# Paradox on the Chandrasekhar Limit

## Main Question or Discussion Point

The Chandrasekhar Limit is defined as the maximum mass of a white dwarf which is said to be 1.44 solar masses.
My doubt here is if it is defined as being the mass of 1.44 suns then the sun should not even be burning fuel right now. Only then will its mass remain the same.

The Sun keeps burning a lot of fuel. Its about 5 million tons of matter is being converted into energy every second.
Then shouldn't the definition of the Chandrasekhar Limit be more precise or am I entirely wrong ?

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Doug Huffman
Gold Member
Why would you expect/want the mass of the Sun to be stable? Why demand more 'precision' of Chandrasekhar than his terms can provide?

mfb
Mentor
The uncertainty in the mass of sun is larger than the mass of earth.

The fuel burning rate is completely negligible. The uncertainty in the Chandrasekhar limit is significantly larger than both of those. If we get much more precise estimates at some point, the limit will probably get expressed in a different unit (like kg). Currently this is not necessary.

Drakkith
Staff Emeritus
The Chandrasekhar limit is for a white dwarf, which is in a state of degeneracy and is extremely dense. It represents the maximum mass that can be supported by electron degeneracy in a non-rotating white dwarf. It has nothing to do with the mass of a star prior to degeneracy. In fact, stars that are much more massive than the Sun, up to about 8-10 solar masses even, are able to evolve into white dwarfs thanks to mass loss over their lifetime, especially during the red giant stage.

The amount of mass the Sun is losing, both in terms of mass lost as radiation through fusion and through mass lost in the solar wind, is completely negligible compared to the mass of the Sun itself. Together they add up to about 5.5 million tons per second, which is about 2.77 * 10^-21 of the Sun's mass lost per second, or 8.72*10^-14 of the Sun's mass lost per year.

Compare this to the stability of the IPK (the definition of a kilogram as a platinum weight in Paris) and the uncertainties in the masses of the Sun, stars and anything else you'd use solar masses as a unit for, and you'll realise that a solar mass is a pretty stable and well-defined unit for the forseeable future!

All stars consume the gases they're made of. The fusion that occurs fights the massive inward pull of gravity and stops the star from collapsing. So a star will, as it ages, lose mass. The Chandrashekar Limit refers to the maximum mass of a star for it to form a white dwarf in the later stages of its life. Stars like the sun which are below the Chandrashekar limit will, lose mass and eventually form a white dwarf.( A white dwarf is a star where the inward gravitational pull is balanced by the repulsion of electrons , due to the exclusion principle.) Stars more massive than the Chandrashekar limit will not form neutron stars, but will instead collapse to form neutron stars or black holes or whatever( sorry but this is where my knowledge gets a bit fuzzy.)

D H
Staff Emeritus
All stars consume the gases they're made of.
Stars lose but a tiny fraction of their mass (less than 1%) to fusion. Stars lose considerably more mass due to stellar wind and mass ejections, particularly during the end of the stars life. Drakkith mentioned in his answer that even an 8 to 10 solar mass star can end up as a white dwarf due extensive mass loss at the end of the stars life.

The Chandrashekar Limit refers to the maximum mass of a star for it to form a white dwarf in the later stages of its life.
No! The limit refers to the mass of the inert, degenerate core, not the mass of the star as a whole.

My doubt here is if it is defined as being the mass of 1.44 suns then the sun should not even be burning fuel right now. Only then will its mass remain the same.

Then shouldn't the definition of the Chandrasekhar Limit be more precise or am I entirely wrong ?
I suspect your confusion is that you don't understand what the Chandrasekhar Limit represents. That limit is the upper limit on the mass of the inert, degenerate core of a star that is nearing the end of its life.

Main sequence stars fuse hydrogen into helium at their core. Main sequence stars have built-in regulation mechanisms that maintain a balance between fusion, temperature, pressure, density, and radiation. This works fine until the star runs out of fuel at the core. That's the start of the end of the star's life. The star leaves the main sequence. Dying stars eventually develop a growing core of degenerate matter. If the star is big enough, that degenerate core will grow close to the Chandrasekhar Limit and die in the form of a supernova. Smaller stars (8 to 10 solar masses or less) never build up that large of a degenerate core.

Why the discrepancy between 8 to 10 solar masses and the much smaller Chandrasekhar Limit? Stars near the end of their life are very good at ejecting mass.

mfb
Why the discrepancy between 8 to 10 solar masses and the much smaller Chandrasekhar Limit? Stars near the end of their life are very good at ejecting mass.
Well then, what happens to stars that possess a mass of less than 8 to 10 solar masses ?

D H
Staff Emeritus
Well then, what happens to stars that possess a mass of less than 8 to 10 solar masses ?
They become white dwarfs. Stars larger than that limit end with a spectacular explosion, a core collapse supernova. That supernova occurs shortly before the mass of the inert, degenerate iron-nickel core at the center of the massive star would exceed the Chandrasekhar Limit.

The ultimate fate of our Sun is to become a carbon (or perhaps carbon-oxygen) white dwarf. Here's a brief description of our Sun in five or so billion years, which is when all the hydrogen at the core of the Sun will have been fused into helium.

Stars on the main sequence have a number of built-in negative feedback thermoregulation systems. (Negative feedback is good. It moves systems toward an equilibrium. Positive feedback is bad. It moves systems away from equilibrium.) Those built-in thermoregulation systems fail when a star consumes all (or almost all) the hydrogen at the core. With no fusion to fend off gravity, that helium core shrinks, which makes it get warmer, which makes it radiate energy, which makes it cool off, which makes it shrink even more. That's a positive feedback loop! The core collapses until a new regulatory mechanism sets in. This collapse brings fresh hydrogen from outer layers downward. Fusion starts up again, but more fiercely than when the Sun was on the main sequence. The outer parts of the Sun will expand greatly. The Sun will become a red giant, burning hydrogen in a shell around an inert core of helium.

That inert core is under such extreme pressure that it becomes degenerate matter. A weird thing happens to degenerate matter with added mass: It shrinks in size. This growing in mass but shrinking in size inert helium core gets hotter and hotter and denser and denser, eventually hot enough and dense enough so as to allow helium fusion, which forms carbon (and possibly some oxygen). The Sun will burn helium at the core, but only for about 100 million years, which is when the helium runs out in the core. Now the same process that made the Sun become a red giant sets in. The Sun will expand once again to become an asymptotic red giant, burning helium in a shell around an inert carbon/oxygen core.

That inert carbon/oxygen core is degenerate matter. For all practical matters, this is a white dwarf. The end times of the Sun involve lots of mass ejection. Low mass asymptotic red giant stars are not very stable. The pulse and shrink, expelling lots of mass in the process. In the end, the white dwarf that has been forming for a million years is exposed. The outer layers of the Sun have been ejected as a planetary nebula that orbits the exposed white dwarf.

Ah. Thanks for the clarification!