# Chandrasekhar limit equation/white dwarf mass-radius relation

1. Sep 4, 2011

### Monkey Face

Hey there,

I have a couple of questions that may seem a little stupid, but anyway:

I've been a bit of research into the Chandrasekhar limit and have unsuccessfully tried to find an equation/estimation that sums it up as I have seen so many floating around on the internet. Variations from the one found on wikipedia ( http://en.wikipedia.org/wiki/Chandrasekhar_limit ) seem to be used a lot but I know wiki isn't exactly the most reliable of sources. If anyone could clarify this for me, that would be great :)

I've been recommended this as a reasonably good source (by my teacher at school) but I've a problem with the equation on that page specifically; the mass-radius relationship for a white dwarf is, as I understand it, such that the more massive it is, the smaller it is. Rearranging that equation for the radius seems to show that the radius is proportional to the mass (as opposed to inversely).

Any help would be great, thanks in advance! :)

2. Sep 4, 2011

### yenchin

Which equation did you start from? Perhaps you would like to show us your working?

3. Sep 4, 2011

### Monkey Face

I literally used what they gave on that link I put above.

4. Sep 4, 2011

### yenchin

Yes. But *which* equation? There are a few of them. And the page explicitly says that "Equating these two relationships shows that the radius is proportional to M^(-1/3)". The reason I asked is that if you don't show us your working then it is hard for anyone here to point out what could have gone wrong. The wikipedia page looks fine by the way.

5. Sep 5, 2011

### Orion1

The best white dwarf mass-radius relation that I have numerically integrated is:
$$R_{\ast} = \frac{(9 \pi)^{2/3} \hbar^2}{8 G m_e m_p^{5/3} M_{\ast}^{1/3}} \; \; \; \; \; \; \mu_e = 2$$

The white dwarf mass-radius relation equation solution that I derived is:
$$\boxed{R_{\ast} = \left( \frac{3}{2} \right)^{4/3} \frac{\pi^{2/3} \hbar^2}{G m_e (\mu_e m_p)^{5/3} M_{\ast}^{1/3}}}$$

Reference:
http://farside.ph.utexas.edu/teaching/sm1/lectures/node87.html" [Broken]

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Last edited by a moderator: May 5, 2017