Carbon burning is a key step in the evolution of massive stars, Type 1a supernovae and superbursts in x-ray binary systems. Nevertheless, our understanding of this critical fusion reaction is not as complete as might be desirable to fully constrain astrophysical models. This limitation centres of the difficulty in determining the $^{12}$C+$^{12}$C fusion cross section at energies corresponding to the Gamow window for these different scenarios as it relies on extrapolation of direct measurements made at higher energies. Such direct fusion measurements are complicated by the presence of resonances at and below the Coulomb barrier. These resonances have traditionally been associated with the formation of short-lived molecular states based on $^{12}$C+$^{12}$C or similar alpha-conjugate systems. Despite study of these resonances over many years, a comprehensive theoretical model accounting for their existence and structure is presently lacking.

Given the difficulties associated with direct fusion studies of the $^{12}$C+$^{12}$C reaction, indirect studies which can identify potential resonances within the respective Gamow windows are of high value. In this respect, a study of the $^{24}$Mg($alpha$,$alpha$’)$^{24}$Mg reaction has identified several 0$^{+}$ states in $^{24}$Mg, close to the $^{12}$C+$^{12}$C threshold, which predominantly decay to $^{20}$Ne(ground state) + $alpha$ [1]. Not only were these states newly identified but surprisingly they were not observed in previously well-studied $^{20}$Ne($alpha$,$alpha_0$)$^{20}$Ne resonance scattering, potentially suggesting that they have a dominant $^{12}$C+$^{12}$C cluster structure. Given the very low angular momentum associated with sub-barrier fusion, these states, which sit in the Gamow window for massive stars, may play a decisive role in $^{12}$C+$^{12}$C fusion. We present estimates of updated $^{12}$C+$^{12}$C fusion reaction rates based on likely parameters for such resonances [1].

A fascinating aspect of the identification of these potential 0$^+$ cluster states in $^{24}$Mg close to the break-up threshold for $^{12}$C+$^{12}$C and similar channels such as $^{16}$O+$^8$Be is the circumstantial similarity to the situation in $^{12}$C with the Hoyle state at the break-up threshold and the critical role that it plays in in helium burning.