We analyze the spatial distributions 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 \sim 1.05 , consistent with its filamentary structure .
The fractal dimension of Upper Sco may be even shallower ( D \sim 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 \lesssim 0.07 ^ { o } in Taurus and \lesssim 1.7 ^ { o } in Upper Sco ; given ages of \sim 1 Myr and \sim 5 Myr , the corresponding internal velocity dispersions are \sim 0.2 km s ^ { -1 } and \sim 1.0 km s ^ { -1 } , respectively .
Finally , we find that binaries can be distinguished from chance alignments at separations of \lesssim 120″ ( 17000 AU ) in Taurus and \lesssim 75″ ( 11000 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 } \lesssim 0.3 M _ { \sun } ) might be chance alignments .