Stochastically lighting up galaxies: Statistical implications of stellar clustering

Stars form discretely. At the very least, they form in units of individual stars. However, their discreteness likely extends to much larger spatially and temporally correlated structures known as star clusters. This discreteness has a profound impact on the light that a population of stars will produce even at fixed star formation rate. Ignoring the effects of this clustering when analyzing observations can lead to significant errors and biases.;This work presents an exploration of the effects of this clustering, the foundation of which is the construction of SLUG, a code which Stochastically Lights Up Galaxies. It accounts for the effects of clustering by populating composite stellar populations ("galaxies") one cluster at a time where each cluster is filled by individual stars whose evolution is tracked. This is the first code capable of exploring stochasticity for stellar populations composed of clusters and led to several significant insights in the field. Most notably, the scatter of luminosities due to stochastically placing clusters over the star formation history of a population greatly exceeds the effects of stochastically sampling a population with a stellar initial mass function. This has profound implications for interpretations of star formation rates, deriving initial mass functions, and the star formation rate distribution of the universe.;We also explore the statistics of luminosities of clusters themselves, deriving an analytical method (CLOC) for calculating the full distribution of cluster order statistics roughly one billion times faster than a suite of Monte Carlo simulations. This giant leap forward in speed provides the groundwork for a previously impossible robust exploration of the relevant parameter space (e.g. dust opacity distributions, cluster mass function shape and cutoffs, and cluster disruption parameters).