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Massive Field Stars and the Stellar Clustering Law

The distribution of N*, the number of OB stars per association or cluster, appears to follow a universal power-law form $N*^{-2}$ in the local Universe. We evaluate the distribution of N* in the Small Magellanic Cloud using recent broadband optical and space-ultraviolet data, with special attention to the lowest values of N*. We find that the power-law distribution in N* continues smoothly down to N*=1. This strongly suggests that the formation of field massive stars is a continuous process with those in associations, and that the field stars do not originate from a different star formation mode. Our results are consistent with the model that field massive stars represent the most massive members in groups of smaller stars, as expected if the clustering law applies to much lower masses as is expected from the stellar initial mass function (IMF). These results are consistent with the simultaneous existence of a universal IMF and a universal clustering law. Jointly, these laws imply that the fraction of field OB stars typically ranges from about 35% to 7% for most astrophysical situations, with an inverse logarithmic dependence on the most populous cluster, and hence, on galaxy size and/or star formation rate. There are important consequences for global feedback effects in galaxies: field stars should therefore contribute proportionately to the volume of the warm ionized medium, and equal relative contributions by superbubbles of all sizes to the interstellar porosity are expected.