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 / v _ { disk } ^ { n } , with n = 0 , 1 , 2 and contrast these models with the successful Bower et al .
model ( B8W7 ) , for which \beta \propto 1 / v _ { disk } ^ { 3.2 } .
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 .
While models with high wind speed and mass loading result in a poor match to the observed SMF , a model with slower wind speed matches the flat portion of the SMF between M _ { \star } \sim 10 ^ { 9 } -10 ^ { 11 } h ^ { -1 } { M _ { \odot } } .
When combined with AGN feedback , the model provides a good description of the observed SMF above 10 ^ { 9 } h ^ { -1 } { M _ { \odot } } .
In order to explore the impact of different feedback schemes further , we examine how the expulsion models compare with a further range of observational data , contrasting the results with the B8W7 model .
In the expulsion models , the brightest galaxies are assembled more recently , and the specific star formation rates of galaxies decrease strongly with decreasing stellar mass .
The expulsion models tend to have a cosmic star formation density that is dominated by lower mass galaxies at z = 1 - 3 , and dominated by 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 .