  Slowly rotating magnetic massive stars develop "dynamical magnetospheres"
(DM's), characterized by trapping of stellar wind outflow in closed magnetic
loops, shock heating from collision of the upflow from opposite loop
footpoints, and subsequent gravitational infall of radiatively cooled material.
In 2D and 3D magnetohydrodynamic (MHD) simulations the interplay among these
three components is spatially complex and temporally variable, making it
difficult to derive observational signatures and discern their overall scaling
trends.Within a simplified, steady-state analysis based on overall conservation
principles, we present here an "analytic dynamical magnetosphere" (ADM) model
that provides explicit formulae for density, temperature and flow speed in each
of these three components -- wind outflow, hot post-shock gas, and cooled
inflow -- as a function of colatitude and radius within the closed (presumed
dipole) field lines of the magnetosphere. We compare these scalings with
time-averaged results from MHD simulations, and provide initial examples of
application of this ADM model for deriving two key observational diagnostics,
namely hydrogen H-alpha emission line profiles from the cooled infall, and
X-ray emission from the hot post-shock gas. We conclude with a discussion of
key issues and advantages in applying this ADM formalism toward derivation of a
broader set of observational diagnostics and scaling trends for massive stars
with such dynamical magnetospheres.
