The Correlation Dimension of Young Stars in Dwarf Galaxies

We present the correlation dimension of resolved young stars in four activelystar-forming dwarf galaxies that are sufficiently resolved and transparent tobe modeled as projections of three-dimensional point distributions. We use datain the Hubble Space Telescope archive; photometry for one of them, UGCA 292, ispresented here for the first time. We find that there are statisticallydistinguishable differences in the nature of stellar clustering among thesample galaxies. The young stars of VII Zw 403, the brightest galaxy in thesample, have the highest value for the correlation dimension and also the mostdramatic decrease with logarithmic scale, falling from $1.68\pm0.14$ to$0.10\pm0.05$ over less than a factor of ten in $r$. This decrease isconsistent with the edge effect produced by a projected Poisson distributionwithin a 2:2:1 ellipsoid. The young stars in UGC 4483, the faintest galaxy inthe sample, exhibit very different behavior, with a constant value of about 0.5over this same range in $r$, extending nearly to the edge of the distribution.This behavior may indicate either a scale-free distribution with an unusuallylow correlation dimension, or a two-component (not scale-free) combination ofcluster and field stars.Comment: 25 pages, 10 figures, accepted by A