Chromium Nucleosynthesis and Silicon–Carbon Shell Mergers in Massive Stars

We use the GCE code OMEGA+ (Côté et al. 2018) to bring NuGrid yields (Ritter et al. 2018c) into a galactic context. This code is part of the open-source JINAPyCEE python package¹⁰ and represents a one-zone GCE model surrounded by a large circumgalactic gas reservoir. The input parameters adopted in this study for regulating the star formation efficiency and the galactic inflow and outflow rates are available online.¹¹ We use the initial mass function of Kroupa (2001). For SNe Ia, we use the yields of Iwamoto et al. (1999) and assume a total number of 10⁻³ SN Ia per unit of stellar mass formed. As shown below, the overproduction of Cr is so strong that the choice of GCE parameters and SN Ia yields is of little importance.

The upper panel of Figure 1 shows the predicted evolution of Cr abundances as a function of [Fe/H]. Near [Fe/H] = 0, our predictions (solid line) have a bump that overestimates disk data by almost an order of magnitude. The 20 M_⊙ stellar model at Z = 0.01 is at the origin of the Cr bump (see also Figure 7 in Herwig et al. 2018). When removing this stellar model from the yields set, the bump disappears entirely (dashed line in Figure 1). The bottom panel shows a production of V accompanying the production of Cr. This is not surprising, as V and Cr are made efficiently at similar stellar conditions (e.g., Woosley & Weaver 1995). In agreement with the simulations reported here, [V/Fe] is typically underestimated in GCE models at all metallicities compared with observations (e.g., Prantzos et al. 2018 and references therein).

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Here we describe the evolution of the 20 ${M}_{\odot }$ model at Z = 0.01. We show that the source of Cr comes from the merging of the C- and Si-burning convective shells during the last hour of evolution before the model collapses. The Kippenhahn diagrams in Figure 2 show the evolution of convection zones (hatched regions) in the inner 6 ${M}_{\odot }$ of the model. Convective boundary mixing was applied during the main sequence and the core He-burning phase, which likely contributed to the large CO and Si cores. No overshooting was applied after the He-core burning phase. We refer to Ritter et al. (2018c) for more details on this stellar model. At ${t}^{* }\equiv ({t}_{\mathrm{collapse}}-t)/\mathrm{yr}\approx {10}^{-3}$, there is a radiative layer that separates the convective Si-burning shell from the convective C-burning shell above. At that time, as shown by the blue dashed line in Figure 3, the jump in entropy between the Si and C shells is relatively small compared with entropy barriers at the base of the Si shell (mass coordinate of $\sim 1.5{M}_{\odot }$) and at the top of the C shell (mass coordinate of $\sim 5{M}_{\odot }$).

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Shortly after, as the O shell completely burns, the top of Si shell reaches the base of the C shell. From that time until ${t}^{* }\approx {10}^{-4},$ the stratified Si- and C-burning convective shells share a convective boundary, which prevents the transport of material from the C shell into the Si shell, and vice versa. Finally, at ${t}^{* }\approx {10}^{-4},$ the convective boundary is eroded and the Si-burning shell extends from the edge of the Fe core almost to the edge of the CO core. The top panel of Figure 2 shows that ⁵²Cr is mixed out to the edge of the CO core and its mass fraction is slightly reduced owing to dilution by the C-shell material. The entropy profile at that time is shown by the orange solid line in Figure 3. The large entropy barriers at the base and the top of the Si–C shell prevent further mixing throughout the stellar interior.

As shown by our GCE model (Figure 1), a boost of [Cr/Fe] is generated above [Fe/H] ≈ −0.2 when the yields of this 20 ${M}_{\odot }$ model are included. One might expect that if the Si-burning shell was mixed out and ejected, then [Cr/Fe] should stay relatively flat, as both Cr and Fe are predominant products of Si burning. However, because the Si shell merges while it is still convective, and hence still burning, the ejected chemical signature is typical of incomplete Si burning.

Si burning produces the neutron-magic isotope ⁵²Cr relatively quickly, and thereafter produces ⁵⁶Fe via a sequence of capture and photodisintegration processes. This is illustrated in Figure 4, which shows the results of a one-zone nuclear reaction network calculation starting from pure ²⁸Si and evolved at density ρ = 2 × 10⁶ g cm⁻³ and temperature T = 2.6 GK, which are approximately the conditions during shell Si burning in the 20 ${M}_{\odot }$ stellar model about an hour before collapse. We note that the timescales of the burning will be different in the star, owing to the evolution of the core acting to increase the density and temperature of the shell. However, we have confirmed that the behavior is similar for a range of temperatures and densities. Only in the most extreme conditions (10¹⁰ g cm⁻³, 5 GK) is Cr produced at the same time as Fe.

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The core-collapse supernova (CCSN) explosion for this star was modeled by Ritter et al. (2018c) in the same way as described in Pignatari et al. (2016), with a mass cut at 2.77 ${M}_{\odot }$ based on remnant mass prescription derived in Fryer et al. (2012). In this particular model with these assumptions, a significant fraction of the incomplete pre-SN Si-shell material, including ⁵²Cr and ⁵¹V, is ejected during the explosion (the convective Si–C shell extends up to ∼ 2 ${M}_{\odot }$ above the assumed mass cut). The stellar yields used in our chemical evolution model account for the supernova shock and the explosive nucleosynthesis. The strong overproduction of Cr seen in Figure 1 shows that this pre-SN Si-shell signature is not significantly destroyed during the explosion.

The overproduction of Cr and V, relative to Fe, during hydrostatic Si burning was already found by Thielemann & Arnett (1985) and is not considered as an anomalous result. However, this material is typically buried in the compact remnant after the CCSN explosion, and therefore not ejected in the interstellar medium, or used as a seed for the explosive nucleosynthesis. Explosive Si-burning material alone may carry a signature with a super-solar Cr/Fe ratio (e.g., Woosley et al. 1973; Thielemann et al. 1996). A composition of explosive Si-burning and O-burning components in CCSN ejecta allowed to overcome such a problem but caused instead a general underproduction of V relative to Fe (e.g., Timmes et al. 1995; Goswami & Prantzos 2000; Kobayashi et al. 2011).

The 2.77 ${M}_{\odot }$ compact remnant is a black hole created by fallback (Fryer et al. 2012). In agreement with Sukhbold et al. (2016) and Ebinger et al. (2019), stars around 20 ${M}_{\odot }$ are generally found to produce more failed explosions and black holes in 1D simulations than for lower initial masses.

Originally, the prescription of Fryer et al. (2012) was designed to reproduce the compact object mass distribution observed in the Milky Way, in particular the presence of a gap in the mass distribution between neutron stars and black holes (see Belczynski et al. 2012 and references therein). Given the nature of the prescription, the mass cut of the massive star models of Ritter et al. (2018c), including the 20 ${M}_{\odot }$ model addressed in the present work, are set independently of the internal structure of the pre-SN model. This lack of connection between pre-SN structure and remnant mass adds uncertainties to whether or not the Cr-rich material of this particular model should have been ejected at all. However, CCSN theory has far from settled on the precise relationship between progenitor structure and explosion properties (Sukhbold & Woosley 2014; Müller 2016; Fryer et al. 2018). Even if we knew the remnant mass for a typical model of this initial mass and metallicity, the structure of the core in our model is affected by the shell merger in ways that are likely important in determining the dynamics of the collapse and subsequent explosion, or lack thereof, and compact remnant mass (e.g., Davis et al. 2019; Yadav et al. 2020).

Two of the most important properties of the progenitor models for determining the outcome of the CCSN are the stratification of density and electron fraction (Y_e). The left panel of Figure 5 shows how the Y_e profile is altered by the merger. The right panel shows that the shell merger erases the density jump that existed at the interface of the two shells (see arrow). Such a jump may facilitate the revival of the stalled CCSN shock wave owing to the rapid drop in accretion rate as the shell arrives at the shock radius (e.g., Buras et al. 2006; Ott et al. 2018). Although this particular density jump appears small, it could still be enough to alleviate the ram pressure at a critical time and allow for a successful explosion. Conversely, it may be that a more realistic simulation of this progenitor model results in direct black hole formation or formation of a much larger black hole than 2.77 ${M}_{\odot }$ by fallback, in which case we would perhaps expect none of the CO core (and hence, none of the Cr) to be ejected. Further implication for the SN explosion may derive from asymmetries that could be seeded right before the explosions in a shell merger, depending on the timescales for convection and burning during the merger.

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The Y_e profile shown in Figure 5 raises another interesting point. The profile is not flat in the newly combined convection zone between 1.4 and 5 ${M}_{\odot }$ (see solid orange line), as revealed by the time-dependent mixing, implemented in the diffusion approximation, when nuclear and mixing timescales are similar. The presupernova profile represents a state of incomplete mixing of the material in the two shells. The convective timescale τ_conv, assuming it is approximately the time taken for a fluid element to complete one cycle of advection around a convective cell whose diameter is the shell's thickness, is given by

$$\begin{eqnarray}&&{\tau }_{\mathrm{conv}}\approx \displaystyle \frac{2\pi {r}_{\mathrm{cell}}}{\langle {v}_{\mathrm{conv}}\rangle }\approx \displaystyle \frac{(7.4\times {10}^{9})\pi \ \mathrm{cm}}{6.3\times {10}^{6}\ \mathrm{cm}\,{{\rm{s}}}^{-1}}=3690\ {\rm{s}}.\end{eqnarray} \tag{ 1 }$$

The shell merger takes place 10⁻⁴ yr or 3154 s before collapse, which is a similar timescale.

This raises the question of how efficient will be the mixing of ⁵²Cr and other Si-burning products into the outer core if there is only one turnover time to do it. Certainly the use of mixing length theory (MLT) for convection becomes inappropriate under these conditions because MLT only predicts convection properties in terms of averages over many convective turnover timescales.

The constitution of the C shell should burn rapidly when exposed to the temperatures in the Si-burning shell. This energetic feedback will likely modify the flow dynamics and it should be considered when modeling the presupernova evolution of such a star (e.g., Herwig et al. 2014; Andrassy et al. 2020; Yadav et al. 2020).

We have estimated the burning timescale of ¹²C by performing a simple nuclear network calculation beginning from 90% ²⁸Si and 10% ¹²C. We keep the temperature fixed at 3 GK and the density at 1.4 × 10⁸ g cm⁻³. We define the burning timescale as the e-folding time of the ¹²C mass fraction X_C under such conditions,

$$\begin{eqnarray}&&{\tau }_{\mathrm{burn}}\approx \displaystyle \frac{{dt}}{d\,\mathrm{ln}{X}_{{\rm{C}}}}.\end{eqnarray} \tag{ 2 }$$

For example, near the bottom of the Si shell the timescale is ∼10⁻³ s, which is much shorter than the $\sim {10}^{3}\,{\rm{s}}$ convective timescale, giving an exceptionally large Damköhler number of Da $=\,{\tau }_{\mathrm{mix}}/{\tau }_{\mathrm{burn}}\approx {10}^{6}$ (Figure 6). This means the material in the C shell will never actually reach the bottom of the convection zone. Instead, the situation is reminiscent of the H-ingestion into He-shell convection in a post-AGB star. The distributed combustion flame is located where Da ∼ 1 (Herwig et al. 2011), which in this case is in the lower third of the Si convection zone. Depending on the energy release of the convective–reactive burn relative to the initial convective kinetic energy, a global non-spherical convective–reactive instability may ensue, such as the Global Oscillation of Shell H-ingestion (GOSH) that has been reported for H-ingestion into He-shell flash convection (Herwig et al. 2014). The exact nature of the convective-reactive event and its impact on yields requires a more comprehensive 3D hydrodynamics and nucleosynthesis simulation approach which is beyond the scope of this work.

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