  We study the sub-Keplerian rotation and dust content of the circumstellar
material around the asymptotic giant branch (AGB) star L$_2$ Puppis. We find
that the thermal pressure gradient alone cannot explain the observed rotation
profile. We find that there is a family of possible dust populations for which
radiation pressure can drive the observed sub-Keplerian rotation. This set of
solutions is further constrained by the spectral energy distribution (SED) of
the system, and we find that a dust-to-gas mass ratio of $\sim10^{-3}$ and a
maximum grain size that decreases radially outwards can satisfy both the
rotation curve and SED. These dust populations are dynamically tightly coupled
to the gas azimuthally. However grains larger than $\sim0.5\mu$m are driven
outward radially by radiation pressure at velocities $\sim5$kms$^{-1}$, which
implies a dust replenishment rate of $\sim3\times10^{-9}$M$_\odot$yr$^{-1}$.
This replenishment rate is consistent with observational estimates to within
uncertainties. Coupling between the radial motion of the dust and gas is weak
and hence the gas does not share in this rapid outward motion. Overall we
conclude that radiation pressure is a capable and necessary mechanism to
explain the observed rotation profile of L$_2$ Pup, and offers other additional
constraints on the dust properties.

Solar and Stellar Astrophysics