N=3 polytropic index questions

[the riddick25]

Homework Statement

From a previous problem, we have found that the pressure inside the sun can be represented by a polytrope with index n=3.
Does this mean that the sun contains relativistic degenerate matter, which is also described by a polytrope with index 3?
Explain how a polytrope with index 3 can represent both cases

Homework Equations

None

The Attempt at a Solution

I answered the first bit, as I know that the sun does not contain relativistic degenerate matter, as it can be modeled as an ideal gas.
But I have no idea how to answer the second part, as I have no idea why they can be modeled by the same polytrope.
I am also unable to find anything on the internet, but maybe I'm looking in the wrong places.

If anyone could point me in the right direction it would be incredibly helpful

Thanks

 

[mark726]

for your question! Polytopic equations of state, like the one with index n=3, are used to describe the relationship between pressure and density in a system. In the case of the sun, the polytropic index n=3 is used to model the relationship between pressure and density in the interior of the sun. This is because the sun is primarily made up of ionized gas, which can be modeled as an ideal gas. In an ideal gas, the relationship between pressure and density is described by the polytropic index n=3.

On the other hand, relativistic degenerate matter is made up of particles that move at relativistic speeds and are subject to the laws of quantum mechanics. This type of matter is found in objects such as white dwarfs and neutron stars. In these objects, the pressure is dominated by the quantum mechanical effects of the particles, rather than the thermal motion of the particles as in an ideal gas.

Despite the differences in the physical properties of these two types of matter, they can both be described by the same polytropic index n=3. This is because the polytropic index describes the overall relationship between pressure and density in a system, rather than the specific mechanisms that contribute to that pressure. In the case of the sun, the pressure is primarily due to thermal motion of particles, while in the case of relativistic degenerate matter, it is due to quantum mechanical effects. However, the overall relationship between pressure and density can still be described by the same index.

In summary, a polytrope with index n=3 can represent both the pressure inside the sun and relativistic degenerate matter because it describes the overall relationship between pressure and density in a system, rather than the specific mechanisms that contribute to that pressure.