Pulsating white dwarfs provide constraints to the evolution of progenitor stars. We revise He-burning stellar models, with particular attention to core convection and to its connection with the nuclear reactions powering energy generation and chemical evolution Theoretical results are compared to the available measurements for the variable white dwarf GD 358, which indicate a rather large abundance of central oxygen. We show that the attempt to constrain the relevant nuclear reaction rate by means of the white dwarf composition is faced with a large degree of uncertainty related to evaluating the efficiency of convection-induced mixing.By combining the uncertainty of the convection theory with the error on the relevant reaction rate we derive that the present theoretical prediction for the central oxygen mass fraction in white dwarfs varies between 0.3 and 0.9. Unlike previous claims, we find that models taking into account semiconvection and a moderate C12(alpha,gamma)O16 reaction rate are able to account for a high central oxygen abundance. The rate of the C12(alpha,gamma)O16 used in these models agrees with the one recently obtained in laboratory experiments (Kunz et al. 2002). On the other hand, when semiconvection is inhibited, as in the case of classical models (bare Schwarzschild criterion) or in models with mechanical overshoot, an extremely high rate of the C12(\alpha,\gamma)O16 reaction is needed to account for a large oxygen production. Finally, we show that the apparent discrepancy between our result and those reported in previous studies depends on the method used to avoid the convective runaways (the so called breathing pulses), which are usually encountered in modeling late stage of core He-burning phase.Comment: 19 pages, 4 figures, accepted for publication in The Astrophysical Journa

We present a comprehensive theoretical investigation of the evolutionary properties of intermediate-mass stars. The evolutionary sequences were computed from the Zero Age Main Sequence up to the central He exhaustion and often up to the phases which precede the carbon ignition or to the reignition of the H-shell which marks the beginning of the thermal pulse phase. The evolutionary tracks were constructed by adopting a wide range of stellar masses ($3\leq$\msun$\leq15$) and chemical compositions. In order to account for current uncertainties on the He to heavy elements enrichment ratio, the stellar models were computed by adopting at Z=0.02 two different He contents (Y=0.27, 0.289) and at Z=0.04 three different He contents (Y=0.29, 0.34, and 0.37). To supply a homogeneous evolutionary scenario which accounts for young Magellanic stellar systems the calculations were also extended toward lower metallicities (Z=0.004, Z=0.01), by adopting different initial He abundances. We evaluated for both solar (Z=0.02) and super-metal-rich (SMR, Z=0.04) models the transition mass $M^{up}$ between the stellar structures igniting carbon and those which develop a full electron degeneracy inside the CO core. This evolutionary scenario allows us to investigate in detail the properties of classical Cepheids. In particular, we find that the range of stellar masses which perform the blue loop during the central He-burning phase narrows when moving toward metal-rich and SMR structures.Comment: 25 pages, 10 figures (4 postscript + 6 gif files), 7 postscript tables. accepted for publication on ApJ (November 2000

The behaviour of carbon-oxygen (CO) white dwarfs (WDs) subject to direct helium accretion is extensively studied. We aim to analyse the thermal response of an accreting WD to mass deposition at different timescales. The analysis has been performed for initial WD masses and accretion rates in the range 0.60–1.02 M_⊙ and 10⁻⁹–10⁻⁵ M_⊙ yr⁻¹, respectively. Thermal regimes in the parameter space M_WD–$$\dot{M}_{\rm He}$$ leading to formation of red-giant-like structures, steady burning of He, and mild, strong and dynamical flashes have been identified and the transition between these regimes has been studied in detail. In particular, the physical properties of WDs experiencing the He-flash accretion regime have been investigated to determine the mass retention efficiency as a function of the accretor total mass and accretion rate. We also discuss to what extent the building up of a He-rich layer via H burning could be described according to the behaviour of models accreting He-rich matter directly. Polynomial fits to the obtained results are provided for use in binary population synthesis computations. Several applications for close binary systems with He-rich donors and CO WD accretors are considered and the relevance of the results for interpreting He novae is discussed.