Astrophysics: Lane-Emden equation, polytropes, low mass red giants

In summary, the problem is asking to calculate the radius of a core of a low mass red giant, assuming it can be described by a polytrope and using the mass-radius relationship. The mass of the core is given as 0.5 times the mass of the sun and the core is said to have completely degenerate free electrons. The Lane-Emden equation and the index, n, are mentioned, but the value of n for the core of a low mass red giant is not clear. Assistance in finding the correct value is requested.
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Homework Statement


The problem reads:
In the core a low mass red giant the free electrons are completely degenerate. Suppose that the mass of the core is 0.5 * M_sun (Mass of the sun). Assume that the core can be described by a polytrope and calculate its radius using the mass-radius relationship.


Homework Equations





The Attempt at a Solution


So I'm aware of the mass-radius relation found from the Lane-Emden equation, but I am not sure what value for index, n, I should use for the core of a low mass red giant--specifically one that has free electrons that are completely degenerate.
 
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I have tried looking for n values in various resources, but I'm somewhat confused as to why I can't seem to find a definitive value. Any help would be greatly appreciated!
 

Related to Astrophysics: Lane-Emden equation, polytropes, low mass red giants

1. What is the Lane-Emden equation and how is it used in astrophysics?

The Lane-Emden equation is a differential equation that describes the structure and behavior of a self-gravitating, spherically symmetric system. It is commonly used in astrophysics to model the internal structure of stars and other celestial bodies.

2. What are polytropes and how do they relate to the Lane-Emden equation?

Polytropes are mathematical models that approximate the structure of a star or other self-gravitating object using the Lane-Emden equation. They are useful for understanding the behavior of low mass red giants and other types of stars.

3. Can the Lane-Emden equation be applied to all types of stars?

No, the Lane-Emden equation is only applicable to stars with a polytropic index of 1.5 or lower. This includes low mass red giants, but not other types of stars such as main sequence stars or white dwarfs.

4. What is the significance of low mass red giants in astrophysics?

Low mass red giants are important objects to study in astrophysics because they represent an intermediate stage in the life cycle of a star. They are also useful for understanding the evolution and behavior of other types of stars, as well as the formation and structure of galaxies.

5. How do the Lane-Emden equation and polytropes contribute to our understanding of the universe?

The Lane-Emden equation and polytropes provide valuable insights into the internal structure and behavior of stars and other self-gravitating objects. By studying these models, scientists can better understand the processes and phenomena that occur within the universe, helping to unlock the mysteries of the cosmos.

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