Cluster formation in molecular clouds: I. stellar populations, star
  formation rates, and ionizing radiation
  We present a model for the radiative output of star clusters in the process
of star formation suitable for use in hydrodynamical simulations of radiative
feedback. Gas in a clump, defined as a region whose density exceeds 10^4 cm^-3,
is converted to stars via the random sampling of the Chabrier IMF. A star
formation efficiency controls the rate of star formation. We have completed a
suite of simulations which follow the evolution of accretion-fed clumps with
initial masses ranging from 0 to 10^5 M_sol and accretion rates ranging from
10^-5 to 10^-1 M_sol yr^-1. The stellar content is tracked over time which
allows the aggregate luminosity, ionizing photon rate, number of stars, and
star formation rate (SFR) to be determined. For a fiducial clump of 10^4 M_sol,
the luminosity is ~4x10^6 L_sol with a SFR of roughly 3x10^-3 M_sol yr^-1. We
identify two regimes in our model. The accretion-dominated regime obtains the
majority of its gas through accretion and is characterized by an increasing SFR
while the reservoir-dominated regime has the majority of its mass present in
the initial clump with a decreasing SFR. We show that our model can reproduce
the expected number of O stars, which dominate the radiative output of the
cluster. We find a nearly linear relationship between SFR and mass as seen in
observations. We conclude that our model is an accurate and straightforward way
to represent the output of clusters in hydrodynamical simulations with
radiative feedback.
