Dredge-up astrophysics

The relative depletion of C and enhancement of Ncould now be observable at the stellar surface.
This first dredge-up is analogous to that which occurs in 1 M⊙ (see Fig. 13 at a time of 6 × 10 7 years).
FIGURE 13.
The evolution of the internal structure of a star of 5 M⊙ with composition similar to that of the sun.

It has long been known that the unstable double-shell burning in AGB stars leads to the phenomenon of third dredge-up (TDUP).
The ashes of helium burning are mixed into the convective envelope enhancing the surface abundance of carbon ( Iben & Renzini 1983 ).

By definition
During a dredge-up
A convection zone extends all the way from the star's surface down to the layers of material that have undergone fusion.
Consequently
The fusion products are mixed into the outer layers of the star's atmosphere
Where they can be seen in stellar spectra .

Third dredge-up occurs in stars of 1 M ⊙ and above and carbon stars were found for models between 1 M ⊙ and 3 M ⊙.
We use the detailed models as input physics for a population synthesis code and generate carbon star luminosity functions.

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

By definition, during a dredge-up, a convection zone extends all the way from the star's surface down to the layers of material that have undergone fusion

Consequently, the fusion products are mixed into the outer layers of the star's atmosphere, where they can be seen in stellar spectra

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