The impact of the new measurement of the $\rm ^{12}C+^{12}C$ fusion cross section on the final compactness of the massive stars

We discuss how the new measurement of the $^{12}C+^{12}C$ fusion cross section carried out with the Trojan Horse Method (Tumino, A., Spitaleri, C., La Cognata, M., et al., 2018, Nature 57, 687) affects the compactness of a star, i.e. basically the binding energy of the inner mantle, at the onset of the core collapse. In particular, we find that this new cross section significantly changes the dependence of the compactness on the initial mass with respect to previous findings obtained in Chieffi & Limongi 2020 (ApJ 890, 43) by adopting the classical cross section provided by Caughlan, G.R., and Fowler, W.D. 1988 (At. Data Nucl. Data Tables 40, 283). A non monotonic but well defined behavior is confirmed also in this case and no scatter of the compactness around the main trend is found. Such an occurrence could impact the possible explodability of the stars.