  The observed stellar mass function (SMF) is very different to the halo mass
function predicted by Lambda-CDM, and it is widely accepted that this is due to
energy feedback from supernovae and black holes. However, the strength and form
of this feedback is not understood. In this paper, we use the phenomenological
model GALFORM to explore how galaxy formation depends on the strength and halo
mass dependence of feedback. We focus on 'expulsion' models in which the wind
mass loading, beta, is proportional to 1/\vdisk^n, with n=0,1,2 and contrast
these models with the successful Bower et al.\ 2008 model (B8W7). A crucial
development is that our code explicitly accounts for the recapture of expelled
gas as the system's halo mass (and thus gravitational potential) increases. We
find that a model with modest wind speed but high mass loading matches the flat
portion of the SMF. When combined with AGN feedback, the model provides a good
description of the observed SMF above 10^9 h^-1 Msol. However, in the expulsion
models, the brightest galaxies are assembled more recently than in B8W7, and
the specific star formation rates of galaxies decrease strongly with decreasing
stellar mass. The expulsion models also tend to have a cosmic star formation
density that is dominated by lower mass galaxies at z=1-3, and dominated high
mass galaxies at low redshift. These trends are in conflict with observational
data, but the comparison highlights some deficiencies of the B8W7 model also.
The experiments in this paper give us important physical insight to the impact
of the feedback process on the formation histories of galaxies, but the strong
mass dependence of feedback adopted in B8W7 still appears to provide the most
promising description of the observed universe.
