ABSTRACT
In hydrostatics, the velocity of the fluid is zero. Meaningful models for atmospheres and stellar structure, in particular, can be devised assuming an approximately hydrostatic fluid. The hydrostatic plane-parallel atmosphere model involves a number of simplifying assumptions that will not be generally applicable. It assumes the atmosphere to be isothermal, plane-parallel, with negligible gravitational pull of its own and obeying a single equation of state (both on account of being isothermal and consisting of the same particles throughout). Isothermal and polytropic stellar structure models provide nice and insightful applications of hydrostatics. The chapter covers the isothermal case, including curvature and self-gravity. Afterwards, relaxing the assumption, the fluid is isothermal and allow for a polytropic fluid. The resulting expression, the Lane-Emden equation, is a famous cornerstone of stellar structure theory. Unlike numerical stellar structure models, hydrodynamics simulations tend to start from a single completely specified boundary and then evolve from there.
