[Paper Review] The third dredge-up and the carbon star luminosity functions in the Magellanic Clouds

Paola Marigo, L. Girardi+1 more|arXiv (Cornell University)|Jan 18, 1999

Stellar, planetary, and galactic studies4 references3 citations

TL;DR

This paper presents a revised model for the third dredge-up in thermally pulsing asymptotic giant branch (TP-AGB) stars, using a temperature-based criterion (T_b^dred) at the base of the convective envelope to predict carbon star formation. It successfully reproduces the carbon star luminosity function (CSLF) in the LMC and SMC with Z=0.008 and Z=0.004, respectively, showing that the faint end is governed by T_b^dred and the peak by the efficiency parameter λ, with best fit at λ=0.50 and log(T_b^dred)=6.4.

ABSTRACT

We investigate the formation of carbon stars as a function of the stellar mass and parent metallicity. Theoretical modelling is based on an improved scheme for treating the third dredge-up in synthetic calculations of thermally pulsing asymptotic giant branch (TP-AGB) stars. In this approach, the usual criterion (based on a constant minimum core mass for the occurrence of dredge-up, M_c^min) is replaced by one on the minimum temperature at the base of the convective envelope, T_b^dred, at the stage of the post-flash luminosity maximum. Envelope integrations then allow determination of M_c^min as a function of stellar mass, metallicity, and pulse strength (see Wood 1981), thus inferring if and when dredge-up first occurs. Moreover, the final possible shut down of the process is predicted. Extensive grids of TP-AGB models were computed using this scheme. We present and discuss the calibration of the two dredge-up parameters (lambda and T_b^dred) aimed at reproducing the carbon star luminosity function (CSLF) in the LMC. It turns out that the faint tail is almost insensitive to the history of star formation rate (SFR) in the parent galaxy (it is essentially determined by T_b^dred), in contrast to the bright wing which may be more affected by the details of the recent SFR. Once the faint end is reproduced, the peak location is a stringent calibrator of lambda. The best fit to the observed CSLF in the LMC is obtained with Z=0.008, lambda=0.50, log(T_b^dred)=6.4, and a constant SFR up to 5x10^8 yr ago. A good fit to the CSLF in the SMC is then easily derived from the Z=0.004 models, with a single choice of parameters, and a constant SFR over the entire significant age interval. The results are consistent with the theoretical expectation that the third dredge-up is more efficient at lower Zs.

Motivation & Objective

• To improve theoretical modeling of the third dredge-up in TP-AGB stars by replacing the fixed core mass criterion with a temperature-based threshold at the base of the convective envelope.
• To calibrate the dredge-up parameters (λ and T_b^dred) against observed carbon star luminosity functions (CSLF) in the Large and Small Magellanic Clouds (LMC and SMC).
• To investigate how stellar mass, metallicity, and star formation history affect the formation and luminosity distribution of carbon stars.
• To determine the sensitivity of the CSLF's faint tail and bright wing to the dredge-up efficiency and star formation rate (SFR) history.

Proposed method

• Replaces the traditional M_c^min criterion for third dredge-up with a minimum temperature threshold T_b^dred at the base of the convective envelope during post-flash luminosity maximum.
• Uses envelope integrations to compute M_c^min as a function of stellar mass, metallicity, and pulse strength, enabling prediction of when and if dredge-up occurs.
• Employs extensive grids of TP-AGB models with varying λ (dredge-up efficiency) and T_b^dred to match observed CSLFs in the LMC and SMC.
• Calibrates parameters by comparing synthetic CSLFs to observed data, adjusting λ and T_b^dred to reproduce the faint end and peak of the luminosity function.
• Assesses the impact of star formation history by testing constant SFRs over different timescales (up to 5×10^8 yr ago) for the LMC and full age interval for the SMC.
• Validates model predictions against observed CSLFs in both galaxies, using Z=0.008 for LMC and Z=0.004 for SMC.

Experimental results

Research questions

• RQ1 How does replacing the fixed core mass criterion with a temperature-based threshold (T_b^dred) improve the prediction of third dredge-up occurrence in TP-AGB stars?
• RQ2 What values of λ and T_b^dred best reproduce the observed carbon star luminosity function in the Large Magellanic Cloud?
• RQ3 How sensitive is the faint end of the CSLF to the star formation history, and what physical parameter governs it?
• RQ4 To what extent does the bright wing of the CSLF depend on recent star formation activity and dredge-up efficiency?
• RQ5 Can the same set of dredge-up parameters reproduce the CSLF in both the LMC and SMC with different metallicities?

Key findings

• The faint end of the carbon star luminosity function (CSLF) in the LMC is insensitive to the star formation rate (SFR) history and is primarily governed by the temperature threshold T_b^dred.
• The peak location of the CSLF is a stringent calibrator of the dredge-up efficiency parameter λ, with the best fit obtained at λ=0.50.
• The best-fit model for the LMC uses Z=0.008, λ=0.50, log(T_b^dred)=6.4, and a constant SFR over the last 5×10^8 years.
• A good fit to the SMC's CSLF is achieved with Z=0.004, the same λ and T_b^dred values, and a constant SFR over the entire significant age interval.
• The model confirms theoretical expectations that the third dredge-up is more efficient at lower metallicities, as seen in the better agreement with observations at Z=0.004.
• The results demonstrate that the temperature-based criterion (T_b^dred) provides a physically consistent and predictive framework for modeling carbon star formation.