Hydrodynamic modelling of pulsation period decrease in the Mira-type variable T UMi

Pulsation period decrease during the initial stage of thermal pulse in helium-burning shell Mira-type variable T UMi is investigated with numerical methods stellar evolution and radiation hydrodynamics. To this end, a grid evolutionary tracks was calculated for stars masses on main sequence $1M_\odot\le M_\textrm{ZAMS}\le 2.2M_\odot$ metallicity $Z=0.01$. Selected models AGB sequences were used determination conditions time--dependent inner boundary equations hydrodynamics describing changes radially pulsating star. The onset shown to nearly coincide peak luminosity. most rapid occurs first three decades. pulsation decreases due both contraction star mode switching from fundamental overtone. time-scale order few dozen cycles. present-day model first-overtone pulsator small-amplitude semi-regular oscillations. Theoretical estimates at rate change decades later are agree available observational data $ 1.04M_\odot\le M\le 1.48M_\odot$.