How to Solve Tolman-Oppenheimer-Volkov Equations for Neutron Stars?

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Discussion Overview

The discussion centers around the challenges of solving the Tolman-Oppenheimer-Volkov equations specifically for neutron stars, with participants exploring references, equations of state (EoS), and modeling approaches. The scope includes theoretical and applied aspects of astrophysics related to stellar structures.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks references for solving the Tolman-Oppenheimer-Volkov equations, expressing difficulty in finding appropriate materials that are neither too elementary nor overly complex.
  • Another participant suggests a specific book, "Black Holes, White Dwarfs, and Neutron Stars" by Shapiro and Teukolsky, as a potential resource.
  • A participant mentions logistical issues with acquiring books in South Africa, indicating a preference for avoiding purchases at this time.
  • A different participant shares their intention to first model a white dwarf and raises questions about the initial pressure to use, the assumption of uniform density, and the relationship between the EoS (polytrope) and central pressure based on density.

Areas of Agreement / Disagreement

Participants do not appear to reach consensus on specific references or methods for modeling, and multiple viewpoints regarding the EoS and assumptions for white dwarfs are presented.

Contextual Notes

Participants express uncertainty regarding the appropriate starting pressure for modeling white dwarfs and the implications of assuming uniform density. There is also a lack of clarity on how the EoS relates to central pressure calculations.

Who May Find This Useful

This discussion may be useful for students and researchers interested in astrophysics, particularly those focusing on neutron stars and white dwarfs, as well as those seeking resources for solving complex equations in stellar modeling.

Karliski
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Does anyone know of a good reference regarding solving the Tolman-Oppenheimer-Volkov equations for neutron stars? Most things I find are either too elementary and others skip multiple steps. I think the EoS to use should be that of a Fermi gas model, but I am not sure.
 
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Have you tried Black Holes, White Dwarfs, and Neutron Stars, by Shapiro and Teukolsky?
 
Hey, not yet. I am trying to avoid buying a book at the moment because getting them to South Africa is a bit expensive.
 
I decided to 1st try and model a white dwarf. My problem is that I can't find a good starting pressure to use. Also, can I assume uniform density for a white dwarf? Does the EoS (polytrope) give me central pressure when a value of rho is inserted into it?

Thanks,
Karl
 

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