The first stars: CEMP-no stars and signatures of spinstars

Aims. The CEMP-no stars are carbon-enhanced-metal-poor stars that in principle show no evidence of s- and r-elements from neutron captures. We try to understand the origin and nucleosynthetic site of their peculiar CNO, Ne-Na, and Mg-Al abundances. Methods. We compare the observed abundances to the nucleosynthetic predictions of AGB models and of models of rotating massive stars with internal mixing and mass loss. We also analyze the different behaviors offf- and CNO-elements, as well the abundances of elements involved in the Ne-Na and Mg-Al cycles. Results. We show that CEMP-no stars exhibit products of He-burning that have gone through partial mixing and processing by the CNO cycle, producing low C-12/C-13 and a broad variety of [C/N] and [O/N] ratios. From a C-12/C-13 vs. [C/N] diagram, we conclude that neither the yields of AGB stars (in binaries or not) nor the yields of classic supernovae can fully account for the observed CNO abundances in CEMP-no stars. Better agreement is obtained once the chemical contribution by stellar winds of fast-rotating massive stars is taken into account, where partial mixing takes place, leading to various amounts of CNO being ejected. The [(C+N+O)/H] ratios of CEMP-no stars vary linearly with [Fe/H] above [Fe/H] = 4 : 0 indicating primary behavior by (C+N+O). Below [Fe/H] = 4 : 0, [(C+N+O)/H] is almost constant as a function of [Fe/H], implying very high [(C+N+O)/Fe] ratios up to 4 dex. In view of the timescales, such abundance ratios reflect more individual nucleosynthetic properties, rather than an average chemical evolution. The high [(C+N+O)/Fe] ratios (as well as the high [(C+N+O)/alpha-elements]) imply that stellar winds from partially mixed stars were the main source of these excesses of heavy elements now observed in CEMP-no stars. The ranges covered by the variations of [Na/Fe], [Mg/Fe], and [Al/Fe] are much broader than for the alpha-elements (with an atomic mass number above 24) and are comparable to the wide ranges covered by the CNO elements. Nevertheless, the ratios [Na/N] and [Mg/Al] are about constant for CEMP-no stars of different [Fe/H]. This is consistent with the view that the Ne-Na and Mg-Al cycles were significantly operating in the source stars. The very different properties of CNO, Ne-Na, and Mg-Al elements from those of alpha-elements further support the idea that these elements (which all give to CEMP-no stars their peculiarities) originate in slow stellar winds of massive stars experiencing partial mixing. Conclusions. CEMP-no stars present a wide variety in the [C/Fe], [N/Fe], [O/Fe], [Na/Fe], [Mg/Fe], [Al/Fe], and [Sr/Fe] ratios. We show that back-and-forth, partial mixing between the He-and H-regions may account for this variety. Some s-elements, mainly of the first peak, may even be produced by these processes in a small fraction of the CEMP-no stars. We propose a classification scheme for the CEMP-no and low-s stars, based on the changes in composition produced by these successive back-and-forth mixing motions.