The VLT-FLAMES Tarantula Survey VIII. Multiplicity properties of the
  O-type star population
  Aims. We analyze the multiplicity properties of the massive O-type star
population. With 360 O-type stars, this is the largest homogeneous sample of
massive stars analyzed to date.
  Methods. We use multi-epoch spectroscopy and variability analysis to identify
spectroscopic binaries. We also use a Monte-Carlo method to correct for
observational biases.
  Results. We observe a spectroscopic binary fraction of 0.35\pm0.03, which
corresponds to the fraction of objects displaying statistically significant
radial velocity variations with an amplitude of at least 20km/s. We compute the
intrinsic binary fraction to be 0.51\pm0.04. We adopt power-laws to describe
the intrinsic period and mass-ratio distributions: f_P ~ (log P)^\pi\ (with
0.15 < log P < 3.5) and f_q ~ q^\kappa\ with 0.1 < q=M_2/M_1 < 1.0. The
power-law indexes that best reproduce the observed quantities are \pi = -0.45
+/- 0.30 and \kappa = -1.0\pm0.4. The obtained period distribution thus favours
shorter period systems compared to an Oepik law. The mass ratio distribution is
slightly skewed towards low mass ratio systems but remains incompatible with a
random sampling of a classical mass function. The binary fraction seems mostly
uniform across the field of view and independent of the spectral types and
luminosity classes. The binary fraction in the outer region of the field of
view (r > 7.8', i.e. approx117 pc) and among the O9.7 I/II objects are however
significantly lower than expected from statistical fluctuations.
  Conclusions. Using simple evolutionary considerations, we estimate that over
50% of the current O star population in 30 Dor will exchange mass with its
companion within a binary system. This shows that binary interaction is greatly
affecting the evolution and fate of massive stars, and must be taken into
account to correctly interpret unresolved populations of massive stars.
