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The binary merger channel for the progenitor of the fastest rotating O-type star VFTS102

VFTS102 has a projected rotational velocity ($>$500\,km s$^{-1}$) and would appear to be the fastest rotating O-type star. We show that its high rotational velocity could be understood within the framework of the binary merger. In the binary merger channel, the progenitor binary of VFTS102 would evolve into contact while two components are still on the main sequence, and then merge into a rapidly rotating single star. Employing Eggleton's stellar evolution code, we performed binary stellar evolution calculations and mapped out the initial parameters of the progenitor of VFTS102 in the orbital period-mass ratio ($P-q$) plane. We found that the progenitor binary of VFTS102 with initial mass ratio $q_0 \la 0.7$ should have an initial orbital period shorter than $3.76-4.25$\,days, while above this mass ratio it should have an initial orbital period shorter than $1.44-1.55$\,days. The progenitor of VFTS102 would evolve into contact during the rapid mass transfer phase or during the subsequent slow mass transfer phase, and might ultimately merge into a rapidly rotating massive star. In addition, we performed Monte Carlo simulations to investigate the binary merger channel. We estimated the fraction of binaries that would merge into single stars and the fraction of single stars that might be produced from the binary merger channel. It is found that about 8.7% of binaries would evolve into contact and merge into rapidly rotating single stars, and about 17.1% of single stars might be produced from the binary merger channel and should have similar properties to VFTS102. This suggests that the binary merger channel might be one of the main channels for the formation of rapidly rotating massive stars like VFTS102.