Radial pulsations of stars on the stage of the final helium flash

TL;DR

This study models the radial pulsations of stars undergoing the final helium flash, linking stellar evolution calculations with hydrodynamic simulations to match observed pulsation periods and star parameters.

Contribution

It provides new hydrodynamic models of pulsating stars during the final helium flash stage, aligning theoretical periods with observations for specific stellar parameters.

Findings

Maximum pulsation period of 117 days matches FG Sge observations.

Star parameters: mass 0.565 solar masses, radius 126 solar radii, temperature 4445 K.

Discrepancy in period change rate between observations and theory.

Abstract

Stellar evolution calculations to the stage of the cooling white dwarf were done for population~I stars with masses on the main sequence $1M_\odot\le M_0\le 1.5M_\odot$. The final helium flash LTP is shown to occur in post--AGB stars with initial masses $1.3M_\odot\le M_0\le 1.32M_\odot$ for the overshooting parameter $f=0.016$. In the case of more effective overshooting ($f=0.018$) the final helium flash occurs at initial masses $1.28M_\odot\le M_0\le 1.3M_\odot$. Fivefold variations of the parameter responsible for the mass loss rate during the post--AGB stage do not affect occurrence of the final helium flash but lead to perceptible changes of the evolutionary time. Selected models of two evolutionary sequences with initial mass $M_0 = 1.3M_\odot$ computed with overshooting parameters $f=0.016$ and $f=0.018$ were used as initial conditions in solution of the equations of hydrodynamics describing radial oscillations of stars on the stage of the final helium flash at effective temperatures less than $10^4$ K. The maximum pulsation period $\Pi=117$ day determined for the evolutionary sequence $M_0=1.3M_\odot$, $f=0.016$ is in a good agreement with observational estimates of the period of FG Sge. The mass, the radius and the effective temperature of the star are $M=0.565M_\odot$, $R=126R_\odot$ and $T_\mathrm{eff}=4445$ K, respectively. At the same time the average period change rate of FG Sge from 1960 to 1990 is nearly three time larger than its theoretical estimate.