Chandrashekhar limit for relativistic fermion gas

[cooper607]

hi fellas, I have been working on Chandrashekhar limit, and I found a mass-radius relationship for the nonrelativistic fermi gases using this formula and i got the graph of this

R=((18pi)^(2/3))/10 *H^2/(GmM^(1/3) ) (0.5/n)^(5/3)

where H=(6.63*10^-34)/2pi
G=6.67*10^-11
m=9.11*10^-31
n=1.67*10^-27
M is the independent variable

but what changes should I make if i want to plot a mass-radius relationship for relativistic fermi gases? actually can you suggest me a reading for differentiating between relativistic and non relativistic fermi gases?
thanks

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[Chronos]

Asking the same question in multiple threads is frowned upon. re: https://www.physicsforums.com/showthread.php?t=761641

 

[cooper607]

all i found out is the relation of radius vs mass for non relativistic gas, but is there any equation of R for non relativistic one where the radius goes to zero as mass goes to 1.44 ?

 

[pmacias]

for your question and for sharing your research on the Chandrashekhar limit for relativistic fermion gas. It is great to see that you are exploring this important concept in astrophysics.

To answer your question, there are a few changes that need to be made in order to plot a mass-radius relationship for relativistic fermi gases. First, the formula you have provided is for nonrelativistic fermi gases, so it will not accurately represent the behavior of relativistic fermi gases. Instead, you will need to use the relativistic fermi gas equation, which takes into account the effects of special relativity on the particles.

The relativistic fermi gas equation is given by:

R = (18π^2 / 10) * (ħc)^2 / (GmM)^(1/3) * (1/ξ)^(4/3)

where ħ is the reduced Planck's constant, c is the speed of light, and ξ is a dimensionless constant that depends on the particular type of fermions in the gas.

As you can see, the main difference between the two equations is the inclusion of the relativistic factor (1/ξ)^(4/3) in the relativistic fermi gas equation. This factor accounts for the relativistic effects on the fermions, which become more significant at higher energies.

In order to plot a mass-radius relationship for relativistic fermi gases, you will need to use this equation and vary the value of ξ to see how it affects the curve. Different types of fermions will have different values of ξ, so this will give you a better understanding of the behavior of different types of relativistic fermi gases.

As for resources to learn more about the difference between relativistic and nonrelativistic fermi gases, I would recommend looking into textbooks or articles on astrophysics and particle physics. You can also consult with experts in the field or attend conferences and seminars on the topic. Good luck with your research!