Free Access
Issue
A&A
Volume 627, July 2019
Article Number A146
Number of page(s) 5
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201936024
Published online 16 July 2019

© ESO 2019

1. Introduction

The nucleosynthesis resulting from type Ia supernovae (SNIa) reflects the thermodynamical history of the progenitor white dwarf (WD) during the explosion and its initial chemical composition. Thus, nucleosynthetic constraints coming from observations of supernovae and their remnants are an important source of knowledge of the conditions achieved during the explosion. The optical properties, spectra, and light curves of SNIa over a few weeks around maximum brightness have been used to infer the chemical profile of the ejecta (Stehle et al. 2005; Mazzali et al. 2008; Tanaka et al. 2011; Sasdelli et al. 2014; Ashall et al. 2016). However, the ability to constrain the nucleosynthetic products based on optical data is hampered by the complex physics that governs the formation of spectral features in the visible, ultraviolet, and infrared bands.

Observations of sufficiently close supernova remnants (SNRs) are an alternative to obtain information about the chemical composition of the ejecta (e.g. Hamilton & Fesen 1988; Fesen et al. 1988). Hundreds to a few thousands of years after the explosion, the ejected elements emit strongly in the X-ray band due to shock heating, and their emission lines can be detected and measured by current X-ray observatories (e.g. Hughes et al. 1995; Vancura et al. 1995; Badenes et al. 2008; Yamaguchi et al. 2014, 2015). Recently, the high spectral resolution of Suzaku has allowed the relative mass ratio of calcium to sulfur, MCa/MS, to be measured in a few SNRs with a precision of ∼5%−16% (Martínez-Rodríguez et al. 2017), with the result that this ratio spans the range 0.17−0.28, with an uncertainty of 0.04 in both limits (for reference, this mass ratio is 0.177 in the solar system; Lodders 2003). These results have been interpreted in terms of metallicity-dependent yields during explosive oxygen burning.

There are two effects to account for in relation with α-rich oxygen burning: first, the strength of the enhancement of the yield of calcium at all metallicities, and second, the metallicity dependence of the mass ratio of calcium to sulfur, MCa/MS, in the ejecta. Both calcium and sulfur are a product of explosive oxygen burning, and they are synthesized in proportion to their ratio in conditions of quasi-statistical equilibrium, which depends on the quantity of α particles available: (De et al. 2014). Woosley et al. (1973) studied the conditions under which explosive oxygen burning would reproduce the solar-system abundances. They explained that oxygen burning can proceed through two different branches: α-poor and α-rich. The α-poor branch has the net effect that for every two 16O nuclei destroyed, one 28Si nuclei and one α particle are created. This branch proceeds mainly through the fusion reaction of two 16O nuclei, but it is contributed as well by the chain 16O(γ, α)12C(16O,γ)28Si. On the other hand, the α-rich branch involves the photo-disintegration of two 16O nuclei to give two 12C plus two α particles, followed by the fusion reaction 12C(12C,α)20Ne(γ, α)16O, which releases a total of four α particles for each 16O nuclei destroyed. Woosley et al. (1973) included the chain 16O(p,α)13N(γ,p)12C in the α-rich branch and listed these two reactions (and their inverses) among the most influential reactions for explosive oxygen burning. Bravo & Martínez-Pinedo (2012) found that the 16O(p,α)13N reaction rate and its inverse are among the ones that impact most the abundance of 40Ca, in agreement with Woosley et al. (1973).

De et al. (2014) and Miles et al. (2016) noticed that MCa/MS can be used to infer the metallicity, Z, of the progenitor of SNIa, but they did not identify the source of the metallicity dependence of the calcium and sulfur yields. Later, Martínez-Rodríguez et al. (2017) used the measured MCa/MS in a few type Ia SNRs of the Milky Way and the Large Magellanic Cloud (LMC) to determine the progenitor metallicity, and concluded that there had to be an unknown source of neutronization of the WD matter before the thermal runaway besides that produced during carbon simmering (Chamulak et al. 2008; Piro & Bildsten 2008; Martínez-Rodríguez et al. 2016; Piersanti et al. 2017). They also pointed out that SNIa models that used the standard set of reaction rates were unable to reproduce the high calcium-to-sulfur mass ratio measured in some remnants.

In the present work, it is shown that the origin of the metallicity dependence of MCa/MS has to be ascribed to the 16O(p,α)13N reaction. In the following section, the mechanisms by which the 16O(p,α)13N reaction controls the α particle abundance as a function of the progenitor metallicity are explained. If the 16O(p,α)13N reaction is switched off, the value of MCa/MS remains insensitive to metallicity. In Sect. 3, the uncertainty of the 16O(p,α)13N rate is reported along with the limits to its value that can be obtained from the measured MCa/MS in SNRs. The conclusions of this work are presented in Sect. 4.

2. 16O(p,α)13N and metallicity

The chain 16O(p,α)13N(γ,p)12C provides a route alternative to 16O(γ, α)12C to convert 16O to 12C and feed the α-rich branch of explosive oxygen burning (Woosley et al. 1973). The chain neither consumes nor produces protons, however its rate depends on the abundance of free protons. In the shells that experience explosive oxygen burning in SNIa, the neutron excess is closely linked to the progenitor metallicity. At small neutron excess, hence low progenitor metallicity, there are enough protons to make 16O(p,α)13N operational. At large neutron excess, hence large progenitor metallicity, the presence of free neutrons neutralizes the protons, and undermines the chain 16O(p,α)13N(γ,p)12C efficiency. This is because in explosive oxygen burning, quasi-statistical equilibrium holds for the abundances of nuclei between silicon and calcium (Truran & Arnett 1970). In quasi-statistical equilibrium, a large neutron-excess leads to a large abundance of neutronized intermediate-mass nuclei such as, for instance, 34S or 38Ar, which react much more efficiently with protons than the α-nuclei such as 32S or 36Ar that are produced in low-neutron-excess conditions.

To illustrate the above ideas, Figs. 13 show the evolution of key quantities related to the branching of explosive oxygen burning into either the α-rich or the α-poor tracks. Specifically, the plots show the evolution of a mass shell reaching a peak temperature of 4 × 109 K in models 1p06_Z2p25e−4_ξCO0p9 and 1p06_Z2p25e−2_ξCO0p9, described in Bravo et al. (2019). In short, both models simulate the detonation of a WD with mass 1.06 M made of carbon and oxygen, whose progenitor metallicities are respectively Z = 2.25 × 10−4 (strongly sub-solar metallicity, hereafter the low-Z case) and Z = 0.0225 (about 1.6 times solar, hereafter the high-Z case). In both models, the rate of the fusion reaction 12C + 16O has been scaled down by a factor 0.1 as suggested by Martínez-Rodríguez et al. (2017; see also Bravo et al. 2019).

thumbnail Fig. 1.

Nucleosynthetic fluxes from 16O to 12C due to the 16O(p,α)13N (solid lines) and the 16O(γ, α)12C (dot-dashed lines) reactions as a function of time, in a mass shell with peak temperature 4 × 109 K, for a 1.06 M WD with either progenitor metallicity Z = 2.25 × 10−4 (red) or Z = 0.0225 (blue). The nucleosynthetic flux of the 12C fusion reaction is also plotted with dotted lines.

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A larger proton abundance in the low-Z case at the same temperature and similar oxygen abundance as in the high-Z case implies a larger nucleosynthetic flux from the 16O(p,α)13N(γ,p)12C chain, as can be seen in Fig. 1, and as a consequence the nucleosynthetic flux from this reaction chain exceeds that from the 16O(γ, α)12C reaction. Thus, the 16O(p,α)13N reaction becomes the main source of 12C at the expense of 16O. In the high-Z case, the nucleosynthetic flux due to the 16O(p,α)13N(γ,p)12C chain remains at all times below that due to the 16O(γ, α)12C reaction.

Figure 2 shows the evolution of the abundances of selected nuclei during the main phase of oxygen burning of the aforementioned mass shell, for both metallicities. The low-Z case displays a proton abundance larger than the high-Z case by a factor of approximately ten, while the mass fractions of α particles and 12C nuclei are also larger by a factor of approximately two. The abundance of oxygen declines faster in the low-Z case, and that of sulfur rises faster at first, but at the end achieves nearly the same equilibrium abundance as in the high-Z case. In contrast, the mass fraction of calcium rises in the low-Z case to approximately five times the value reached in the high-Z case. The final values of the calcium-to-sulfur mass ratios obtained in the mass shell are: MCa/MS = 0.45 in the low-Z case, and MCa/MS = 0.17 in the high-Z case.

thumbnail Fig. 2.

Chemical composition of a detonated mass shell in the same conditions as in Fig. 1, with progenitor metallicity Z = 2.25 × 10−4 (left) or Z = 0.0225 (right). The plot shows the initial phases of oxygen burning, starting shortly after the shell was hit by the detonation wave and ending when the oxygen abundance had declined significantly. The peak temperature was reached at time 0.3188 s.

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Figure 3 shows the α-efficiency of oxygen burning for both the low-Z and the high-Z case. For the purposes of the present work, the α-efficiency is defined as the number of α particles created through both the α-rich and the α-poor branches divided by the number of 16O nuclei destroyed in the same processes, and is equal to:

thumbnail Fig. 3.

α-efficiency of explosive oxygen burning for the same mass shells depicted in Figs. 1 and 2, for the low-Z case (in red) and the high-Z case (in blue). The limit efficiencies for α-rich oxygen burning, δα/δ16O = 4, and α-poor oxygen burning, δα/δ16O = 0.25, are drawn as dotted lines.

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(1)

where R is the nucleosynthetic flux due to a given reaction in mol g−1 s−1, ROpα = ρNAvσvY(16O)Y(P) makes reference to the 16O(p,α)13N reaction and ROγα to the 16O(γ, α)12C photodisintegration, Y is the molar fraction of each species involved in the reaction, RO + O makes reference to the fusion reaction 16O + 16O, and so on. As explained before, the α-efficiency of α-poor oxygen burning is 0.5, which would correspond, for instance, to all reaction rates being zero, except that of 16O + 16O. The α-efficiency of α-rich oxygen burning is equal to 4, which would be obtained if RO + O = RC + O = 0, and RC + C = (ROpα+ROγα)/2. In Fig. 1, it can be seen that RC + C is close to the mean of ROpα and ROγα. As could be expected, the α-efficiency shown in Fig. 3 lies between the two limits, and is larger for the low-Z case, which attains a value close to 2.5.

To test the extent to which the 16O(p,α)13N reaction accounts for the metallicity dependence of MCa/MS and MAr/MS in type Ia supernova models, I ran one-dimensional SNIa models with a range of progenitor metallicities and the 16O(p,α)13N reaction switched off, that is,

(2)

with f0 = 0. The code used is the same as in Bravo et al. (2019), where it is described in detail. The thermonuclear reaction rates used in the simulations are those recommended by the JINA REACLIB compilation (Cyburt et al. 2010, hereafter REACLIB). Detailed balance is assumed to hold for forward and reverse reactions, that is, the factor f0 is applied as well to the 13N(α, p)16O rate.

The results are shown in Fig. 4, together with the results obtained with the standard rates (f0 = 1) and the observational constraints derived from the emission lines of SNRs as measured with Suzaku (Martínez-Rodríguez et al. 2017). Switching off the 16O(p,α)13N reaction rate makes MCa/MS and MAr/MS almost insensitive to the WD progenitor metallicity, at all Z for the mass ratio of argon to sulfur, and at solar and sub-solar Z for the mass ratio of calcium to sulfur. The figure highlights the fact that without the 16O(p,α)13N reaction rate these mass ratios cannot cover the full range of measured values at SNRs for any metallicity. The same conclusion holds for different scalings of the 12C + 16O reaction rate, and for models of delayed detonation of Chandrasekhar-mass WDs.

thumbnail Fig. 4.

Theoretical mass ratios of calcium to sulfur (in green) and argon to sulfur (in magenta) from models of detonation of a 1.06 M WD, as function of the progenitor metallicity, with either the standard 16O(p,α)13N reaction rate (f0 = 1) or the rate switched off (f0 = 0). The argon-to-sulfur mass ratio for Z = 2.25 × 10−4 is shown as well for several other values of f0, from bottom to top: f0 = 0.1, 0.3, and 0.5. The vertical bars on the left of the figure show the range of observational mass ratios derived from measurements of X-ray emission of SNRs (Martínez-Rodríguez et al. 2017).

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3. Limits to the rate of 16O(p,α)13N deduced from supernova remnants

At present, the uncertainty on the 16O(p,α)13N reaction rate remains unconstrained. Its rate can be found in the STARLIB (Sallaska et al. 2013) and REACLIB (Cyburt et al. 2010) compilations. In STARLIB, this rate was computed using Hauser–Feshbach theory and assigned a conventional (recommended) uncertainty of a factor ten, because of the lack of enough experimental information. The REACLIB rate is a fit to the rate of 16O(p,α)13N in Caughlan & Fowler (1988), and is the rate used in the SNIa models reported here. In the temperature range of interest for explosive oxygen burning, T ≃ (3.5−5) × 109 K, the STARLIB rate is larger than the REACLIB rate by a factor that varies between 1.5 and 2.5.

An enhanced 16O(p,α)13N reaction rate may also increase the calcium-to-sulfur mass ratio, and becomes an alternative to the scaling down of the 12C + 16O reaction rate by a factor 0.1 suggested by Martínez-Rodríguez et al. (2017) in order to match the range of MCa/MS and MAr/MS in SNRs. This is because the 16O(p,α)13N reaction and its inverse are not in statistical equilibrium at the temperatures reached during explosive oxygen burning, unlike most of the reactions linking intermediate-mass nuclei from silicon to calcium.

Figure 5 shows the relative change in the elemental yields of the SNIa model consisting in the detonation of a 1.06 M WD with Z = 0.009, when either the 12C + 16O rate is scaled down by a factor ten or when the 16O(p,α)13N rate is scaled up by a factor seven (both models named as MALT in the plot), compared to the same model with all the rates at their standard values (identified in the plot as MON). The graph shows that the elements synthesized in significant quantities in the SNIa model, iron-group elements plus intermediate-mass α-nuclei, are made in equal proportions in the two MALT models. The same result is obtained for different parameters of the SNIa model; for example, the WD progenitor metallicity. In practice, it is possible to obtain the same proportions of the most abundant elements with intermediate modifications of both the 12C + 16O and the 16O(p,α)13N reaction rates.

thumbnail Fig. 5.

Relative change in the elemental yields obtained in the detonation of a 1.06 M WD, with progenitor metallicity Z = 0.009, derived from using alternative reaction rates (MALT) instead of the standard ones MON. The solid coloured circles belong to the model with the 12C + 16O reaction rate scaled down by a factor 0.1, and the colour is assigned as a function of the yield of each element in model MON. The black circles belong to the model with the standard 12C + 16O reaction rate and the 16O(p,α)13N reaction rate enhanced by a factor f0 = 7.

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The strong suppression of the metallicity dependence of MCa/MS and MAr/MS when the 16O(p,α)13N reaction is switched off suggests that there should be a minimum for its rate, below which the SNR measurements could not be reproduced. I ran the same model of the detonation of a 1.06 M WD with Z = 2.25 × 10−4 (the effect is most evident at low metallicities) and the 16O(p,α)13N reaction rate scaled by different factors, f0 = 0.1, 0.3, and 0.5. The results are shown in Fig. 5. The mass ratios belonging to f0 = 0.1 and 0.3 fall short of covering the observational data, while the results for f0 = 5 are acceptable, in the sense that the resulting MAr/MS is within 3σ of the upper limit of the corresponding observational range (the 1σ uncertainty of the upper limit of the argon-to-sulfur mass ratio is 0.01; see Martínez-Rodríguez et al. 2017). Therefore, I chose the last factor, f0 = 0.5, to establish a lower limit to the 16O(p,α)13N reaction rate.

The restrictions to the 16O(p,α)13N reaction rate derived from the measurements of MCa/MS and MAr/MS in SNRs are displayed in Fig. 6, together with the rates from STARLIB, REACLIB, and from Wagoner (1969), the one used by Woosley et al. (1973). The SNR observational data lead to tighter rate constraints than the uncertainty listed in STARLIB, although the rates provided by this compilation lie within the observationally based rate uncertainty (shaded band in Fig. 6). On the other hand, the rates from Wagoner (1969) are too large at high temperatures. It is to be expected that future X-ray observatories will be able to provide more stringent constraints on this rate through more accurate data concerning the strength of the emission lines of intermediate-mass elements in SNRs.

thumbnail Fig. 6.

Rate of the reaction 16O(p,α)13N, as a function of temperature in units of 109 K, from different compilations: Caughlan & Fowler (1988, CF88), Wagoner (1969, WAG69), and Sallaska et al. (2013, STARLIB). The uncertainty listed in the STARLIB compilation is plotted as a vertical error bar. The shaded band shows the uncertainty on the rate as determined using measured calcium-to-sulfur and argon-to-sulfur mass ratios in SNRs (see text for details).

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4. Conclusions

The so-called α-rich explosive oxygen burning during type Ia supernova explosions enhances the production of calcium with respect that of sulfur. From previous studies, it is known that there are two effects to account for in relation to α-rich oxygen burning. First, the strength of the enhancement of the yield of calcium at all metallicities, and second, the metallicity dependence of the mass ratio of calcium to sulfur, MCa/MS, in the ejecta.

Here, it is demonstrated that a single reaction, 16O(p,α)13N (followed by 13N+γ → p+12C), is responsible for the metallicity dependence of MCa/MS in the ejecta of type Ia supernovae. This reaction chain boosts α-rich oxygen burning when proton abundance is large, increasing the synthesis of argon and calcium with respect to sulfur and silicon. For high-metallicity progenitors, the presence of free neutrons leads to a drop in the proton abundance and the above chain is not efficient. Through one-dimensional modeling of supernova explosions, it is shown that switching off the 16O(p,α)13N rate makes the nucleosynthesis insensitive to the metallicity of the supernova progenitor.

Although the rate of 16O(p,α)13N can be found in astrophysical reaction rate libraries, its uncertainty is unconstrained. Assuming that all reaction rates other than 16O(p,α)13N retain their standard values, an increase by a factor of approximately seven of the 16O(p,α)13N rate at temperatures in the order 3−4 × 109 K is enough to explain the whole range of calcium-to-sulfur mass ratios measured in Milky Way and LMC supernova remnants. These same measurements provide a lower limit to the 16O(p,α)13N rate in the mentioned temperature range, on the order of a factor 0.5 with respect to the rate reported by Caughlan & Fowler in 1988. Future measurements of the 16O(p,α)13N rate at the energies of the Gamow-peak for temperatures in the range 3−4 × 109 K are encouraged, as they would help to determine the precise role of this reaction in the synthesis of calcium in type Ia supernovae.

Acknowledgments

This work has benefited from discussions about explosive oxygen burning with Frank Timmes, Broxton Miles, Dean Townsley, Carles Badenes, and Héctor Martínez-Rodríguez. Support by the MINECO-FEDER grant AYA2015-63588-P is acknowledged.

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All Figures

thumbnail Fig. 1.

Nucleosynthetic fluxes from 16O to 12C due to the 16O(p,α)13N (solid lines) and the 16O(γ, α)12C (dot-dashed lines) reactions as a function of time, in a mass shell with peak temperature 4 × 109 K, for a 1.06 M WD with either progenitor metallicity Z = 2.25 × 10−4 (red) or Z = 0.0225 (blue). The nucleosynthetic flux of the 12C fusion reaction is also plotted with dotted lines.

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In the text
thumbnail Fig. 2.

Chemical composition of a detonated mass shell in the same conditions as in Fig. 1, with progenitor metallicity Z = 2.25 × 10−4 (left) or Z = 0.0225 (right). The plot shows the initial phases of oxygen burning, starting shortly after the shell was hit by the detonation wave and ending when the oxygen abundance had declined significantly. The peak temperature was reached at time 0.3188 s.

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In the text
thumbnail Fig. 3.

α-efficiency of explosive oxygen burning for the same mass shells depicted in Figs. 1 and 2, for the low-Z case (in red) and the high-Z case (in blue). The limit efficiencies for α-rich oxygen burning, δα/δ16O = 4, and α-poor oxygen burning, δα/δ16O = 0.25, are drawn as dotted lines.

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In the text
thumbnail Fig. 4.

Theoretical mass ratios of calcium to sulfur (in green) and argon to sulfur (in magenta) from models of detonation of a 1.06 M WD, as function of the progenitor metallicity, with either the standard 16O(p,α)13N reaction rate (f0 = 1) or the rate switched off (f0 = 0). The argon-to-sulfur mass ratio for Z = 2.25 × 10−4 is shown as well for several other values of f0, from bottom to top: f0 = 0.1, 0.3, and 0.5. The vertical bars on the left of the figure show the range of observational mass ratios derived from measurements of X-ray emission of SNRs (Martínez-Rodríguez et al. 2017).

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In the text
thumbnail Fig. 5.

Relative change in the elemental yields obtained in the detonation of a 1.06 M WD, with progenitor metallicity Z = 0.009, derived from using alternative reaction rates (MALT) instead of the standard ones MON. The solid coloured circles belong to the model with the 12C + 16O reaction rate scaled down by a factor 0.1, and the colour is assigned as a function of the yield of each element in model MON. The black circles belong to the model with the standard 12C + 16O reaction rate and the 16O(p,α)13N reaction rate enhanced by a factor f0 = 7.

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In the text
thumbnail Fig. 6.

Rate of the reaction 16O(p,α)13N, as a function of temperature in units of 109 K, from different compilations: Caughlan & Fowler (1988, CF88), Wagoner (1969, WAG69), and Sallaska et al. (2013, STARLIB). The uncertainty listed in the STARLIB compilation is plotted as a vertical error bar. The shaded band shows the uncertainty on the rate as determined using measured calcium-to-sulfur and argon-to-sulfur mass ratios in SNRs (see text for details).

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In the text

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