Classification of extremely metal-poor stars: absent region in A(C)-[Fe/H] plane and the role of dust cooling

Extremely metal-poor (EMP) stars are the living fossils with records of chemical enrichment history at the early epoch of galaxy formation. By the recent large observation campaigns, statistical samples of EMP stars have been obtained. This motivates us to reconsider their classification and formation conditions. From the observed lower limits of carbon and iron abundances of A(cr)(C) similar to 6 and [Fe/H](cr) similar to -5 for C-enhanced EMP (CE-EMP) and C-normal EMP (CN-EMP) stars, we confirm that gas cooling by dust thermal emission is indispensable for the fragmentation of their parent clouds to form such low mass, i.e. long-lived stars, and that the dominant grain species are carbon and silicate, respectively. We constrain the grain radius r(i)(cool) of a species i and condensation efficiency f(ij) of a key element j as f(c)(cool)/fc,c = 10 mu m and r(Sil)(cool)/f(Sil,Mg) = 0.1 mu m to reproduce A(cr)(C) and [Fe/H](cr), which give a universal condition 10([C/H]-2.30) + 10([Fe/H]) > 10(-5.07) for the formation of every EMP star. Instead of the conventional boundary [C/Fe] = 0.7 between CE-EMP and CN-EMP stars, this condition suggests a physically meaningful boundary [C/Fe](b) = 2.30 above and below which carbon and silicate grains are dominant coolants, respectively.