Chandrasekhar Mass and the Relativistic Star: Finding the Value of K for n=3

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Discussion Overview

The discussion revolves around the determination of the constant K for a relativistic star with a polytropic index of n=3, as derived from the mass-radius relation. Participants seek clarification on the symbols used and the connection between pressure and density in this context.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents a mass-radius relation for a relativistic star and requests information on the value of K for n=3.
  • Another participant asks for clarification on the symbols used, specifically questioning the meanings of n, k, K, and M3.
  • A participant confirms that n is the polytropic index, k is the constant relating pressure and density, and M3 refers to the mass of the star.
  • Concerns are raised about the consistency of notation, particularly the distinction between k and K, and the non-standard use of M3.
  • One participant suggests that the original poster refer to Wikipedia for insights on the origin of K.
  • A later reply indicates that a simple algebraic manipulation could relate the participant's K to the notation used in Wikipedia.

Areas of Agreement / Disagreement

There is no consensus on the value of K or its derivation, and participants express differing views on the clarity of notation and definitions.

Contextual Notes

Participants note the need for consistent notation and the potential for confusion arising from non-standard symbols. The discussion does not resolve the specific value of K or its derivation.

Apashanka das
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From the mass radius relation I have gone through mass of a relativistic star ( polytrophic index 3) which is
4piM3(K/piG)3/2
can anyone please suggest me any information of where the value of k is determined for relativistic star( for n=3) via any link
Where k is constt
 
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Apashanka das said:
From the mass radius relation I have gone through mass of a relativistic star ( polytrophic index 3) which is
4piM3(K/piG)3/2
can anyone please suggest me any information of where the value of k is determined for relativistic star( for n=3) via any link
Where k is constt
Please clarify your symbols. What is n -- is it the polytropic index? What is k -- is it the same as K? M3 must be a mass -- but the mass of what? (What does the subscript 3 signify?)
 
JMz said:
Please clarify your symbols. What is n -- is it the polytropic index? What is k -- is it the same as K? M3 must be a mass -- but the mass of what? (What does the subscript 3 signify?)
yes all the standard notations
n is polytrophic index
k is the constt connecting pressure and density
M3 is the mass of a star for p
JMz said:
Please clarify your symbols. What is n -- is it the polytropic index? What is k -- is it the same as K? M3 must be a mass -- but the mass of what? (What does the subscript 3 signify?)
yes standard notations from the book dina prialnik
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You must be more consistent in your notation: k and K are two different symbols. Also, M3 is not a standard symbol in physics, it is apparently one that this specific author chose.

To answer your question: I suggest you start with WP: https://en.wikipedia.org/wiki/Chandrasekhar_limit, which should enable you to determine the origin of the author's K.
 
JMz said:
You must be more consistent in your notation: k and K are two different symbols. Also, M3 is not a standard symbol in physics, it is apparently one that this specific author chose.

To answer your question: I suggest you start with WP: https://en.wikipedia.org/wiki/Chandrasekhar_limit, which should enable you to determine the origin of the author's K.
actually K is the connection coefficient between pressure and density
Hence I am looking for the K for polytrophic index 3 ,that's only I want where
P=Kρ(n+1)/n
where n is the polytrophic index
P is the pressure
And ρ is the density of the star
 
I believe requires only a little algebra to relate your K to Wikipedia's notation.
 

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