Abstract
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.