Intracluster planetary nebulae in the Virgo Cluster. III. Luminosity of the intracluster light and tests of the spatial distribution

Intracluster planetary nebulae are a useful tracer of the evolution of galaxies and galaxy clusters. We analyze our catalog of 318 intracluster planetary nebulae candidates found in 0.89 deg(-2) of the Virgo Cluster. We give additional evidence for the great depth of the Virgo Cluster's intracluster stellar population, which implies that the bulk of the intracluster stars come from late-type galaxies and dwarfs. We also provide evidence that the intracluster stars are clustered on the sky on arcminute scales, in agreement with tidal-stripping scenarios of intracluster star production. Although significant systematic uncertainties exist, we find that the average fraction of intracluster starlight in the Virgo Cluster is 15.8% +/- 3.0% (statistical) +/- 5.0% (systematic) and may be higher if the intracluster stars have a large spatial line-of-sight depth. We find that the intracluster star density changes little with radius or projected density over the range surveyed. These results, along with other intracluster star observations, imply that intracluster star production in Virgo is ongoing and consistent with the cluster's known dynamical youth.