Status of the ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ reaction rate at stellar temperatures

Background: The ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ reaction influences the production of magnesium and silicon isotopes during carbon burning and is one of eight reaction rates found to significantly impact the shape of calculated x-ray burst light curves. The reaction rate is based on measured resonance strengths and known properties of levels in ${}^{28}\mathrm{Si}$.

Purpose: It is necessary to update the astrophysical reaction rate for ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ incorporating recent modifications to the nuclear level data for ${}^{28}\mathrm{Si}$, and to determine if any additional as-yet unobserved resonances could contribute to the ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ reaction rate.

Methods: The reaction rate has been recalculated incorporating updated level assignments from ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime }){}^{28}\mathrm{Si}$ data using the ratesmc Monte Carlo code. Evidence from the ${}^{28}\mathrm{Si}(p,p^{\prime }){}^{28}\mathrm{Si}$ reaction suggests that there are no further known resonances which could increase the reaction rate at astrophysically important temperatures, though some resonances do not yet have measured resonance strengths.

Results: The reaction rate is substantially unchanged from previously calculated rates, especially at astrophysically important temperatures. However, the reaction rate is now constrained to better than 20% across the astrophysically relevant energy range, with 95% confidence. Calculations of the x-ray burst light curve show no appreciable variations when varying the reaction rate within the uncertainty from the Monte Carlo calculations.

Conclusion: The ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ reaction rate, at temperatures relevant to carbon burning and Type I x-ray bursts, is well constrained by the available experimental data. This removes one reaction from the list of eight previously found to cause variations in x-ray burst light-curve calculations.

Figure 1

Relative difference (see the text for the definition) of resonance strengths from the data of Maas [15], Smulders and Endt [8], Lyons [9], and Strandberg [4].

Figure 2

Excitation-energy spectrum from the ${}^{28}\mathrm{Si}(p,p^{\prime }){}^{28}\mathrm{Si}$ reaction at field settings 1 (blue) and 2 (red).

Figure 3

Reaction-rate ratios relative to the STARLIB reaction rate for the reaction rates calculated in the present paper, the rate of Strandberg et al. [4], and reaction rates taken from the statistical-model codes talys [37] and non-smoker [38]. Reaction rates with talys were computed with the full range of $\alpha$-particle optical-model potentials with the band representing the most extreme values corresponding to the potentials of Avrigeanu et al. [39] and the dispersive model of Demetriou, Grama, and Goriely [40].

Figure 4

Reaction-rate uncertainty bands for scenario IV. The color represents the probability distribution function while the 68% and 95% confidence limits are denoted by thick and thin black lines, respectively.

Figure 5

Fractional contribution plot of individual resonances to the ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$ reaction rate, calculated using the complete set of possible additional resonances. Only resonances which contribute significantly to the reaction rate are plotted; the sum of the plotted contributions is below 100% at some temperatures. The temperature regions corresponding to x-ray burst, carbon-shell burning, and neon burning are also shown. The impact of potential new resonances ($E_r\le 794$ keV) on the reaction rate is limited to temperatures below the astrophysically important temperature ranges.

Figure 6

x-ray burst light curve 68% confidence interval bands calculated with mesa using the median (black line), upper 95% (red-hash area), and lower 95% (blue-hash area) STARLIB reaction rates for ${}^{24}\mathrm{Mg}(\alpha ,\gamma ){}^{28}\mathrm{Si}$, compared to observations of the year 2007 bursting epoch of GS 1826-24 (gray boxes) for context. The inset shows the residual over the light curve rise to mesa results obtained with the median STARLIB rate, where the gray box indicates the average observational uncertainty in that time frame. Note that the mesa light curve bands are asymmetric uncertainties, where the dashed or dotted line indicates the average, with the uncertainty for a single band owing to burst-to-burst variability.