A highly abnormal massive star mass function in the Orion Nebula cluster   and the dynamical decay of trapezia systems
  The ONC appears to be unusual on two grounds: The observed constellation of the OB stars of the entire Orion Nebula cluster and its Trapezium at its centre implies a time-scale problem given the age of the Trapezium, and an IMF problem for the whole OB star population in the ONC. Given the estimated crossing time of the Trapezium, it ought to have totally dynamically decayed by now. Furthermore, by combining the lower limit of the ONC mass with a standard IMF it emerges that the ONC should have formed at least about 40 stars heavier than 5 M_sun while only ten are observed. Using N-body experiments we (i) confirm the expected instability of the trapezium and (ii) show that beginning with a compact OB-star configuration of about 40 stars the number of observed OB stars after 1 Myr within 1 pc radius and a compact trapezium configuration can both be reproduced. These two empirical constraints thus support our estimate of 40 initial OB stars in the cluster. Interestingly, a more-evolved version of the ONC resembles the Upper Scorpius OB association. The N-body experiments are performed with the new C-code CATENA by integrating the equations of motion using the chain-multiple-regularisation method. In addition, we present a new numerical formulation of the initial mass function. 
J. Pflamm-Altenburg and P. Kroupa