The structure of young star clusters

In this paper we analyse and compare the clustering of young stars in Chamaeleon I and Taurus. We compute the mean surface density of companion stars N as a function of angular displacement theta from each star. We then fit N theta) with two simultaneous power laws, i.e. N(theta) ~ K_bintheta^-beta_bin + K_clutheta^-beta_clu. For Chamaeleon I, we obtain beta_bin= 1.97 +/- and beta_clu= 0.28 +/- 0.06, with the elbow at theta_elb~ 0 011 +/- 0 004. For Taurus, we obtain beta_bin= 2.02 +/- 0.04 and beta _clu= 0.87 +/- 0.01, with the elbow at theta _elb~ 0 013 +/- 0 003. For both star clusters the observational data make large (~ 5 sigma) systematic excursions from the best-fitting curve in the binary regime (theta < theta_elb). These excursions are visible also in the data used by Larson and Simon, and may be attributable to evolutionary effects of the types discussed recently by Nakajima et al. and Bate et al. In the clustering regime (theta > theta_elb) the data conform to the best-fitting curve very well, but the beta_clu values we obtain differ significantly from those obtained by other workers. These differences are due partly to the use of different samples, and partly to different methods of analysis. We also calculate the box dimensions for the two star clusters: for Chamaeleon I we obtain D_box~=1.51+/-0.12, and for Taurus D_box~=1.39+/-0.01. However, the limited dynamic range makes these estimates simply descriptors of the large-scale clustering, and not admissible evidence for fractality. We propose two algorithms for objectively generating maps of constant stellar surface density in young star clusters. Such maps are useful for comparison with molecular-line and dust-continuum maps of star-forming clouds, and with the results of numerical simulations of star formation. They are also useful because they retain information that is suppressed in the evaluation of N(theta). Algorithm I (SCATTER) uses a universal smoothing length, and therefore has a restricted dynamic range, but it is implicitly normalized. Algorithm II (GATHER) uses a local smoothing length, which gives it much greater dynamic range, but it has to be normalized explicitly. Both algorithms appear to capture well the features that the human eye sees. We are exploring ways of analysing such maps to discriminate between fractal structure and single-level clustering, and to determine the degree of central condensation in small-N clusters.