The convective kissing instability in low-mass M-dwarf models: convective overshooting, semi-convection, luminosity functions, surface abundances and star cluster age dating

Abstract

Low-mass models of M-dwarfs that undergo the convective kissing instability fluctuate in luminosity and temperature resulting in a gap in the main sequence that is observed in the $Gaia$ data. During this instability, the models have repeated periods of full convection where the material is mixed throughout the model. Stellar evolution models are performed using MESA with varying amounts of convective overshooting and semi-convection. We find that the amplitude and intensity of the instability is reduced with increasing amounts of overshooting but sustained when semi-convection is present. This is reflected in the loops in the evolutionary tracks in the Hertzsprung-Russell diagram. The surface abundances of $^1$H, $^3$He, $^4$He, $^{12}$C, $^{14}$N and $^{16}$O increase or decrease over time due to the convective boundary, however the relative abundance changes are very small and not likely observable. The mass and magnitude values from the models are assigned to a synthetic population of stars from the mass-magnitude relation to create colour-magnitude diagrams, which reproduce the M-dwarf gap as a large indent into the blueward edge of the main sequence (MS). This is featured in the luminosity function as a small peak and dip. The width of the MS decreases over time along with the difference in width between the MS at masses higher and lower than the instability. The parallel offset and relative angle between the upper and lower parts of the MS also change with time along with the mass-magnitude relation. Potential age-dating methods for single stars and stellar populations are described.