Topological charge and cooling scales in pure SU(2) lattice gauge theory

Using Monte Carlo simulations with overrelaxation, we have equilibrated lattices up to $\beta=2.928$, size $60^4$, for pure SU(2) lattice gauge theory with the Wilson action. We calculate topological charges with the standard cooling method and find that they become more reliable with increasing $\beta$ values and lattice sizes. Continuum limit estimates of the topological susceptibility $\chi$ are obtained of which we favor $\chi^{1/4}/T_c=0.643\,(12)$, where $T_c$ is the SU(2) deconfinement temperature. Differences between cooling length scales in different topological sectors turn out to be too small to be detectable within our statistical errors.