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Aims: Projected rotational velocities (\vsini) have been estimated for 334targets in the VLT-FLAMES Tarantula survey that do not manifest significantradial velocity variations and are not supergiants. They have spectral typesfrom approximately O9.5 to B3. The estimates have been analysed to infer theunderlying rotational velocity distribution, which is critical forunderstanding the evolution of massive stars.  Methods: Projected rotational velocities were deduced from the Fouriertransforms of spectral lines, with upper limits also being obtained fromprofile fitting. For the narrower lined stars, metal and non-diffuse heliumlines were adopted, and for the broader lined stars, both non-diffuse anddiffuse helium lines; the estimates obtained using the different sets of linesare in good agreement. The uncertainty in the mean estimates is typically 4%for most targets. The iterative deconvolution procedure of Lucy has been usedto deduce the probability density distribution of the rotational velocities.  Results: Projected rotational velocities range up to approximately 450 \kmsand show a bi-modal structure. This is also present in the inferred rotationalvelocity distribution with 25% of the sample having $0\leq$\ve$\leq$100\,\kmsand the high velocity component having \ve$\sim 250$\,\kms. There is noevidence from the spatial and radial velocity distributions of the twocomponents that they represent either field and cluster populations ordifferent episodes of star formation. Be-type stars have also been identified.  Conclusions: The bi-modal rotational velocity distribution in our sampleresembles that found for late-B and early-A type stars. While magnetic brakingappears to be a possible mechanism for producing the low-velocity component, wecan not rule out alternative explanations.

The VLT-FLAMES Tarantula Survey X: Evidence for a bimodal distribution of rotational velocities for the single early B-type stars