INTERPRETING THE MEAN SURFACE-DENSITY OF COMPANIONS IN STAR-FORMING REGIONS

We study the interpretation of the mean surface density of stellar com panions as a function of separation (or, equivalently, the two-point c orrelation function of stars) in star-forming regions. First, we consi der the form of the functions for various simple stellar distributions (binaries, global density profiles, clusters and fractals) and the ef fects of survey boundaries. Following this, we study the dependences o f the separation at which a transition from the binary to the large-sc ale clustering regime occurs. Larson found that the mean surface densi ty of companions follows different power-law functions of separation i n the two regimes. He identified the transition separation with the ty pical Jeans length in the molecular cloud. However, we show that this is valid only for special cases. In general, the transition separation depends on the volume density of stars, the depth of the star-forming region, the volume-filling nature of the stellar distribution, and th e parameters of the binaries. Furthermore, the transition separation e volves with time. We also note that in young star-forming regions, bin aries with separations greater than the transition separation may exis t, while in older unbound clusters that have expanded significantly th e transition contains a record of the stellar density when the stars f ormed. We then apply these results to the Taurus-Auriga, Ophiuchus, an d Orion Trapezium star-forming regions. We find that while the transit ion separation in the Taurus-Auriga star-forming region may indicate a typical Jeans length, this is not true of the Orion Trapezium cluster . We caution against overinterpreting the mean surface density of stel lar companions; while Larson showed that Taurus-Auriga is consistent w ith the stars having a fractal large-scale distribution, we show that Taurus-Auriga is also consistent with stars being grouped in non-hiera rchical clusters. We also argue that to make a meaningful study of the stellar distribution in a star-forming region requires a relatively c omplete stellar survey over a large area. Such a survey does not curre ntly exist for Ophiuchus. Finally, we show that there is no evidence f or subclustering or fractal structure in the stars of the Orion Trapez ium cluster. This is consistent with the fact that, if such structure were present when the stars formed, it would have been erased by the c urrent age of the cluster due to the stellar velocity dispersion.