# Chandrasekhar Limit: Explained

• quasar987
In summary, the Chandrasekhar limit is the maximum mass that a white dwarf star can have without collapsing into a neutron star or black hole. This limit was estimated using the assumptions of zero temperature, uniform mass density, and high momentum compared to mass. However, a more realistic calculation takes into account non-uniform density and still gives a limit of 1.4 solar masses. This limit is also related to relativistic degeneracy and the concept of momentum in relativity.
quasar987
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In my thermo text, we arrived at an estimate of the chandrasekhar limit using the assumptions T=0, uniform mass density and... p>>mc.

I can maaaaaybe accept that in the context of a very rough approximation, but then the text says, "A more realistic calculation, which does not suppose a uniform density, gives $M_C=1.4 M_{\bigodot}$". Thats means that in their so-called more realistic calculation, they still assume the unphysical p>>mc.

That someone explain that?

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quasar987 said:
I can maaaaaybe accept that in the context of a very rough approximation, but then the text says, "A more realistic calculation, which does not suppose a uniform density, gives $M_C=1.4 M_{\bigodot}$". Thats means that in their so-called more realistic calculation, they still assume the unphysical p>>mc.

If the momenta were not much greater than mc throughout much of the star, then the star would be sub-Chandrasekhar, practically by definition. Another way of thinking of the Chandrasekhar mass is the limit of relativistic degeneracy for a self-gravitating, electron-degenerate object.

Oh wait a sec. My problem is that I was thinking classically about momentum. p>>mc does not imply v>>c. So there is nothing unphysical about p>>mc.

quasar987 said:
In my thermo text, we arrived at an estimate of the chandrasekhar limit using the assumptions T=0, uniform mass density and... p>>mc.

Remember, in relativity, the spatial part of momentum is given by

$$p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}},$$

not by the Newtonian expression $p = mv$.

Thu,s $p >> mc$ when $v >> c/\sqrt{2}$, so $v > c$ is not needed.

Edit: While I was typing, you saw the light.

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## 1. What is the Chandrasekhar Limit?

The Chandrasekhar Limit is a theoretical limit in astrophysics, named after Indian-American physicist Subrahmanyan Chandrasekhar. It describes the maximum mass that a white dwarf star can sustain before it collapses into a neutron star or black hole.

## 2. How is the Chandrasekhar Limit calculated?

The Chandrasekhar Limit is calculated using the mass-radius relation for white dwarf stars, as derived by Chandrasekhar himself. This relation takes into account the degeneracy pressure of electrons, which prevents the star from collapsing under its own weight. The limit is approximately 1.4 times the mass of the sun.

## 3. What happens when a white dwarf exceeds the Chandrasekhar Limit?

When a white dwarf exceeds the Chandrasekhar Limit, it can no longer support its own weight and begins to collapse. This collapse can trigger a supernova explosion, as the sudden collapse increases the temperature and density within the star. The remaining core may then become a neutron star or black hole.

## 4. How does the Chandrasekhar Limit impact our understanding of the universe?

The Chandrasekhar Limit is an important concept in astrophysics as it helps us understand the life cycle of stars and the formation of compact objects such as neutron stars and black holes. It also plays a crucial role in the study of supernovae and the chemical enrichment of the universe.

## 5. Is the Chandrasekhar Limit a fixed value?

No, the Chandrasekhar Limit is not a fixed value. It depends on the composition of the white dwarf, as well as the assumptions made in the mass-radius relation. Additionally, the limit may also vary slightly depending on the initial mass of the star before it becomes a white dwarf.

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