Are C-rich ultra iron-poor stars also He-rich?

Context. The three most iron-poor stars presently known ([Fe/H] equal to -5.96, -5.4 and -4.75) are carbon-rich, so they are called C-Rich Ultra-Metal Poor Stars (CRUMPS). The origin of their peculiar surface abundances is not understood. Aims. We propose a synthetic view of the different models proposed so far to explain the peculiar abundances observed on the surface of the CRUMP stars. We deduce some expected trends based on nucleosynthetic arguments and look for signatures that allow models to be distinguished. We discuss the conditions for having CRUMP stars which are He-rich, i.e. with a mass fraction of helium greater than 0.30 and up to 0.60. Methods. We discuss the chemical composition of stars made of interstellar medium mixed with wind material of very metal-poor massive stars, with wind plus supernova ejecta and with material extracted from the envelope of early asymptotic giant branch (AGB) stars. Rotating and non-rotating models are considered. Results. The high nitrogen abundances observed in CRUMP stars imply that the material that is responsible for their peculiar abundance pattern must be heavily enriched in primary nitrogen. We show that rotating stars (both massive and intermediate-mass stars) can produce the required amount of primary nitrogen, and can also account for the observed enhancements in C, O, Na, Mg, and Al. CRUMP stars formed from wind material of massive stars mixed with small amounts of pristine interstellar medium are He-rich (helium mass fraction between 0.30 and 0.60), Li-depleted, and present low C-12/C-13 ratios (inferior to 10 in number). Such He-rich stars, if discovered, would confirm that the most metal-poor CRUMPs formed from essentially pure wind/envelope material. They would provide the most direct way of probing the nucleosynthetic outputs of the first generations of stars. Conclusions. We show that rotation is a key ingredient in explaining the abundance patterns of CRUMPS stars and probably also of at least some carbon-enhanced metal poor (CEMP) stars, in particuliar the CEMP-no stars. Similar non-rotating models, without any extra-mixing, do not succeed in explaining the enhancements in the three CNO elements.