The star cluster mass--galactocentric radius relation: Implications for
  cluster formation
  Whether or not the initial star cluster mass function is established through
a universal, galactocentric-distance-independent stochastic process, on the
scales of individual galaxies, remains an unsolved problem. This debate has
recently gained new impetus through the publication of a study that concluded
that the maximum cluster mass in a given population is not solely determined by
size-of-sample effects. Here, we revisit the evidence in favor and against
stochastic cluster formation by examining the young ($\lesssim$ a few $\times
10^8$ yr-old) star cluster mass--galactocentric radius relation in M33, M51,
M83, and the Large Magellanic Cloud. To eliminate size-of-sample effects, we
first adopt radial bin sizes containing constant numbers of clusters, which we
use to quantify the radial distribution of the first- to fifth-ranked most
massive clusters using ordinary least-squares fitting. We supplement this
analysis with an application of quantile regression, a binless approach to
rank-based regression taking an absolute-value-distance penalty. Both methods
yield, within the $1\sigma$ to $3\sigma$ uncertainties, near-zero slopes in the
diagnostic plane, largely irrespective of the maximum age or minimum mass
imposed on our sample selection, or of the radial bin size adopted. We conclude
that, at least in our four well-studied sample galaxies, star cluster formation
does not necessarily require an environment-dependent cluster formation
scenario, which thus supports the notion of stochastic star cluster formation
as the dominant star cluster-formation process within a given galaxy.
