Astron. Astrophys. 344, 123-142 (1999)

The third dredge-up and the carbon star luminosity functions in the Magellanic Clouds

Paola Marigo ^1,2, Léo Girardi ¹ and Alessandro Bressan <sup>3

1</sup> Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, D-85740 Garching bei München, Germany
² Department of Astronomy, University of Padova, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy
³ Astronomical Observatory, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy

Received 19 October 1998 / Accepted 18 December 1998

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, ) is replaced by one on the minimum temperature at the base of the convective envelope, , at the stage of the post-flash luminosity maximum. Envelope integrations then allow determination of 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 by Marigo (1998a,b) using this scheme. In this paper, we present and discuss the calibration of the two dredge-up parameters (i.e. efficiency and ) aimed at reproducing the carbon star luminosity function (CSLF) in the LMC, using TP-AGB models with original metallicity . In addition to this, the effects of different input quantities on the theoretical CSLF are analyzed. It turns out that the faint tail is almost insensitive to the history of star formation rate (SFR) in the parent galaxy, in contrast to the bright wing which may be more affected by the details of the recent history. Actually, we find that the faint end of the CSLF is essentially determined by the temperature parameter . Once the faint end is reproduced, the peak location is a stringent calibrator of the efficiency parameter . The best fit to the observed CSLF in the LMC is obtained with , , and a constant SFR up to an age of about yr. This recent drop of the SFR is invoked to remove a slight excess of bright carbon stars otherwise predicted.

A good fit to the observed CSLF in the SMC is then easily derived from the models, with a single choice of parameters , , and a constant SFR over the entire significant age interval. The result for is consistent with the theoretical expectation that the third dredge-up is more efficient at lower metallicities.

Key words: galaxies: Magellanic Clouds stars: carbon stars: mass-loss stars: AGB and post-AGB stars: evolution

Send offprint requests to: Paola Marigo (paola@mpa-garching.mpg.de; marigo@pd.astro.it)

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Contents

• 1. Introduction
• 2. The role of synthetic calculations
• 3. The minimum core mass for dredge-up
  • 3.1. The relation
  • 3.2. A characteristic temperature for dredge-up
  • 3.3. from envelope integrations
    • 3.3.1. Consistency checks
    • 3.3.2. The choice of
    • 3.3.3. The dependence of on M and Z
  • 3.4. The inter-shell chemical composition
  • 3.5. Other computational details
• 4. The observed carbon star luminosity functions in the MCs
• 5. The theoretical carbon star luminosity function
  • 5.1. The stellar birth rate
  • 5.2. The rate of brightening
  • 5.3. Transition luminosities
  • 5.4. The effect of the low-luminosity dip
• 6. The calibration of the dredge-up parameters for the LMC
  • 6.1. The temperature parameter:
  • 6.2. The efficiency parameter:
  • 6.3. Sensitivity to the SFR and IMF
• 7. The calibration of dredge-up parameters for the SMC
• 8. Conclusions
• Acknowledgements
• References

© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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