  Renewed interest in the first stars that were formed in the universe has led
to the discovery of extremely iron-poor stars. Since several competing
scenarios exist, our understanding of the mass range that determines the
observed elemental abundances remains unclear. In this study, we consider three
well-studied metal-poor stars in terms of the theoretical supernovae (SNe)
model. Our results suggest that the observed abundance patterns in the
metal-poor star BD +80 245 and the pair of stars HD 134439/40 agree strongly
with the theoretical possibility that these stars inherited their heavy element
abundance patterns from SNe initiated by thermonuclear runaways in the
degenerate carbon-oxygen cores of primordial asymptotic giant branch stars with
\~3.5-5 solar masses. Recent theoretical calculations have predicted that such
SNe could be originated from metal-free stars in the intermediate mass range.
On the other hand, intermediate mass stars containing some metals would end
their lives as white dwarfs after expelling their envelopes in the wind due to
intense momentum transport from outgoing photons to heavy elements. This new
pathway for the formation of SNe requires that stars are formed from the
primordial gas. Thus, we suggest that stars of a few solar masses were formed
from the primordial gas and that some of them caused thermonuclear explosions
when the mass of their degenerate carbon-oxygen cores increased to the
Chandrasekhar limit without experiencing efficient mass loss.
