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 \(1.7\;M_{\odot}\leq M_{\textrm{ZAMS}}\leq 5.2\;M_{\odot}\). 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 to 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 \(M=4.8\;M_{\odot}\) and the mass loss rate parameter of the Blöcker formula \(0.03\leq\eta_{\textrm{B}}\leq 0.07\). Theoretical mass estimates of R Hya are in the range \(4.44\;M_{\odot}\leq M\leq 4.63\;M_{\odot}\), whereas the mean stellar radius (\(421\;R_{\odot}\leq\bar{R}\leq 445\;R_{\odot}\)) corresponding to the pulsation period \(\Pi\approx 380\) d agrees well with measurements of the angular diameter by methods of the optical interferometric imaging.