Spatial Distributions of Young Stars

We analyze the spatial distribution of young stars in Taurus-Auriga and Upper Sco, as determined from the two-point correlation function (i.e., the mean surface density of neighbors). The corresponding power-law fits allow us to determine the fractal dimensions of each association's spatial distribution, measure the stellar velocity dispersions, and distinguish between the bound binary population and chance alignments of members. We find that the fractal dimension of Taurus is D ~ 1.05, consistent with its filamentary structure. The fractal dimension of Upper Sco may be even shallower (D ~ 0.7), but this fit is uncertain due to the limited area and possible spatially variable incompleteness. We also find that random stellar motions have erased all primordial structure on scales of lsim0.07° in Taurus and lsim1.7° in Upper Sco; given ages of ~1 and ~5 Myr, the corresponding internal velocity dispersions are ~0.2 and ~1.0 km s^-1, respectively. Finally, we find that binaries can be distinguished from chance alignments at separations of lsim120'' (17,000 AU) in Taurus and lsim75'' (11,000 AU) in Upper Sco. The binary populations in these associations that we previously studied, spanning separations of 3''-30'', is dominated by binary systems. However, the few lowest mass pairs (M_prim <~ 0.3 M_⊙) might be chance alignments.