Theoretical mass estimates for the Mira-type variable R Hydrae

Abstract

Calculations of stellar evolution at initial abundances of helium $Y=0.28$ and heavier elements $Z=0.014$ were done for stars with masses on the main sequence $1.7M_\odot\le M_\textrm{ZAMS}\le 5.2M_\odot$. Evolutionary sequences corresponding to the AGB stage were used for modelling the pulsation period decrease observed for almost two centuries in the Mira--type variable R Hya. Diminution of the period from $\Pi\approx$ 495 d in the second half of the eighteenth century to $\Pi\approx 380$ d in the 1950s is due stellar radius decrease accompanying dissipation of the radiation--diffusion wave generated by the helium flash. For all the history of its observations R Hya was the fundamental mode pulsator. The best agreement with observations is obtained for eight evolutionary models with initial mass $M_\textrm{ZAMS}=4.8M_\odot$ and the mass loss rate parameter of the Bl\"ocker formula $0.03\le\eta_\mathrm{B}\le 0.07$. Theoretical mass estimates of R Hya are in the range $4.44M_\odot\le M\le 4.63M_\odot$, whereas the mean stellar radius ($421R_\odot\le \bar R \le 445R_\odot$) corresponding to the pulsation period $\Pi\approx 380$ agrees well with measurements of the angular diameter by methods of the optical interferometric imaging.