We consider the relevance of known constraints from each of Hide's theorem,
the angular momentum conserving (AMC) model, and the equal-area model on the
extent of cross-equatorial Hadley cells. These theories respectively posit that
a Hadley circulation must span: all latitudes where the radiative convective
equilibrium (RCE) absolute angular momentum ($M_\mathrm{rce}$) satisfies
$M_\mathrm{rce}>\Omega a^2$ or $M_\mathrm{rce}<0$ or where the RCE absolute
vorticity ($\eta_\mathrm{rce}$) satisfies $f\eta_\mathrm{rce}<0$; all latitudes
where the RCE zonal wind exceeds the AMC zonal wind; and over a range such that
depth-averaged potential temperature is continuous and that energy is
conserved. The AMC model requires knowledge of the ascent latitude
$\varphi_\mathrm{a}$, which need not equal the RCE forcing maximum latitude
$\varphi_\mathrm{m}$. Whatever the value of $\varphi_\mathrm{a}$, we
demonstrate that an AMC cell must extend at least as far into the winter
hemisphere as the summer hemisphere. The equal-area model predicts
$\varphi_\mathrm{a}$, always placing it poleward of $\varphi_\mathrm{m}$. As
$\varphi_\mathrm{m}$ is moved poleward (at a given thermal Rossby number), the
equal-area predicted Hadley circulation becomes implausibly large, while both
$\varphi_\mathrm{m}$ and $\varphi_\mathrm{a}$ become increasingly displaced
poleward of the minimal cell extent based on Hide's theorem (i.e. of
supercritical forcing). In an idealized dry general circulation model,
cross-equatorial Hadley cells are generated, some spanning nearly pole-to-pole.
All homogenize angular momentum imperfectly, are roughly symmetric in extent
about the equator, and appear in extent controlled by the span of supercritical
forcing.Comment: 18 pages, 9 figures, publishe