We have devised fitting formulae for evolution tracks of massive stars with 8 \lesssim M / M _ { \odot } \lesssim 160 under extreme metal poor ( EMP ) environments for \log ( Z / Z _ { \odot } ) = -2 , -4 , -5 , -6 , and -8 , where M _ { \odot } and Z _ { \odot } 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 ( HG ) 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 ( CHeB ) 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 .