Constraining mixing in asymptotic giant branch stars using stellar pulsation

Low- to intermediate-mass (0.8-8 solar mass) stars will eventually reach the asymptotic giant branch (AGB), during which they experience strong mass-loss and key nucleosynthesis. These stars experience thermal pulses, which drive mixing between the intershell and the envelope to enrich the stellar surface with carbon and slow neutron capture process elements, in a process known as third dredge-up (TDU). However, the lowest mass at which TDU can occur remains an uncertainty in detailed stellar models. While observations indicate that the lowest mass for an AGB star to become carbon-rich (C/O > 1) is 1.5 solar masses, TDU may still occur at lower masses. Stars of spectral type S show modest signs of TDU, and are useful objects to address this uncertainty. AGB stars are also long period variables undergoing radial pulsations, and using recently available long-term photometry we can use their variability to infer important stellar parameters.In this talk I will present my work in which I analyse the pulsation characteristics of Galactic S-type AGB stars to estimate their masses. We find that the initial mass distribution of semiregular S-type AGB stars peaks at approximately 1.4 solar masses, with a low mass tail that requires follow-up. I will also discuss similar ongoing work on a broader set of stars including Mira variables. We ultimately hope to calibrate the TDU in detailed models while reproducing the interactions between pulsation and mass-loss during the AGB.