A highly abnormal massive star mass function in the Orion Nebula cluster and the dynamical decay of trapezium systems

Abstract

The ONC appears to be unusual on two grounds: The observed constellation of\nthe OB stars of the entire Orion Nebula cluster and its Trapezium at its centre\nimplies a time-scale problem given the age of the Trapezium, and an IMF problem\nfor the whole OB star population in the ONC. Given the estimated crossing time\nof the Trapezium, it ought to have totally dynamically decayed by now.\nFurthermore, by combining the lower limit of the ONC mass with a standard IMF\nit emerges that the ONC should have formed at least about 40 stars heavier than\n5 M_sun while only ten are observed. Using N-body experiments we (i) confirm\nthe expected instability of the trapezium and (ii) show that beginning with a\ncompact OB-star configuration of about 40 stars the number of observed OB stars\nafter 1 Myr within 1 pc radius and a compact trapezium configuration can both\nbe reproduced. These two empirical constraints thus support our estimate of 40\ninitial OB stars in the cluster. Interestingly, a more-evolved version of the\nONC resembles the Upper Scorpius OB association. The N-body experiments are\nperformed with the new C-code CATENA by integrating the equations of motion\nusing the chain-multiple-regularisation method. In addition, we present a new\nnumerical formulation of the initial mass function.\n