Massive binary star mergers in galactic nuclei: implications for blue
  stragglers, binary S-stars and gravitational waves
  Galactic nuclei are often found to contain young stellar populations and, in
most cases, a central supermassive black hole (SMBH). Most known massive stars
are found in binaries or higher-multiplicity systems, and in a galactic nucleus
the gravitational interaction with the SMBH can affect their long-term
evolution. In this paper, we study the orbital evolution of stellar binaries
near SMBHs using high precision $N$-body simulations, and including tidal
forces and Post-Newtonian corrections to the motion. We focus on the
Lidov-Kozai (LK) effect induced by the SMBH on massive star binaries. We
investigate how the properties of the merging binaries change with varying the
SMBH mass, the slope of the initial mass function, the distributions of the
binary orbital parameters and the efficiency in energy dissipation in
dissipative tides. We find that the fraction of merging massive binary stars is
in the range $\sim 4\%$--$15\%$ regardless of the details of the initial
distributions of masses and orbital elements. For a Milky Way-like nucleus, we
find a typical rate of binary mergers $\Gamma\approx 1.4\times 10^{-7}$
yr$^{-1}$. The merger products of massive binaries can be rejuvenated
blue-straggler stars, more massive than each of their original progenitors, and
G2-like objects. Binary systems that survive the LK cycles can be source of
X-rays and gravitational waves, observable with present and upcoming
instruments.
