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[Context] Two competing models describe the formation of massive stars in objects like the Orion Trapezium. In the turbulent core accretion model, the resulting stellar masses are directly related to the mass distribution of the cloud condensations. In the competitive accretion model, the gravitational potential of the protocluster captures gas from the surrounding cloud for which the individual cluster members compete. [Aims] With high resolution submillimeter observations of the structure, kinematics, and chemistry of the proto-Trapezium cluster W3 IRS5, we aim to determine which mode of star formation dominates. [Methods] We present 354 GHz Submillimeter Array observations at resolutions of 1-3 (1800-5400 AU) of W3 IRS5. ...... [Results] The observations show five emission peaks (SMM1-5). SMM1 and SMM2 contain massive embedded stars (~20 Msun); SMM3-5 are starless or contain low-mass stars (<8 Msun). The inferred densities are high, >= 10^7 cm^-3, but the core masses are small, 0.2-0.6 Msun. The detected molecular emission reveals four different chemical zones. ...... [Conclusions] The proto-Trapezium cluster W3 IRS5 is an ideal test case to discriminate between models of massive star formation. Either the massive stars accrete locally from their local cores; in this case the small core masses imply that W3 IRS5 is at the very end stages (1000 yr) of infall and accretion, or the stars are accreting from the global collapse of a massive, cluster forming core. We find that the observed masses, densities and line widths observed toward W3 IRS 5 and the surrounding cluster forming core are consistent with the competitive accretion of gas at rates of Macc~10^-4 Msun yr^-1 by the massive young forming stars. ......
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