A Density Dependence for Protostellar Luminosity in Class I Sources:
  Collaborative Accretion
  Class I protostars in three high-mass star-forming regions are found to have
correlations among the local projected density of other Class I protostars, the
summed flux from these other protostars, and the protostellar luminosity in the
WISE 22 micron band. Brighter Class I sources form in higher-density and
higher-flux regions, while low luminosity sources form anywhere. These
correlations depend slightly on the number of neighbors considered (from 2 to
20) and could include a size-of-sample effect from the initial mass function
(i.e., larger numbers include rarer and more massive stars). Luminosities seem
to vary by neighborhood with nearby protostars having values proportional to
each other and higher density regions having higher values. If Class I
luminosity is partially related to the accretion rate, then this luminosity
correlation is consistent with the competitive accretion model, although it is
more collaborative than competitive. The correlation is also consistent with
primordial mass segregation, and could explain why the stellar initial mass
function resembles the dense core mass function even when cores form multiple
stars.
