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 ${\chi }^{1\mathrm{/}4}\mathrm{/}{T}_c=0.643(12)$, 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.