So the way I understand it, it is generally accepted in the astronomical community that there is a shortage of massive stars of spectral classes O and B in the Orion Nebula and the Trapezium. My question is how they can know that. How can you look at a young cluster and say that there are "too few" OB stars in it?Ladislav Šubr, Pavel Kroupa, and Holger Baumgardt wrote:
We investigate the dynamical evolution of the Orion Nebula Cluster (ONC) by means of direct N-body integrations. A large fraction of residual gas was probably expelled when the ONC formed, so we assume that the ONC was much more compact when it formed compared with its current size, in agreement with the embedded cluster radius-mass relation from Marks & Kroupa. Hence, we assume that few-body relaxation played an important role during the initial phase of evolution of the ONC. In particular, three-body interactions among OB stars likely led to their ejection from the cluster and, at the same time, to the formation of a massive object via "runaway" physical stellar collisions. The resulting depletion of the high-mass end of the stellar mass function in the cluster is one of the important points where our models fit the observational data.
For that matter, how can you measure the parameters of a young cluster very carefully and say that there are too few OB stars in it?
I know that there is something called the initial mass function (IMF) of a cluster. I know that the IMF says something about how many OB stars you can expect in different kinds of young clusters, and I also know, of course, that high-mass stars are vastly more rare than low-mass stars. But I have never managed to get a real grip of the IMF, because it is way too mathematical for me. I know it says something about how many OB stars you can expect to find in a young cluster whose mass is 100 M☉, or 1000 M☉, or 10,000 M☉. But I have no idea just how many OB stars we should expect to find in a young cluster whose mass is, let's say, 1000 M☉.
Can you help me here? How many OB stars should there be in a young cluster of 1000 M☉? How many OB stars should there have been in the Orion Nebula, if the high-mass end of stars there had not been depleted?