Models of long-period variables of the globular cluster 47 Tuc

Abstract

Stellar evolution computations were carried out for stars with a main sequence mass $M_\mathrm{ZAMS}=0.86M_\odot$ and initial metal abundance $Z=0.003$ and $Z=0.004$. Selected models of evolutionary sequences were used for calculation of radial pulsations in the RGB, eAGB and TP-AGB evolutionary stages. Not all pulsating red giants of the globular cluster 47 Tuc are shown to belong to the Mira variables because the lower limit of pulsation periods at the TP-AGB stage is $\approx 70$ day, whereas during the eAGB evolutionary stage the periods of radial oscillations range from $\approx 5$ to $\approx 40$ day. Periods and luminosities of hydrodynamic models of eAGB and TP--AGB pulsating stars locate along the common period-luminosity relation. Small masses of Mira variables in the globular cluster 47 Tuc ($0.54M_\odot\le M\le 0.70M_\odot$) is the main reason for irregular large-amplitude oscillations and the dynamical instability of outer stellar layers at pulsation periods $Π> 200$ day.

Figures (6)

• Figure 1: Evolutionary tracks near the RGB tip for the metal abundance $Z=0.003$ and $Z=0.004$ with parameters of mass loss rate $\eta_\mathrm{R}=0.3$ (solid lines) and $\eta_\mathrm{R}=0.5$ (dashed lines). Arrows indicate the direction of the star evolution along the track. Location of hydrodynamic models of pulsating red giants is shown by circles (fundamental mode pulsators) and triangles (first overtone pulsators). Filled symbols correspond to the models with limiting amplitude pulsations, whereas open symbols mark the models with decaying oscillations.
• Figure 2: Specific mechanical work $\oint PdV$ done by the gas layer over the oscillation cycle (solid line) and the adiabatic exponent $\Gamma_1$ at the hydrostatic equilibrium (dashed line) versus the zone number $j$ of the hydrodynamic model. The temperature $T$ at the initial equilibrium conditions is given along the upper horizontal axis.
• Figure 3: Evolutionary variations of the stellar luminosity during the eAGB stage. Designations are the same as in Fig. \ref{['fig1']}.
• Figure 4: Evolutionary variations of the pulsation period (a) and the radial displacement amplitude at the outer boundary of the hydrodynamic model (b) for the metal abundance $Z=0.003$ with mass loss parameters $\eta_\mathrm{R}=0.3$ (solid lines) and $\eta_\mathrm{R}=0.5$ (dashed lines).
• Figure 5: Luminosity variations in stars of the evolutionary sequence $Z=0.003$, $\eta_\mathrm{R}=0.3$ after thermal flashes $2\le i_\mathrm{TP}\le 4$. Hydrodynamic models pulsating in the first overtone and fundamental mode are marked by triangles and circles, respectively. Models with irregular large amplitude oscillations are marked by squares. Open symbols correspond to models with decaying oscillations. The stellar masses correspond to $t_\mathrm{ev}=0$.