What is the Chandrashekhar Limit and How is it Calculated?

[aniket]

HI friends,
What is Chandrashekhar limit? HOw is it calculated? Does it remain same for every star? What are its dimensions?
Any suggestions are welcome.

 

[turbo]

HI friends,
What is Chandrashekhar limit? HOw is it calculated? Does it remain same for every star? What are its dimensions?
Any suggestions are welcome.

Here is a reference:

http://scienceworld.wolfram.com/physics/ChandrasekharLimit.html

For the mechanics: the Pauli exclusion principle says that no two similar Fermions (like electrons, protons, neutrons) can occupy the same quantum state. They expert a pressure resisting being forced into the same quantum state with a similar particle. It is the Fermionic repulsion between electrons that keeps a white dwarf from further gravitational collapse. The Chandrasekhar limit is a calculated limit (based on solar mass equivalents). If a white dwarf has a mass any greater than about 1.4 solar masses, the fermionic repulsion between electrons will not be able to prevent further collapse. The electrons and protons will merge to become neutrons, making a neutron star - severely degenerate matter indeed. If the mass of the neutron star exceeds about 4 solar masses or so, the Fermionic behavior of the neutrons will be unable to prevent further collapse, and the neutron star will collapse further and become a black hole.

 

[ek]

Something the linked reference doesn't mention...

Though the Chandrasekhar limit is 1.4Mo, that is not to say a star 40% more massive than the Sun will become a neutron star. Throughout a star's lifetime and primarily during its death a star loses a lot of its mass through various processes. So while the Chandrasekhar limit is 1.4Mo, the corresponding mass for main sequence stars is actually approximately 5-7Mo. So a star would have to be considerably larger than the Sun to become a neutron star, not slightly more massive as indicated on the surface by the Chandrasekhar Limit.

This same stipulation goes for the Oppenheimer-Volkov limit, which is ~2.0Mo.

So basically what this means is a star with a dying mass of under 1.4Mo becomes a white dwarf, a star of dying mass of between 1.4 and 2.0Mo becomes a degenerate neutron star, and a star of dying mass larger than 2.0Mo becomes a black hole.

Edit: Dying mass is not a technical term. It's just a term I use to differentiate from a star's main sequence mass.

 

[Labguy]

Something the linked reference doesn't mention...

Though the Chandrasekhar limit is 1.4Mo, that is not to say a star 40% more massive than the Sun will become a neutron star. Throughout a star's lifetime and primarily during its death a star loses a lot of its mass through various processes. So while the Chandrasekhar limit is 1.4Mo, the corresponding mass for main sequence stars is actually approximately 5-7Mo. So a star would have to be considerably larger than the Sun to become a neutron star, not slightly more massive as indicated on the surface by the Chandrasekhar Limit.

This same stipulation goes for the Oppenheimer-Volkov limit, which is ~2.0Mo.

So basically what this means is a star with a dying mass of under 1.4Mo becomes a white dwarf, a star of dying mass of between 1.4 and 2.0Mo becomes a degenerate neutron star, and a star of dying mass larger than 2.0Mo becomes a black hole.

Edit: Dying mass is not a technical term. It's just a term I use to differentiate from a star's main sequence mass.

True, a lot of people think of a star's initial mass and should be thinking of the mass remaining after all the mass ejections, usually as a Red Giant. It is always the remaing mass (usually a "core") that should be considered. The Chandrasekhar Limit is well known as 1.44 M_s for most star remaining material (C, N. O, Si, etc,), but he also calculated another for a remaining iron core. This number is 1.39 M_s.

The Oppenheimer-Volkov limit is actually ~3.2 M_s.

 

[ek]

The Oppenheimer-Volkov limit is actually ~3.2 M_s.

I learned it as ~2, but googling it it seems there are lots of numbers between 2 and 3. It also says it has been calculated only very roughly, which is obviously understandable.

Can you shed some light on this ambiguity? Is this akin to the Hubble constant in terms of accuracy?

 

[marlon]

HI friends,
What is Chandrashekhar limit? HOw is it calculated? Does it remain same for every star? What are its dimensions?
Any suggestions are welcome.

The "Chandrasekhar mass",is the mass of a star beyond which electron degeneracy pressure cannot hold a star up from gravity. Hence gravity becomes stronger than the counter-acting electron pressure and the star implodes. This mass is around 1.4 times the mass of the sun. Once it's passed (thus, during the implosion), the electrons and protons undergo inverse beta decay and form neutrons. This leads to a star that is instead held up by neutron degeneracy pressure, called a neutron star. There is also a mass beyond which neutron degeneracy pressure will fail and the object will collapse to a black hole.

regards
marlon

 

[SpaceTiger]

Can you shed some light on this ambiguity? Is this akin to the Hubble constant in terms of accuracy?

Even worse, I would say. The condition of matter (and, thus, the equation of state) in neutron stars is very poorly understood. There are theories that give a variety of numbers, but as far as I know, the observations don't rule out anything much above the Chandrasekhar limit. If anyone knows of some reliable observations of more massive neutron stars, I'd be curious to see the paper.

 

[Labguy]

Even worse, I would say. The condition of matter (and, thus, the equation of state) in neutron stars is very poorly understood. There are theories that give a variety of numbers, but as far as I know, the observations don't rule out anything much above the Chandrasekhar limit. If anyone knows of some reliable observations of more massive neutron stars, I'd be curious to see the paper.

A "minimum mass" for a black hole is not a direct correlation to the maximum mass of a neutron star, but I found the 3.2 M_s # in several books I have. Also it is interesting to note that ~4.25 is the smallest BH detected that I have heard of.

From: http://casswww.ucsd.edu/dawn.html :

The nature of the compact object is based upon its mass. The generally accepted maximum mass of a neutron star is between 3-3.2 solar masses. Therefore, if an object is found with a mass larger than this and it is very compact, it is designated as a black hole.
Last month, Gelino submitted results to the Astrophysical Journal Letters that identify a 4.25-solar mass black hole in the system known as J0422+32, using data from the 3.5-meter telescope at Apache Point Observatory in New Mexico. This system has a separation of just 2.5 solar radii, and is most likely the lowest mass black hole currently known in the Universe.

And the chart at: http://hoku.as.utexas.edu/~gebhardt/blackhole.html has interesting BH masses, but since it is mainly about AGN's, one would expect large masses.

So, if a white dwarf collapses to a neutron star if mass exceeds (accretion?) 1.44 M_s, and anything above ~3.2 M_s will become a black hole, what objects between 1.44 and 3.2 M_s are there?? (legit question)

 

[SpaceTiger]

A "minimum mass" for a black hole is not a direct correlation to the maximum mass of a neutron star

That's true; in fact, I don't know of any minimum mass for a black hole (perhaps the Planck mass). Everything I've read has referred to the Oppenheimer-Volkov limit as the maximum mass for a neutron star, not the minimum for a black hole.

, but I found the 3.2 M_s # in several books I have.

I don't doubt that there are such theoretical predictions, but I would not call any of them reliable without observations to back them up. Observations of black holes aren't necessarily reliable for this purpose because black holes can form by other methods and they can grow by accretion/mergers. The only way to put definitive observational constrains on the OV limit would be to find massive neutrons stars.

 

[daveed]

So, if a white dwarf collapses to a neutron star if mass exceeds (accretion?) 1.44 Ms, and anything above ~3.2 Ms will become a black hole, what objects between 1.44 and 3.2 Ms are there?? (legit question)

uhh?
they'll be stars, and eventually neutron stars.

 

[ek]

uhh?
they'll be stars, and eventually neutron stars.

White dwarfs.

Or am I reading your post wrong? Hmmm...

The question is "what objects are there between 1.4 and 3 solar masses?"

There are stars. And there are neutron stars. But a star that was in this range when it was on the main sequence will not be in this range when it dies. A main sequence star in this range will become a white dwarf, not a neutron star.

And to the guy who asked the question, remember that while a neutron star is very small radius wise, it is still approximately the same mass as the dying star.

 

[SpaceTiger]

And to the guy who asked the question, remember that while a neutron star is very small radius wise, it is still approximately the same mass as the dying star.

If, by approximately, you mean within a factor of a few. Neutron stars and white dwarfs are what remains of the star's core, the rest having been expelled either by supernova or stellar winds.

 

[Labguy]

If, by approximately, you mean within a factor of a few. Neutron stars and white dwarfs are what remains of the star's core, the rest having been expelled either by supernova or stellar winds.

Yes, of course. And as to the 2 posts above I was referring only to masses of remaining cores (matter) at the end of a star's life, as was the subject of this thread. Main sequence stars were not considered in my posts... :zzz:

 

[LURCH]

Isn't this the range of mass in which stellar remnants are expected to form "Quark stars"?

 

[Labguy]

Isn't this the range of mass in which stellar remnants are expected to form "Quark stars"?

If meaning the range of 1.44 to 3.2 M_s, this is where I would expect to find neutron stars even though none have yet been detected near the 3.0 level. That doesn't rule out their existence though. Actually, since it is now known that neutron stars are not composed of only neutrons, have a small "atmosphere" and Nickle/Iron surfaces, I expect that several new types will be found in this mass range such as the "quark" star:
http://spaceflightnow.com/news/n0204/11newmatter/
http://www.arxiv.org/PS_cache/astro-ph/pdf/0405/0405262.pdf

 

[ek]

If, by approximately, you mean within a factor of a few. Neutron stars and white dwarfs are what remains of the star's core, the rest having been expelled either by supernova or stellar winds.

I thought it was a little less than a factor of a few...like maybe a factor of 2. But you know more than me so I'll believe what you say!

But by approximately I meant that it wasn't all of a sudden the mass of a brown dwarf or something.

 

[SpaceTiger]

I thought it was a little less than a factor of a few...like maybe a factor of 2. But you know more than me so I'll believe what you say!

It varies along the main sequence, I just wanted to make sure you weren't suggesting that there was no mass loss.