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We present a detailed analysis of the surface brightness distribution of thebrightest cluster galaxy (BCG) in each of 24 galaxy clusters at 0.03<z<0.13. Weuse two-dimensional profile fitting to model the surface brightness out tor=300 kpc for each BCG, comparing r^{1/4}, r^{1/n}, and double r^{1/4} models.We obtain statistically superior fits using a two component model consisting ofa pair of r^{1/4} profiles with independent scale lengths, ellipticities, andorientations. The two component model can simply reproduce the observedposition angle and ellipticity gradients, which cannot generally be explainedpurely by triaxiality. The inner component of our two component model hasproperties similar to a typical massive elliptical galaxy and is clearlyassociated with the BCG. The outer component is 10-40 times larger in scale,has ~10 times the total luminosity of the inner component, and exhibits asteeper <\mu>-r_e relation than that of the elliptical fundamental plane. Weinterpret this outer component as a population of intracluster stars tracingthe cluster potential. The two components are strongly aligned(|\Delta\theta|<10\degr) in roughly 40% of the clusters. When they are notaligned, the components tend toward high degrees of misalignment, suggestingthat accretion of infalling material may change the orientation of some BCGsfor a time. The extent of the outer component and its similar elongation topublished cluster galaxy distributions indicates that the evolution of theintracluster light is tied to the cluster as a whole rather than to the BCG.Comment: 22 pages, 13 figures (1 color), accepted to ApJ; replaces submitted  versio

Intracluster Light in Nearby Galaxy Clusters: Relationship to the Halos of Brightest Cluster Galaxies