Nucleosynthetic yields of Z=$10^{-5}$ intermediate-mass stars
  Abridged: Observed abundances of extremely metal-poor (EMP) stars in the Halo
hold clues for the understanding of the ancient universe. Interpreting these
clues requires theoretical stellar models at the low-Z regime. We provide the
nucleosynthetic yields of intermediate-mass Z=$10^{-5}$ stars between 3 and 7.5
$M_{sun}$, and quantify the effects of the uncertain wind rates. We expect
these yields can be eventually used to assess the contribution to the chemical
inventory of the early universe, and to help interpret abundances of selected
C-enhanced EMP stars. By comparing our models and other existing in the
literature, we explore evolutionary and nucleosynthetic trends with wind
prescriptions and with initial metallicity. We compare our results to
observations of CEMP-s stars belonging to the Halo. The yields of
intermediate-mass EMP stars reflect the effects of very deep second dredge-up
(for the most massive models), superimposed with the combined signatures of
hot-bottom burning and third dredge-up. We confirm the reported trend that
models with initial metallicity Z$_{ini}$ <= 0.001 give positive yields of
$^{12}C, ^{15}N, ^{16}O$, and $^{26}Mg$. The $^{20}Ne, ^{21}Ne$, and $^{24}Mg$
yields, which were reported to be negative at Z$_{ini}$ = 0.0001, become
positive for Z=$10^{-5}$. The results using two different prescriptions for
mass-loss rates differ widely in terms of the duration of the thermally-pulsing
(Super) AGB phase, overall efficiency of the third dredge-up episode, and
nucleosynthetic yields. The most efficient of the standard wind rates
frequently used in the literature seems to favour agreement between our yield
results and observational data. Regardless of the wind prescription, all our
models become N-enhanced EMP stars.
