Most carbon-enhanced metal-poor (CEMP) stars are thought to result from past mass transfer of He-burning material from an asymptotic giant branch (AGB) star to a low-mass companion star, which we now observe as a CEMP star. Because AGB stars of intermediate mass efficiently cycle carbon into nitrogen in their envelopes, the same evolution scenario predicts the existence of a population of nitrogen-enhanced metal-poor (NEMP) stars, with [N/Fe] > 1 and [N/C] > 0.5. Such NEMP stars are rare, although their occurrence depends on metallicity: they appear to be more common at [Fe/H] < -2.8 by about a factor of 10 compared to less metal-poor stars. We analyse the observed sample of metal-poor stars with measurements of both carbon and nitrogen to derive firm constraints on the occurrence of NEMP stars as a function of metallicity. We compare these constraints to binary population synthesis calculations in which we vary the initial distributions of mass, mass ratio and binary orbital periods. We show that the observed paucity of NEMP stars at [Fe/H] > -2.8 does not allow for large modifications in the initial mass function, as have been suggested in the literature to account for the high frequency of CEMP stars. The situation at lower metallicity is less clear, and we do not currently have stellar models to perform this comparison for [Fe/H] < -2.8. However, unless intermediate-mass AGB stars behave very differently at such low metallicity, the observed NEMP frequency at [Fe/H] < -2.8 appears incompatible with the top-heavy forms of the initial mass function suggested in the literature.
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