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We study the effects of failure to equilibrate the squared topological charge$Q^2$ on lattice calculations of pseudoscalar masses and decay constants. Theanalysis is based on chiral perturbation theory calculations of the dependenceof these quantities on the QCD vacuum angle $\theta$. For the light-lightpartially quenched case, we rederive the known chiral perturbation theoryresults of Aoki and Fukaya, but using the nonperturbatively-valid chiral theoryworked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. Wethen extend these calculations to heavy-light mesons. Results when staggeredtaste-violations are important are also presented. The derived $Q^2$ dependenceis compared to that of simulations using the MILC collaboration's ensembles oflattices with four flavors of HISQ dynamical quarks. We find agreement, albeitwith large statistical errors. These results can be used to correct for theleading effects of unequilibrated $Q^2$, or to make estimates of the systematicerror coming from the failure to equilibrate $Q^2$. In an appendix, we showthat the partially quenched chiral theory may be extended beyond a lower boundon valence masses discovered by Sharpe and Shoresh. Subtleties occurring when asea-quark mass vanishes are discussed in another appendix.

Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants