 and u12.0 are on the branch with higher yields of ⁵⁷Ni. In these two models, the final mass cut is in the Si-rich layer where Y_e ∼ 0.498, allowing for the synthesis of asymmetric nickel isotopes.

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The elemental yields of the iron-group elements show similar trends (see bottom four panels of Figure 9). To understand these trends, we need to look at the isotopes from which the elemental yields originate. For example, elemental titanium is mainly synthesized as ⁴⁸Cr (a symmetric isotope), and chromium is synthesized as ⁵²Fe (also a symmetric isotope). Thus, the elemental yields of Ti and Cr, similar to ⁴⁴Ti and ⁵⁶Ni, show linear correlations with compactness, having experienced the highest temperatures and an alpha-rich freeze-out. Manganese is made as (asymmetric) ⁵⁵Co, and stable nickel is dominated by ⁵⁸Ni and ⁶⁰Ni, which are made as ⁵⁸Ni and ⁶⁰Cu. Hence, the yields of elemental Mn and Ni strongly depend on the local Y_e value. With the exception of z15.0, all models of the u-series and z-series result in low elemental Mn yields. Only u11.0, u12.0, u14.0, and z15.0 have relatively high elemental Ni yields (synthesized at relatively low Y_e values).

In Section 3.3, we discussed explosion details of the models that do not follow the general correlation between explosion energy and ⁵⁶Ni yields. Here we analyze the detailed nucleosynthesis yields of these models using the z31.0 model, which we compare to model z30.0 to illustrate the differences. Figures 10 and 11 show the post-explosion profiles of the innermost ∼1 M_⊙ of ejecta above the mass cut. For z30.0 (a model that follows the general E_expl–⁵⁶Ni trend) the mass cut resides inside the Si layer. The ejected ⁵⁶Ni is explosively synthesized from ²⁸Si. For z31.0 (an almost-failing model with low explosion energy and high Ni yields), the final mass cut is located farther from the center in the O-rich layer. Here, the ejected ⁵⁶Ni originates from explosively processed ¹⁶O instead. However, the total amount of ejecta heated to temperatures above 6 GK (and hence resulting in ⁵⁶Ni) is similar in z30.0 and z31.0. While z30.0 and z31.0 both have ejecta with similar peak electron fractions of Y_e ∼ 0.515, the z31.0 model has some ejecta just above the mass cut with low enough Y_e values that the ⁵⁸Ni production is enhanced to approximately the same level as ⁵⁷Ni. The yields of alpha-elements and iron-group elements are very similar between z30.0 and z31.0. Only beyond mass number A ≈ 80 are there some (small) differences in individual isotopes, but the overall abundance pattern is the same.

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We display in Figure 12 the abundances of selected stable isotopes (¹⁶O, ²⁸Si, and ⁴⁰Ca) and of three iron-group elements (Mn, Ni, Zn) for six different ZAMS masses to analyze their dependence on the initial metallicity of the pre-explosion model. The ¹⁶O is mainly produced in helium and neon burning and is expected to be mostly independent of the initial stellar metallicity. In our models, there is no trend of ¹⁶O abundance with initial metallicity. However, we find higher abundances of ¹⁶O for higher ZAMS mass owing to the overall larger stellar mass and larger CO core. The decrease in ¹⁶O yield for the s28.0 model is due to explosive O burning. Of the models shown, s28.0 is the only model with an extended layer consisting of a mixture of ¹⁶O and ²⁸Si, which allows for ¹⁶O being explosively burned (the other models have a sharp transition from ²⁸Si to ¹⁶O at the Si–O interface). For ²⁸Si and ⁴⁰Ca, we find weak trends with initial metallicity: For the higher ZAMS mass models, there are somewhat higher abundances of ²⁸Si and ⁴⁰Ca ejected. In the lower ZAMS mass models, our results do not exhibit any metallicity dependence in those abundances. The yields of iron-group elements, such as Ni, are more sensitive to the details of the explosion, as they are synthesized during explosive burning in the innermost ejecta. The yields of symmetric iron-group nuclei depend mostly on the explosion strength and hence the local peak temperature. For odd-Z elements, the final abundances are also quite sensitive to the local Y_e-values, as previously discussed. With very few exceptions, all models of the z-, u-, and s-series only synthesize a very low abundance of Mn. As discussed in Paper III, the small nuclear network used for modeling the pre-explosion evolution artificially keeps the Y_e closer to 0.5, which is not favorable for the production of Mn. As expected, the Ni yields are mostly independent of the initial metallicity. The higher yields of Ni (and also of other iron-group elements) in some of the solar-metallicity models (e.g., s28.0 and s30.0) are due to these models having larger explosion energies than their low/zero-metallicity counterparts. In our models, zinc is synthesized as ⁶⁴Zn in layers with Y_e > 0.5 and as neutron-rich isotopes of Zn in neutron-rich layers close to the mass cut. The final abundances of Zn are very sensitive to the amount of proton-rich and neutron-rich ejecta, which depends on the explosion strength, the neutrino/antineutrino luminosities, the local Y_e, and the location of the mass cut. Our models span a range of conditions that is reflected in the range of Zn yields we obtain. We do not find any clear trends with metallicity or with ZAMS mass.

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First, we compare our simulations to observations of CCSNe. In the top panel of Figure 13 we show the explodability for the progenitors in our sample in comparison with observed explosion energies (black crosses). The observational data shown are the same as in Paper II, complemented with the sample of Müller et al. (2017). Note that the observed SNe are in the local universe (redshift z < 0.01). Hence, we do not expect a perfect agreement of the models from low- and zero-metallicity progenitors with the observational data. Nevertheless, including the observational data in the figure is useful to identify general trends. The overall trend in explosion energy is very similar to what we found for pre-explosion models at solar metallicity (see Paper II). The explosion energies for both sets (u and z) increase from lower values for low-mass progenitors ("Crab-like SNe") to explosions with energies E_expl ≈ 0.8–1.6 B between 15 and 21 M_⊙. We find the strongest explosions around 15 M_⊙ for the u-series and at slightly higher masses around 17 M_⊙ for the z-series. For ZAMS masses above 20 M_⊙ we find predominantly BHs (denoted by short vertical lines along the bottom axis), interspersed with some explosions. As expected from the higher compactness values, we find more failed explosions and BHs, and overall lower explosion energies, for a given ZAMS mass (especially for ZAMS masses >25 M_⊙) at low and zero metallicity compared to solar metallicity. As already seen in Figure 1, the compactness curves for the four sets of progenitors are quite similar in shape. The only big difference is a shift of the peak compactness values in the u-series to lower ZAMS masses when compared to the other three series. From this we expect quite similar behaviors from the four series, only with a shift of the peak explosion energies to slightly lower ZAMS masses for the u-series, as seen in Figure 13.

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In the bottom panel of Figure 13 we show the resulting ⁵⁶Ni yields against the corresponding explosion energies. When comparing the ⁵⁶Ni yields from our simulations with observations, we find that most models agree well with observations (as in the case of solar-metallicity models). We find that the amount of ⁵⁶Ni increases with ZAMS mass up to ∼15 M_⊙ and then remains roughly constant, similar to our findings in Paper III. The almost-failing models with ⁵⁶Ni yields of ∼0.1 M_⊙ and with very low explosion energies (<0.5 B) discussed in Section 3.3 can be seen above and to the left of the observational data. It is worth reminding the reader that the ⁵⁶Ni (and the iron group in general) is synthesized from completely dissociated material after shock passage. Hence, the initial metallicity does not directly impact the yield of ⁵⁶Ni (and other iron-group nuclei). The lower observed explosion energies and ⁵⁶Ni ejecta masses originate from progenitors at or below 10 M_⊙ ZAMS mass, which are not included in our samples.

Next, we compare our predicted yields with the observationally derived abundances in metal-poor stars. The atmospheres of these low-mass, long-lived, metal-poor stars carry the signature of one or a few previously exploded CCSNe from massive stars that deposited their yields in the interstellar medium. The iron-group elements are of particular interest to test our CCSN nucleosynthesis predictions, as they are made in primary explosive nucleosynthesis processes. In Figure 14 we compare our predictions for iron-group elements with the abundances of metal-poor star HD 84937 (z-series in the top panel; u-series in the bottom panel). The abundances of this metal-poor star have recently been determined using improved laboratory data for neutral and singly ionized transitions in iron-group elements (Sneden et al. 2016). Each transparent square represents one of our models. Our results are not weighted with an initial mass function (IMF) to illustrate how sensitive or robust the results for each element are. The triangles indicate the observational data (neutral and singly ionized species). Overall, we find a good agreement between our predictions and the observational data. We do not find significant differences between the u-series and the z-series. Scandium and zinc are synthesized at levels comparable to the observed values of [Sc/Fe] and [Zn/Fe], respectively. Both elements are difficult to produce in sufficient amounts in traditional piston and thermal bomb nucleosynthesis calculations that neglect the neutrino interactions and employ a canonical explosion energy of 10⁵¹ erg. Enhanced explosion energies, such as in hypernovae, lead to enhanced production of Sc and Zn, even without the inclusion of neutrino interactions (Nomoto et al. 2006). A careful treatment of the neutrino interactions robustly leads to enhanced production of Sc and Zn already at canonical explosion energies (Fröhlich et al. 2006a). Our models (u-series and z-series) co-produce Zn with Fe. We find a smaller spread of [Zn/Fe] values in the u-series and z-series as at solar metallicity (top panel of Figure 9 in Paper III). As in the case of the s-series, we find that [Mn/Fe] is significantly lower than the observations in both the u- and the z-series. We attribute this to the relatively small network used in the pre-explosion models of WHW02 at all metallicities, which results in Y_e values of ∼0.4995 in the relevant layers. As discussed above, the production of manganese is quite sensitive to the local Y_e value. Hence, a Y_e value of ∼0.4995 yields small amounts of manganese. The pre-explosion models of the w-series employ a much larger network during the stellar evolution phase, which results in a somewhat lower final Y_e (∼0.4992) and hence larger values of [Mn/Fe]; see Paper III for details.

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