The current understanding of the evolution of binary stars is firmly based on observations of many types of binary systems, from wide non-interacting pairs to very close compact binaries consisting of remnants of stellar evolution. The largest uncertainties in the specific parameters of the double compact binary formed at the end of the evolution of a massive binary system are related to the physical properties of the pre-supernovae: masses, magnetic fields, equation of state (for NSs), spins, possible kick velocities, etc. This situation is due to our limited understanding of both the late stages of stellar evolution and especially of the supernovae explosion mechanisms. The understanding of the origin and evolution of compact white dwarf binaries also suffers from incompleteness of our knowledge of white dwarf formation and, in particular, on the common envelope treatment. The progress in these fields, both observational and theoretical, will have a major effect on the apprehension of the formation and evolution of compact binary systems. On the other hand, the phenomenological approach used to describe these uncertainties proves to be successful in explaining many observed properties of various binary stars, so the constraints derived from the studies of binary stars should be taken into account in modeling stellar evolution and supernovae explosions.
Of course, specifying and checking the initial distributions of orbital parameters of binary stars and parameters of binary evolution (such as evolution in the common envelopes) stay in the short-list of the important actions to be done. Here an essential role belongs to detailed numerical simulations.
Further observations of compact binaries. Clearly, discoveries of new types of compact binary systems have provided the largest impetus for studies of binary star evolution. The well known examples include the discovery of X-ray binaries, relativistic binary pulsars, and millisecond recycled pulsars. In the nearest future we expect the discovery of NS + BH binaries which are predicted by the massive binary evolution scenario in the form of binary radio pulsars with BH companions [230, 222, 310]. It is very likely that we already observe the coalescence of double NS/BH systems as short gamma-ray bursts in other galaxies . We also anticipate that coalescences of NS + BH or BH + BH binaries can be found first in GW data analysis . The efforts of the LIGO collaboration to put constraints on the compact binary coalescences from the analysis of the existing GW observations are very important [2, 3, 1].
The formation and evolution of compact binaries is a very interdisciplinary field of modern astrophysics, ranging from studies of the equation of state for superdense matter inside neutron stars and testing effects of strong gravity in relativistic compact binaries to hydrodynamical effects in stellar winds and formation of common envelopes. So, further progress in this field, which will be made by means of traditional astronomical observations and new tools, like gravitational wave and neutrino detectors, will undoubtedly have an impact on astronomy and astrophysics as a whole.
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