Context :

Aims : The incidence of multiplicity in cool , luminous massive stars is relatively unknown compared to their hotter counterparts .
Here we present radial velocity ( RV ) measurements and investigate the multiplicity properties of red supergiants ( RSGs ) in the 30 Doradus region of the Large Magellanic Cloud using multi-epoch visible spectroscopy from the VLT-FLAMES Tarantula Survey .

Methods : Exploiting the high density of absorption features in visible spectra of cool stars , we use a novel slicing technique to estimate RVs of 17 candidate RSGs in 30 Doradus from cross-correlation of the observations with model spectra .

Results : We provide absolute RV measurements ( precise to better than \pm 1 \mbox { km s } ^ { -1 } ) for our sample and estimate line-of-sight velocities for the Hodge 301 and SL 639 clusters , which agree well with those of hot stars in the same clusters .
By combining results for the RSGs with those for nearby B-type stars , we estimate systemic velocities and line-of-sight velocity dispersions for the two clusters , obtaining estimates for their dynamical masses of \log ( M _ { dyn } / M _ { \odot } ) = 3.8 \pm 0.3 for Hodge 301 , and an upper limit of \log ( M _ { dyn } / M _ { \odot } ) < 3.1 \pm 0.8 for SL 639 , assuming Virial equilibrium .
Analysis of the multi-epoch data reveals one RV-variable , potential binary candidate ( VFTS 744 ) , which is likely a semi-regular variable asymptotic giant branch star .
Calculations of semi-amplitude velocities for a range of RSGs in model binary systems and literature examples of binary RSGs were used to guide our RV variability criteria .
We estimate an upper limit on the observed binary fraction for our sample of 0.3 , where we are sensitive to maximum periods for individual objects in the range of 1 to 10 000 days and mass-ratios above 0.3 depending on the data quality .
From simulations of the RV measurements from binary systems given the current data we conclude that systems within the parameter range q > 0.3 , \log P [ days ] < 3.5 , would be detected by our variability criteria , at the 90 % confidence level .
The intrinsic binary fraction , accounting for observational biases , is estimated using simulations of binary systems with an empirically defined distribution of parameters where orbital periods are uniformly distributed in the 3.3 < \log P [ days ] < 4.3 range .
A range of intrinsic binary fractions are considered ; a binary fraction of 0.3 is found to best reproduce the observed data .

Conclusions : We demonstrate that RSGs are effective extragalactic kinematic tracers by estimating the kinematic properties , including the dynamical masses of two LMC young massive clusters .
In the context of binary evolution models , we conclude that the large majority of our sample consists of currently effectively single stars ( either single or in long period systems ) .
Further observations at greater spectral resolution and/or over a longer baseline are required to search for such systems .