The most iron-poor stars in the Milky Way provide important observational clues to the astrophysical objects that enriched the primordial gas with heavy elements .
Among them , the recently discovered iron-deficient star SMSS J031300.36-670839.3 shows a remarkable chemical composition with non-detection of iron ( [ Fe/H ] < -7.1 ) and large enhancement of carbon and magnesium relative to calcium .
We investigate supernova yields of metal-free ( Population III ) stars to interpret the abundance pattern observed in this star .
We report that the high [ C/Ca ] and [ C/Mg ] ratios and upper limits of other elemental abundances are well reproduced with the yields of core-collapse supernovae ( that have normal kinetic energies of explosion E of E _ { 51 } = E / 10 ^ { 51 } erg = 1 ) and hypernovae ( E _ { 51 } \geq 10 ) of Population III 25 M _ { \odot } or 40 M _ { \odot } stars .
The best-fit models assume that the explosions undergo extensive matter mixing and fallback , leaving behind a black hole remnant .
In these models , Ca is produced by static/explosive O burning and incomplete Si burning in the Population III supernova/hypernova , in contrast to the suggestion that Ca is originated from the hot-CNO cycle during the presupernova evolution .
Chemical abundances of four carbon-rich iron-poor stars with [ Fe/H ] < -4.5 , including SMSS J031300.36-670839.3 are consistently explained by the faint supernova models with the ejected mass of ^ { 56 } Ni less than 10 ^ { -3 } M _ { \odot } .