Theoretical mass estimates for the Mira-type variable R Hydrae

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 $1.7M_{\odot }\le M_{\text{ZAMS}}\le 5.2M_{\odot }$. 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 $\mathrm{\Pi }\approx$ 495 d in the second half of the eighteenth century to $\mathrm{\Pi }\approx 380$ 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 $M_{\text{ZAMS}}=4.8M_{\odot }$ and the mass loss rate parameter of the Blöcker 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 $\mathrm{\Pi }\approx 380$ agrees well with measurements of the angular diameter by methods of the optical interferometric imaging.