Dredge-up Phase Research Articles

Fundamental problems and basic tests of stellar evolution theory — The case of carbon stars

Carbon stars are thought to be in the asymptotic giant branch (AGB) phase of evolution, alternately burning hydrogen and helium in shells above an electron-degenerate carbon-oxygen (CO) core. The excess of carbon relative to oxygen at the surfaces of these stars is thought to be due to convective dredge-up which occurs following a thermal pulse. During a thermal pulse, carbon and neutron-rich isotopes are made in a convective helium-burning zone. In model stars of large CO core mass, the source of neutrons for producing the neutron-rich isotopes is the 22Ne(α, n)25Mg reaction and the isotopes are produced in the solar system s-process distribution. In models of small core mass, the 13C(α, n) 16O reaction is thought to be responsible for the release of neutrons, and the resultant distribution of neutron-rich isotopes is expected to vary considerably from one star to the next, with the distribution in isolated instances possibly resembling the solar system distribution of r-process isotopes. After the dredge-up phase following each pulse, the 13C is made by the reactions 12C(p,γ) 13N(β+ v) 13C in a zone of large 12C abundance and small 1H abundance that has been established by semiconvective mixing during the dredge-up phase. There is qualitative accord between the properties of carbon stars in the Magellanic Clouds and properties of model stars, but considerably more theoretical work is required before a quantitative match is achieved.The observed paucity of AGB stars more luminous than MBOL ∼ −6 is interpreted to mean that the AGB lifetime of a star more luminous than this is at least a factor of ten smaller than the AGB lifetime of stars less luminous than this, or, at most 105 yr. Since, with current estimates of the 22Ne(α, n)25Mg reaction rate R22, only AGB model stars more luminous than MBOL ∼ −6 can produce s-process isotopes in the solar system distribution, it is inferred that either (1) the current estimates of R22 are too small by one to two orders of magnitude, allowing less luminous AGB stars to contribute, (2) the solar system distribution is not equivalent to the average Galactic distribution, being rather the consequence of a unique injection into the protosolar nebula of matter from a massive intermediate-mass AGB star, or (3) the estimates of the temperatures in the convective shell that are given by extant models are too low by, sav, 10 or 15 percent.The absence of carbon stars more luminous than MBOL ∼ −6 is suggested to be due primarily to the fact that ∼ 106 yr of AGB evolution is necessary to produce surface C/O > 1, rather than to be due to the burning of dredged-up carbon into nitrogen at the base of the convective envelope during the interpulse quiescent hydrogen-burning phase. Thus, the positive correlation between the nitrogen and helium abundances in planetary nebulae is perhaps primarily a consequence of the second dredge-up episode rather than a consequence of processes occurring during the thermally pulsing phase.

The asymptotic giant branch evolution of intermediate-mass stars as a function of mass and composition. II - Through the first major thermal pulse and the consequences of convective dredge-up

The aysmptotic giant branch evolution of intermediate-mass stars is further investigated following the end of the second dredge-up phase. The limiting mass for nondegenerate core carbon ignition is determined as a function of initial model mass and composition. A detailed description is given concerning the reignition of the hydrogen-burning shell through the appearance of the first major thermal pulse the luminosity of the heliun-burning shell is found to undergo a number of small oscillations which ultimately grow to become the first major pulse. The behavior of the first major thermal pulse is discussed in detail. The results of our calculations and those of other authors are combned for further elucidation of the core mass--interflash period relation and the core mass--luminosity relation. We present more information to support the idea that the latter relationship does depend on both the initial model mass and the initial Y abundance. Model lifetimes for models on the asymptotic giant branch are discussed both for the prethermal pulse phase and for the later thermal pulse phase.

The asymptotic giant branch evolution of intermediate-mass stars as a function of mass and composition. I - Through the second dredge-up phase

The asymptotic giant branch evolution of stars prior to the onset of thermal pulses is found to be highly sensitive to both initial composition and total stellar mass. Models investigated have masses in the range 3-11 M0. and initial compositions of (Y, Z) = (0.28, 0.001), (0.28, 0.01), (0.28, 0.02), (0.28, 0.03), (0.20, 0.02), (0.36, 0.02), and (0.20, 0.001). The effects produced by varying the overall rate of neutrino emission and by varying the size of the mixing length in convective regions are studied; the role played by convective overshoot, semiconvection, and the energy cost of mixing across the hydrogen-helium discontinuity are discussed. A general description of the evolutionary behavior of our models from the start of the asymptotic giant branch to the first major thermal pulse is also presented. The inward advance of the base of the convective envelope results in a reduction in the size of the hydrogen-exhausted core for stellar masses in a specific range: > > MCRIT. The magnitudes of both McRIT and Mup (defined as the minimum mass for nondegenerate carbon ignition) depend on the initial composition in ways that can be approximated analytically. The final size of the hydrogen-exhausted core that results after the dredge-up phase is, for a given initial mass, larger in models with a lower Z or higher Y. The abundance changes that occur as a result of dredge-up are, for a given mass, greater in models with a lower Z or higher Y. Typically, 4He and 14N are enhanced while `H, `2C, and 160 are depleted. For the most massive models undergoing dredge-up, significant enhancements in 180 also occur. Subject headings: clusters: globular - stars: abundances - stars: evolution - stars: interiors