The abundance of massive dark matter halos hosting galaxy clusters provides an important test of the masses of relic neutrino species .
The dominant effect of neutrino mass is to lower the typical amplitude of density perturbations that eventually form halos , but for neutrino masses \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 0.4 eV the threshold for halo formation can be changed significantly as well .
We study the spherical collapse model for halo formation in cosmologies with neutrino masses in the range m _ { \nu i } = 0.05 eV - 1 eV and find that halo formation is differently sensitive to \Omega _ { \nu } and m _ { \nu } .
That is , different neutrino hierarchies with common \Omega _ { \nu } are in principle distinguishable .
The added sensitivity to m _ { \nu } is small but potentially important for scenarios with heavier sterile neutrinos .
Massive neutrinos cause the evolution of density perturbations to be scale-dependent at high redshift which complicates the usual mapping between the collapse threshold and halo abundance .
We propose one way of handling this and compute the correction to the halo mass function within this framework .
For \sum m _ { \nu i } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ < $ } } 0.3 eV , our prescription for the halo abundance is only \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } 15 \% different than the standard calculation .
However for larger neutrino masses the differences approach 50 - 100 \% which , if verified by simulations , could alter neutrino mass constraints from cluster abundance .