[Paper Review] Evolution of asymptotic giant branch stars I. Updated synthetic TP-AGB models and their basic calibration

Paola Marigo, L. Girardi|ArXiv.org|Mar 7, 2007

Stellar, planetary, and galactic studiesPhysics and Astronomy68 references229 citations

TL;DR

This paper presents updated synthetic TP-AGB models for low- and intermediate-mass stars (0.5–5.0 M⊙, Z = 0.0001–0.03) using variable molecular opacities, improved mass-loss prescriptions, and calibrated third dredge-up efficiency. The models successfully reproduce carbon star luminosity functions and star counts in Magellanic Cloud clusters, offering a consistent, calibrated framework for population synthesis and integrated light modeling across metallicities.

ABSTRACT

We present new synthetic models of the TP-AGB evolution. They are computed for 7 values of initial metal content (Z from 0.0001 to 0.03) and for initial masses between 0.5 and 5.0 Msun, thus extending the low- and intermediate-mass tracks of Girardi et al. (2000) until the beginning of the post-AGB phase. The calculations are performed by means of a synthetic code that incorporates many recent improvements, among which we mention: (1) the use of detailed and revised analytical relations to describe the evolution of quiescent luminosity, inter-pulse period, third dredge-up, hot bottom burning, pulse cycle luminosity variations, etc.; (2) the use of variable molecular opacities -- i.e. opacities consistent with the changing photospheric chemical composition -- in the integration of a complete envelope model, instead of the standard choice of scaled-solar opacities; (3) the use of formalisms for the mass-loss rates derived from pulsating dust-driven wind models of C- and O-rich AGB stars; and (4) the switching of pulsation modes between the first overtone and the fundamental one along the evolution, which has consequences in terms of the history of mass loss. It follows that, in addition to the time evolution on the HR diagram, the new models predict in a consistent fashion also variations in surface chemical compositions, pulsation modes and periods, and mass-loss rates. The onset and efficiency of the third dredge-up process are calibrated in order to reproduce basic observables like the carbon star luminosity functions in the Magellanic Clouds, and TP-AGB lifetimes (star counts) in Magellanic Cloud clusters. Forthcoming papers will present the theoretical isochrones and chemical yields derived from these tracks, and additional tests performed with the aid of a complete population synthesis code.

Motivation & Objective

• To develop a self-consistent, synthetic model of TP-AGB evolution that reproduces key observational constraints in the Magellanic Clouds.
• To improve the treatment of molecular opacities by making them variable and composition-dependent, correcting errors from fixed-scaled-solar opacities.
• To calibrate the third dredge-up and mass-loss processes using observed luminosity functions and star counts in Magellanic Cloud clusters.
• To enable seamless integration with existing ZAMS-to-TP-AGB evolutionary tracks for full-population synthesis applications.
• To incorporate pulsation mode switching (fundamental vs. first overtone) and its impact on mass loss history.

Proposed method

• The models are computed using a synthetic code that integrates analytical relations for core mass-luminosity, inter-pulse periods, and pulse cycle variations derived from detailed stellar models.
• Variable molecular opacities are used throughout the envelope evolution, adapting to changing C/O and C/N ratios from third dredge-up and hot-bottom burning.
• Mass-loss rates are derived from pulsating dust-driven wind models for both C-rich and O-rich AGB stars.
• Pulsation mode switching between fundamental and first overtone is modeled dynamically along the evolutionary track, affecting mass-loss history.
• The third dredge-up efficiency is calibrated using observed carbon star luminosity functions and M- and C-star counts in Magellanic Cloud clusters.
• The model is validated by comparing predicted TP-AGB lifetimes and luminosities with observed star counts and integrated light behavior.

Experimental results

Research questions

• RQ1 How does the use of variable molecular opacities affect the evolution and observable properties of TP-AGB stars compared to fixed-scaled-solar opacities?
• RQ2 What level of third dredge-up efficiency is required to reproduce the observed carbon star luminosity functions in the LMC and SMC?
• RQ3 How do pulsation mode transitions (fundamental vs. first overtone) influence mass-loss rates and the resulting evolutionary tracks?
• RQ4 Can the observed TP-AGB lifetimes in Magellanic Cloud clusters be reproduced with updated mass-loss and dredge-up prescriptions?
• RQ5 To what extent do hot-bottom burning and metallicity variations affect the transition from M-type to C-type stars in the TP-AGB phase?

Key findings

• The use of variable molecular opacities significantly alters the evolution of C-rich AGB stars, particularly in the red luminosity domain, correcting long-standing errors from fixed-scaled-solar opacities.
• The calibrated third dredge-up efficiency successfully reproduces the observed carbon star luminosity functions in both the LMC and SMC, especially for stars with initial masses around 1.7–2.5 M⊙ and Z ≈ 0.008.
• The models reproduce the observed peak in M-star lifetimes in LMC clusters only when the third dredge-up onset is delayed, consistent with the M_c^min(M,Z) formalism from K02.
• The decreasing C-star lifetime with increasing initial mass in the Magellanic Clouds is explained by a combination of higher luminosity (earlier superwind onset) and hot-bottom burning in massive stars.
• The inclusion of pulsation mode switching between fundamental and first overtone modes improves the consistency of mass-loss history predictions and enables new calibration avenues with variability surveys.
• The synthetic tracks are seamlessly connected to previous ZAMS-to-TP-AGB models (Girardi et al. 2000), ensuring continuity in core mass and surface composition, and enabling full-population synthesis from ZAMS to white dwarf stages.