  Weak-temperature-gradient influences from the tropics and quasigeostrophic
influences from the extratropics plausibly constrain the subtropical-mean
static stability in terrestrial atmospheres. Because mean descent acting on
this static stability is a leading-order term in the thermodynamic balance, a
state-invariant static stability would impose constraints on the Hadley cells,
which this paper explores in simulations of varying planetary rotation rate. If
downdraft-averaged effective heating (the sum of diabatic heating and eddy heat
flux convergence) too is invariant, so must be vertical velocity -- an "omega
governor." In that case, the Hadley circulation overturning strength and
downdraft width must scale identically -- the cell can strengthen only by
widening or weaken only by narrowing. Simulations in two idealized, dry GCMs
with a wide range of planetary rotation rates exhibit nearly unchanging
downdraft-averaged static stability, effective heating, and vertical velocity,
as well as nearly identical scalings of the Hadley cell downdraft width and
strength. In one, eddy stresses set this scaling directly (the Rossby number
remains small); in the other, eddy stress and bulk Rossby number changes
compensate to yield the same, ({\sim}\Omega^{-1/3}) scaling. The consistency of
this power law for cell width and strength variations may indicate a common
driver, and we speculate that Ekman pumping could be the mechanism responsible
for this behavior. Extending to moist atmospheres, in an idealized aquaplanet
GCM the subtropical static stability is also insensitive to rotation rate but
the effective heating and vertical velocity are not.
