How Does Hydrostatic Equilibrium Apply to a Polytropic Star?

In summary, the conversation is about calculating the hydrostatic equilibrium for a spherically symmetric star using a polytropic equation of state. The main concern is determining the appropriate variables and considering the Lane-Emden equation. The Wikipedia article on the Lane-Emden equation provides information on choosing a polytropic specific index, and solutions for different indices are given. The discussion also notes that pressure and gravity are only equal at the surface, and this may not be the case at the center of the star.
  • #1
Void123
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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

 
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  • #2
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.
 

FAQ: How Does Hydrostatic Equilibrium Apply to a Polytropic Star?

What is hydrostatic equilibrium?

Hydrostatic equilibrium is a state in which the forces due to gravity and pressure are balanced, resulting in a stable system. In the context of fluid dynamics, it refers to a fluid that is at rest or moving at a constant velocity.

How does hydrostatic equilibrium occur?

Hydrostatic equilibrium occurs when the downward force of gravity on a fluid is balanced by the upward force of pressure. This can happen in various systems, such as in the Earth's atmosphere, oceans, and even within stars.

What are the factors that affect hydrostatic equilibrium?

The primary factors that affect hydrostatic equilibrium are the density and pressure of the fluid, as well as the strength of the gravitational force. Changes in any of these factors can disrupt the balance and lead to a non-equilibrium state.

Why is hydrostatic equilibrium important in astronomy?

Hydrostatic equilibrium plays a crucial role in understanding the structure and behavior of celestial bodies, such as stars and planets. It helps explain how these objects maintain their shape and how they evolve over time.

How is hydrostatic equilibrium related to buoyancy?

Buoyancy is a result of hydrostatic equilibrium. When an object is submerged in a fluid, it experiences an upward force equal to the weight of the fluid it displaces. This force, known as buoyancy, helps objects float and maintain their position in a fluid.

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