The influence of initial orbital period on helium and carbon-oxygen core masses in massive case a binary systems with low accretion efficiency

The evolutionary models of 33 massive Case A binary systems in mass range from 30M(circle dot) to 40M(circle dot) with initial orbital periods of 3, 4 and 5 days, accretion efficiency of 10% and at the solar metallicity are presented. The models are obtained with the MESA (Modules for Experiments in Stellar Astrophysics) numerical code. The evolution is followed from a double 0-type star, through Case A and Case AB mass transfer, to the formation of a carbon-oxygen (CO) core in the primary. The evolution of the secondary star in each binary system is further modeled with the same numerical code in an approximation of a single star, also to the formation of a carbon-oxygen core. The resulting helium core masses are in the range of 7.94M(circle dot) - 13.19M(circle dot) and 12.30M(circle dot) and 19.12M circle dot for primary and secondary stars, respectively. The carbon-oxygen core masses are between 5.26M(circle dot) and 10M(circle dot) for primaries and between 8.96M(circle dot) and 15.32M(circle dot) for secondaries. A clear influence of the initial orbital period on the resulting helium and CO core masses is demonstrated: primary stars in binary systems with initial orbital periods of 3, 4 and 5 days have on average about 15%, 8% and 2.5% smaller CO cores than single stars with the same initial masses. On the other hand, it was found that the correlation between the CO and helium core mass does not depend on the initial orbital period and can be approximated with the same linear fit for all binary systems. The CO/helium core mass ratio is found to be larger in binary systems than for single stars. It is also shown that the black hole formation limit for primary stars depends on the initial orbit and is between 33M(circle dot) - 34M(circle dot), 32M(circle dot) - 33M(circle dot) and 30M(circle dot) - 31M(circle dot), for the initial orbital periods of 3, 4 and 5 days, respectively. The resulting double compact objects are of two types: mixed neutron star - black hole systems (6 models) and double black holes (27 models). The resulting black hole masses are estimated to be in the range of 5M(circle dot) to 17M(circle dot).