SIMBAD references

We have devised fitting formulae for evolution tracks of massive stars with 8 <= M/M_☉ <= 160 under extreme metal-poor (EMP) environments for log (Z/Z_☉) = -2, -4, -5, -6, and -8, where M_☉ and Z_☉ are the solar mass and metallicity, respectively. Our fitting formulae are based on reference stellar models which we have newly obtained by simulating the time evolutions of EMP stars. Our fitting formulae take into account stars ending with blue supergiant (BSG) stars, and stars skipping Hertzsprung gap phases and blue loops, which are characteristics of massive EMP stars. In our fitting formulae, stars may remain BSG stars when they finish their core Helium burning phases. Our fitting formulae are in good agreement with our stellar evolution models. We can use these fitting formulae on the SSE, BSE, NBODY4, and NBODY6 codes, which are widely used for population synthesis calculations and star cluster simulations. These fitting formulae should be useful to make theoretical templates of binary black holes formed under EMP environments.