In addition to this, the effects of different input quantities on the theoretical CSLF are analyzed. efficiency lambda and T_b() dred) aimed at reproducing the carbon star luminosity function (CSLF) in the LMC, using TP-AGB models with original metallicity Z=0.008. In this paper, we present and discuss the calibration of the two dredge-up parameters (i.e. Extensive grids of TP-AGB models were computed by Marigo (1998a,b) using this scheme. Moreover, the final possible shut down of the process is predicted. 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. 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. 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. We investigate the formation of carbon stars as a function of the stellar mass and parent metallicity.
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