How Does Hydrostatic Equilibrium Apply to a Polytropic Star?

[Void123]

Homework Statement

I am working on a problem in which I need to calculate the hydrostatic equilibrium for a spherically symmetric star described by a polytropic equation of state.

There are two boundary conditions.

Homework Equations

All I know is gravity and pressure are going to be equal. This subject is [academically] new to me, so I don't really know where to start. Are there any other variables I need to consider? How would the lane-emden equation relate to this?

The Attempt at a Solution

 

[pellman]

Wikipedia has the equation of state http://en.wikipedia.org/wiki/Lane–Emden_equation

This topic is new to me. But it seems you have to choose a polytropic specific index n. Solutions are for a few such indeces are given in the article.

Pressure and gravity are only necessarily equal at the surface. For instance, consider that at the center gravity will be zero but the pressure will definitely be non-zero.

That's all I can add. Good hunting.