The late stages of evolution of helium star-neutron star binaries and the formation of double neutron star systems

With a view to understanding the formation of double neutron star binaries, we investigate the late stages of evolution of helium stars with masses of 2.8-6.4 M-circle dot in binary systems with a 1.4-M-circle dot neutron star companion. We found that mass transfer from 2.8- to 3.3-M-circle dot helium stars (originating from main-sequence stars with masses of 10-12 M-circle dot that underwent case B evolution, or 9-10 M-circle dot that experienced case C mass transfer) as well as from 3.3 to 3.8 M-circle dot in very close orbits (P-orb less than or similar to 0.25 d) will end up in a common-envelope and spiral-in phase due to the development of a convective helium envelope at the end of the calculation. If the neutron star has sufficient time to complete the spiralling-in process in the envelope of the helium star before the core collapses, the system will produce very tight double neutron star binaries (P-orb similar to 0.01 d) with a very short merger time-scale, i.e. of the order of 1 Myr or less. These systems would have important consequences for the detection rate of gravitational-wave radiation and for the understanding of gamma-ray burst progenitors. On the other hand, if the time left until the explosion is shorter than the orbital-decay time-scale, the system will undergo a supernova (SN) explosion during the common-envelope phase. Helium stars with masses 3.3-3.8 M-circle dot in wider orbits (P-orb greater than or similar to 0.25 d) and those more massive than 3.8 M-circle dot do not develop a convective envelope and therefore are not expected to go through common-envelope evolution. The remnants of these massive helium stars are double neutron star pulsars with periods in the range of 0.1-1 d. This suggests that this range of mass (originating from main-sequence stars more massive than 12 M-circle dot that underwent case B evolution, or more massive than 10 M-circle dot that experienced case C mass transfer) includes the progenitors of the galactic double neutron star pulsars with close orbits (B1913 + 16 and B1534 + 12). A minimum kick velocity of 70 and 0 km s(-1) (for B1913 + 16 and B1534 + 12, respectively) must have been imparted at the birth of the companion to the pulsar. The double neutron stars with wider orbits (J1518 + 4904 and probably J1811-1736) are produced from helium star-neutron star binaries that avoid Roche lobe overflow, with the helium star being more massive than 2.5 M-circle dot, i.e. the remnants of main-sequence stars more massive than 10 M-circle dot in relatively wide orbits. For these systems, the minimum kick velocities are 50 and 10 km s(-1) (for J1518 + 4904 and J1811-1736, respectively).