Impact of neutrino magnetic moments on the evolution of the helium flash and lithium-rich red clump stars

The detection of the neutrino magnetic moment (NMM, ${\ensuremath{\mu}}_{v}$) is one of the most significant challenges in physics. The additional energy loss due to NMM can significantly influence the helium flash evolution in low-mass stars. Therefore, studying this process serves as the most robust method to constrain NMM. Using the Modules for Experiments in Stellar Astrophysics stellar evolution code, we investigated the impact of NMM on the helium flash evolution in low-mass stars. We found that NMM leads to an increase in both the critical helium core mass required for the helium flash and the luminosity of the tip of the red giant branch (TRGB). For a typical $Z=1{Z}_{\ensuremath{\bigodot}}$, $M=1.0{M}_{\ensuremath{\bigodot}}$, and ${\ensuremath{\mu}}_{v}=3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\ensuremath{\mu}}_{\mathrm{B}}$ model, the helium core mass increases by $\ensuremath{\sim}5%$, and the TRGB luminosity increases by $\ensuremath{\sim}35%$ compared to the model without NMM. However, contrary to previous conclusions, our model indicates that the helium flash occurs earlier, rather than delayed, with increasing NMM values. This is because the additional energy loss from NMM accelerates the contraction of the helium core, releasing more gravitational energy that heats the hydrogen shell and increases the hydrogen-burning rate, thereby causing the helium core to reach the critical mass faster and advancing the helium flash. An increase in NMM results in a higher peak luminosity for the first helium flash, a more off-center ignition position, and subflashes with higher luminosities, shorter intervals, and higher frequency. We found that the internal gravity wave (IGW) mixing generated by the helium flash can induce sufficient mixing in the radiative zone, turning the overshoot region into a low-${D}_{\mathrm{mix}}$ bottleneck within the stellar interior. The increase in NMM in the model narrows the overshoot bottleneck region, enabling Li to enter the surface convection zone more quickly, thereby enhancing the enrichment effect of IGW mixing on surface Li. For models incorporating both NMM and IGW mixing, the reduction in the overshoot bottleneck region allows them to effectively produce super-Li-rich red clump (RC) stars samples.