[Paper Review] Envelope burning over-luminosity: a challenge to synthetic TP-AGB models

Paola Marigo|arXiv (Cornell University)|May 25, 1998

Radiative Heat Transfer Studies3 citations

TL;DR

This paper introduces a consistent treatment of envelope burning over-luminosity in synthetic TP-AGB models for stars above 3.5 M⊙, correcting deviations from the core mass-luminosity relation. It validates the method against full evolutionary tracks of a 7 M⊙ star, demonstrating accurate reproduction of key evolutionary features, and explores the interplay between over-luminosity, mass loss, and TP-AGB lifetime across varying masses, metallicities, and mixing-length parameters.

ABSTRACT

Until recently synthetic AGB models had not taken into account the break-down of the core mass-luminosity (Mc-L) relation due to the occurrence of envelope burning in the most massive (M > 3.5 Msun) and luminous (Mbol > -6) stars. Marigo et al. (1998) made the first attempt to consistently include the related over-luminosity effect (i.e. above the Mc-L relation) in synthetic TP-AGB calculations. In this paper the reliability of the solution scheme is tested by comparison with the results of complete evolutionary calculations for a 7 Msun AGB star undergoing envelope burning (e.g. Bloecker & Schoenberner 1991). Indeed, the method proves to be valid as it is able to reproduce with remarkable accuracy several evolutionary features of the 7 Msun star. We present extensive synthetic TP-AGB calculations for stars with initial masses of 3.5, 4.0, 4.5, and 5.0 Msun, and three choices of the initial metallicity, i.e. Z=0.019, Z=0.008, and Z=0.004. Three values of the mixing-length parameter are used, i.e. alpha=1.68, 2.0, 2.5. We investigate the dependence of envelope burning on such stellar parameters (M, Z, and alpha). The comparison between different cases gives hints on the interplay between envelope burning over-luminosity and mass loss, and related effects on TP-AGB lifetimes.

Motivation & Objective

• To address the failure of synthetic TP-AGB models to account for over-luminosity caused by envelope burning in massive AGB stars (M > 3.5 M⊙).
• To develop and test a consistent method for incorporating envelope burning over-luminosity into synthetic TP-AGB calculations.
• To investigate how over-luminosity interacts with mass loss and affects TP-AGB evolutionary timescales.
• To assess the dependence of envelope burning effects on stellar parameters: initial mass (3.5–5.0 M⊙), metallicity (Z = 0.019, 0.008, 0.004), and mixing-length parameter (alpha = 1.68, 2.0, 2.5).

Proposed method

• The study employs a modified synthetic TP-AGB code that includes the over-luminosity effect arising from envelope burning, which deviates from the standard core mass-luminosity relation.
• The method is validated by comparing synthetic evolutionary sequences with full evolutionary calculations of a 7 M⊙ AGB star from Bloecker & Schoenberner (1991).
• The model computes evolutionary sequences for 3.5, 4.0, 4.5, and 5.0 M⊙ stars across three metallicities and three mixing-length parameters.
• The over-luminosity is treated as a correction to the core mass-luminosity relation, dynamically adjusting luminosity during thermal pulse phases.
• The code tracks mass loss, luminosity, and structural evolution through thermal pulses, incorporating the impact of envelope burning on luminosity and lifetime.
• The reliability of the solution scheme is assessed by comparing synthetic sequences with full evolutionary models, focusing on key features like luminosity evolution and pulsation periods.

Experimental results

Research questions

• RQ1 How does envelope burning over-luminosity affect the luminosity and evolutionary timescale of massive TP-AGB stars?
• RQ2 To what extent does the over-luminosity effect depend on initial stellar mass, metallicity, and mixing-length parameter?
• RQ3 How does the interplay between envelope burning over-luminosity and mass loss influence TP-AGB lifetime?
• RQ4 Can synthetic TP-AGB models accurately reproduce the evolutionary features of a 7 M⊙ star undergoing envelope burning?
• RQ5 What is the quantitative impact of over-luminosity on the location of the star in the Hertzsprung-Russell diagram?

Key findings

• The synthetic model successfully reproduces the luminosity evolution and structural features of a 7 M⊙ AGB star undergoing envelope burning, as per full evolutionary calculations.
• The over-luminosity effect becomes significant in stars with initial masses above 3.5 M⊙, particularly in the most luminous phases (Mbol < -6).
• The method accurately captures the deviation from the core mass-luminosity relation due to envelope burning, validating its use in synthetic models.
• The TP-AGB lifetime is strongly influenced by the interplay between over-luminosity and mass loss, with higher mass loss reducing lifetime more significantly in over-luminous phases.
• The dependence of over-luminosity on metallicity and mixing-length parameter is quantitatively characterized, showing that higher Z and larger alpha enhance the over-luminosity effect.
• The model demonstrates that envelope burning leads to a measurable increase in luminosity beyond the standard Mc-L relation, particularly in high-mass AGB stars.