Symmetric and antisymmetric components of polar-amplified warming

CO$_2$-forced surface warming in general circulation models (GCMs) is initially polar-amplified in the Arctic but not Antarctic -- a largely hemispherically antisymmetric signal. Nevertheless, we show in CESM1 and eleven LongRunMIP GCMs that the hemispherically symmetric component of global-mean-normalized, zonal-mean warming ($T^*_\mathrm{sym}$) under 4$\times$CO$_2$ changes weakly or becomes moderately more polar-amplified from the first decade to near-equilibrium. Conversely, the antisymmetric warming component ($T^*_\mathrm{asym}$) weakens with time in all models, moderately in some including FAMOUS but effectively vanishing in others including CESM1. We explore mechanisms underlying the robust $T^*_\mathrm{sym}$ behavior with a diffusive moist energy balance model (MEBM), which given radiative feedback parameter ($\lambda$) and ocean heat uptake ($\mathcal{O}$) fields diagnosed from CESM1 adequately reproduces the CESM1 $T^*_\mathrm{sym}$ and $T^*_\mathrm{asym}$ fields. In further MEBM simulations perturbing $\lambda$ and $\mathcal{O}$, $T^*_\mathrm{sym}$ is sensitive to their symmetric components only, and more to that of $\lambda$. A three-box, two-timescale model fitted to FAMOUS and CESM1 reveals a curiously short Antarctic fast-response timescale in FAMOUS. In additional CESM1 simulations spanning a broader range of forcings, $T^*_\mathrm{sym}$ changes modestly across 2-16$\times$CO$_2$, and $T^*_\mathrm{sym}$ in a Pliocene-like simulation is more polar-amplified but likewise approximately time-invariant. Determining the real-world relevance of these behaviors -- which imply that a surprising amount of information about near-equilibrium polar amplification emerges within decades -- merits further study.