The Parameter Space of Galaxy Formation
  Semi-analytic models are a powerful tool for studying the formation of
galaxies. However, these models inevitably involve a significant number of
poorly constrained parameters that must be adjusted to provide an acceptable
match to the observed universe. In this paper, we set out to quantify the
degree to which observational data-sets can constrain the model parameters. By
revealing degeneracies in the parameter space we can hope to better understand
the key physical processes probed by the data. We use novel mathematical
techniques to explore the parameter space of the GALFORM semi-analytic model.
We base our investigation on the Bower et al. 2006 version of GALFORM, adopting
the same methodology of selecting model parameters based on an acceptable match
to the local bJ and K luminosity functions. The model contains 16 parameters
that are poorly constrained, and we investigate this parameter space using the
Model Emulator technique, constructing a Bayesian approximation to the GALFORM
model that can be rapidly evaluated at any point in parameter space. By
combining successive waves of emulation, we show that only 0.26% of the initial
volume is of interest for further exploration. However, within this region we
show that the Bower et al. 2006 model is only one choice from an extended
sub-space of model parameters that can provide equally acceptable fits. We
explore the geometry of this region and begin to explore the physical
connections between parameters that are exposed by this analysis. We also
consider the impact of adding additional observational data to further
constrain the parameter space.
