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We have devised fitting formulae for evolution tracks of massive stars with$8 \lesssim M/M_\odot \lesssim 160$ under extreme metal poor (EMP) environmentsfor $\log (Z/Z_\odot) = -2, -4, -5, -6$, and $-8$, where $M_\odot$ and$Z_\odot$ are the solar mass and metallicity, respectively. Our fittingformulae are based on reference stellar models which we have newly obtained bysimulating the time evolutions of EMP stars. Our fitting formulae take intoaccount stars ending with blue supergiant (BSG) stars, and stars skippingHertzsprung gap (HG) phases and blue loops, which are characteristics ofmassive EMP stars. In our fitting formulae, stars may remain BSG stars whenthey finish their core Helium burning (CHeB) phases. Our fitting formulae arein good agreement with our stellar evolution models. We can use these fittingformulae on the SSE, BSE, NBODY4, and NBODY6 codes, which are widely used forpopulation synthesis calculations and star cluster simulations. These fittingformulae should be useful to make theoretical templates of binary black holesformed under EMP environments.

monthly notices of the royal astronomical society

Fitting formulae for evolution tracks of massive stars under extreme  metal poor environments for population synthesis calculations and star  cluster simulations