Reaction rate uncertainties and ²⁶Al in AGB silicon carbide stardust

Context: Stardust is a class of presolar grains each of which presents an ideally uncontaminated stellar sample. Mainstream silicon carbide (SiC) stardust formed in the extended envelopes of carbon-rich asymptotic giant branch (AGB) stars and incorporated the radioactive nucleus ²⁶Al as a trace element. Aims: The aim of this paper is to analyse in detail the effect of nuclear uncertainties, in particular the large uncertainties of up to four orders of magnitude related to the ²⁶Al_g(p, γ) ²⁷Si reaction rate, on the production of ²⁶Al in AGB stars and compare model predictions to data obtained from laboratory analysis of SiC stardust grains. Stellar uncertainties are also briefly discussed. Methods. We use a detailed nucleosynthesis postprocessing code to calculate the ²⁶Al/²⁷Al ratios at the surface of AGB stars of different masses (M= 1.75, 3, and 5 M_⊙) and metallicities (Z=0.02, 0.012, and 0.008). Results: For the lower limit and recommended value of the ²⁶Al_g(p, γ)²⁷Si reaction rate, the predicted ²⁶Al/²⁷Al ratios replicate the upper values of the range of the ²⁶Al/²⁷Al ratios measured in SiC grains. For the upper limit of the ²⁶Al_g(p,γ)²⁷Si reaction rate, instead, the predicted ²⁶Al/²⁷Al ratios are ≈100 times lower and lie below the range observed in SiC grains. When considering models of different masses and metallicities, the spread of more than an order of magnitude in the ²⁶Al/²⁷Al ratios measured in stellar SiC grains is not reproduced. Conclusions: We propose two scenarios to explain the spread of the ²⁶Al/²⁷ Al ratios observed in mainstream SiC, depending on the choice of the ²⁶Al _g + p reaction rate. One involves different times of stardust formation, the other involves extra-mixing processes. Stronger conclusions on the interpretation of the Al composition of AGB stardust will be possible after more information is available from future nuclear experiments on the ²⁶Al_g + p reaction.