Stellar evolution and the triple-α reactions

Nuclear reaction rates play a crucial role in the evolution of stars. For low-mass stars, the triple-α reaction controls the helium burning stars in the red giant and asymptotic giant branch (AGB) phase. More importantly, the cross section of the triple-α reaction has a great impact on the helium ignition at the center of the electron degenerate helium core of red giants and on the helium shell flashes of AGB stars. It is to be noted that stellar evolution models are influenced not only by the value of the cross section, but also by the temperature dependence of the reaction rate. In this paper, I present the impact of the triple-α reaction rates on the evolution of low-mass metal-free stars and intermediate-mass AGB stars. According to the previous study, the constraint on the triple-α reaction rate is derived based on stellar evolution theory. It is found that the recent revisions of the rate proposed by nuclear physics calculations satisfy the condition for the ignition of the helium core flash in low-mass stars