Astrophysical Mechanisms
Carbon stars are explained by more than one astrophysical mechanism. Classical carbon stars are distinguished from non-classical ones on the grounds of mass, with classical carbon stars being the more massive.
In the classical carbon stars, those belonging to the modern spectral types C-R and C-N, the abundance of carbon is thought to be a product of helium fusion, specifically the triple-alpha process within a star, which giants reach near the end of their lives in the asymptotic giant branch (AGB). These fusion products have been brought to the stellar surface by episodes of convection (the so-called third dredge-up) after the carbon and other products were made. Normally this kind of AGB carbon star fuses hydrogen in a hydrogen burning shell, but in episodes separated by 104-105 years, the star transforms to burning helium in a shell, while the hydrogen fusion temporarily ceases. In this phase, the star's luminosity rises, and material from the interior of the star (notably carbon) moves up. Since the luminosity rises, the star expands so that the helium fusion ceases, and the hydrogen shell burning restarts. During these shell helium flashes, the mass loss from the star is significant, and after many shell helium flashes, an AGB star is transformed into a hot white dwarf and its atmosphere becomes material for a planetary nebula.
The non-classical kinds of carbon stars, belonging to the types C-J and C-H, are believed to be binary stars, where one star is observed to be a giant star (or occasionally a red dwarf) and the other a white dwarf. The star presently observed to be a giant star accreted carbon-rich material when it was still a main sequence star from its companion (that is, the star that is now the white dwarf) when the latter was still a classical carbon star. That phase of stellar evolution is relatively brief, and most such stars ultimately end up as white dwarfs. We are now seeing these systems a comparatively long time after the mass transfer event, so the extra carbon observed in the present red giant was not produced within that star. This scenario is also accepted as the origin of the barium stars, which are also characterized as having strong spectral features of carbon molecules and of barium (an s-process element). Sometimes the stars whose excess carbon came from this mass transfer are called "extrinsic" carbon stars to distinguish them from the "intrinsic" AGB stars which produce the carbon internally. Many of these extrinsic carbon stars are not luminous or cool enough to have made their own carbon, which was a puzzle until their binary nature was discovered.
The enigmatic hydrogen deficient carbon stars (HdC), belonging to the spectral class C-Hd, seems to have some relation to R Coronae Borealis variables (RCB), but aren't variable themselves and lack a certain infrared radiation typical for RCB:s. Only five HdC:s are known, and none is known to be binary, so the relation to the non-classical carbon stars is not known.
Other less convincing theories, such as CNO cycle unbalancing and core helium flash have also been proposed as mechanisms for carbon enrichment in the atmospheres of smaller carbon stars.
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