  Flavor SU(3) is used for studying the time-dependent CP asymmetry in $B^0 \to
\pi^0 K_S$ by relating this process to $B^0\to \pi^0\pi^0$ and $B^0 \to
K^+K^-$. We calculate correlated bounds on $S_{\pi K} - \sin 2\beta$ and
$C_{\pi K}$, with maximal magnitudes of 0.2 and 0.3, where $S_{\pi K}$ and
$C_{\pi K}$ are coefficients of $\sin\Delta mt$ and $\cos\Delta mt$ in the
asymmetry. Stronger upper limits on $B^0 \to K^+K^-$ are expected to reduce
these bounds and to imply nonzero lower limits on these observables. The
asymmetry is studied as a function of a strong phase and the weak phase
$\gamma$.
