# The maximum mass of white dwarf star

• feynmann
And even then, these effects would be so small that they would have no significant impact on the overall mass of the white dwarf. This is why the Chandrasekhar Limit of 1.44 solar masses is considered a maximum mass for white dwarfs, as the effects of QM on the overall mass are negligible.

#### feynmann

It's well known that white dwarf stars are supported by degenerate-electron pressure. Calculation shows that maximum mass of white dwarf star is about 1.4 solar mass. My question is why it has a maximum mass? The postulate of Quantum mechanics says that it should be a distribution of mass, since the momentum and energy are not certain in QM but probabilistic.

An object of that size is not governed by QM. QM becomes inaccurate at that level.

And if you know how to derive this Chandrasekhar-limit, you would not ask this question ;-)

An electron has a fixed rest mass ...

malawi_glenn said:
An object of that size is not governed by QM. QM becomes inaccurate at that level.

And if you know how to derive this Chandrasekhar-limit, you would not ask this question ;-)

An electron has a fixed rest mass ...

Why an object of that size is not governed by QM? Chandrasekhar's calculation shows that it is still governed by the Pauli exclusion principle of QM, since only QM can explain the degenerate-electron pressure.

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feynmann said:
Why an object of that size is not governed by QM? Chandrasekhar's calculation shows that it is still governed by the Pauli exclusion principle of QM, since only QM can explain the degenerate-electron pressure.

It is still a macroscopic object, goverened by statistical mechanics. It is like talking of boiling point of water at 1 atm pressure (which is 373 K right?) but if you apply the same argument, one should not say that it IS 373 K since one can and will have quantum and statistical fluctuations. Do you follow me on this one? The fluctuations although is of the order 10E-15 if i remember my Mandl correctly.

The white dwarf will of course be goverened by QM and Statstical Mechanics in it's most elementary constituents, but the fluctuations around this limit 1.44M_sun will be of the order 1 part in 1 billion and less... The fluctuations are so small that it is meaningless to speak of them. Macroscopic objects global properties like cups of water, gas containers, white dwarfs etc, are most accurately described in terms of macroscopical units. And vice versa, one can not speak of the temperature of ONE particle

Pressure is macroscopic measure, which is the average of microscopical particles motion and interactions. If we want to determine a macroscopic body's properties, we must average.

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Chandrasekhar Limit...

feynmann said:
It's well known that white dwarf stars are supported by degenerate-electron pressure. Calculation shows that maximum mass of white dwarf star is about 1.4 solar mass. My question is why it has a maximum mass?

A white dwarf is primarily supported by positive electron degeneracy core pressure against negative gravitational core pressure within its stellar core, preventing the star from collapsing.

If the stars mass is increased, its negative gravitational core pressure also increases until a limit is approached with respect to its positive electron degeneracy pressure. If the negative gravitational core pressure exceeds its positive electron degeneracy core pressure, the star implodes and flashes a runaway carbon fusion reaction in its core and at this point the star will explode in a core-collapse Type Ia supernova, leaving behind either a neutron star or a black hole.

If a white dwarf gradually accretes mass from a binary companion, its core is believed to reach the ignition temperature for carbon fusion as it approaches the limit. Within a few seconds of initiation of nuclear fusion, a substantial fraction of the matter in the white dwarf undergoes a runaway fusion reaction, releasing enough energy (1-2 × 10^44 joules) to unbind the star in a supernova explosion.

For type II supernovae, the collapse is eventually halted by short-range repulsive neutron-neutron interactions mediated by the strong force, and neutron degeneracy core pressure.

Reference:
http://en.wikipedia.org/wiki/Chandrasekhar_Limit" [Broken]
http://en.wikipedia.org/wiki/Core-collapse_supernova#Core_collapse"
http://en.wikipedia.org/wiki/Type_Ia_supernovae" [Broken]

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Orion1 said:

A white dwarf is primarily supported by positive electron degeneracy core pressure against negative gravitational core pressure within its stellar core, preventing the star from collapsing.

If the stars mass is increased, its negative gravitational core pressure also increases until a limit is approached with respect to its positive electron degeneracy pressure. If the negative gravitational core pressure exceeds its positive electron degeneracy core pressure, the star implodes and flashes a runaway carbon fusion reaction in its core and at this point the star will explode in a core-collapse Type Ia supernova, leaving behind either a neutron star or a black hole.

If a white dwarf gradually accretes mass from a binary companion, its core is believed to reach the ignition temperature for carbon fusion as it approaches the limit. Within a few seconds of initiation of nuclear fusion, a substantial fraction of the matter in the white dwarf undergoes a runaway fusion reaction, releasing enough energy (1-2 × 10^44 joules) to unbind the star in a supernova explosion.

For type II supernovae, the collapse is eventually halted by short-range repulsive neutron-neutron interactions mediated by the strong force, and neutron degeneracy core pressure.

Reference:
http://en.wikipedia.org/wiki/Chandrasekhar_Limit" [Broken]
http://en.wikipedia.org/wiki/Core-collapse_supernova#Core_collapse"
http://en.wikipedia.org/wiki/Type_Ia_supernovae" [Broken]

But this does not answer OP's question, we want to know WHY and IF this 1.44M_sun is really a maximum value since due to QM we would expect a range of masses.

He did not ask how it works etc.

The answer to that question I gave in my latest post, that the fluctuations are of the order 1E-9 or smaller.

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We wouldn't expect a range of masses from QM. Why would we? QM tells us about the very small (like carbon nucleii), even if it is interacting with the very big (like the rest of the star) and there's nothing in QM that indicates a mass range for something very big. The "random fluctuations" of the nucleii all cancel out when averaged in such immense numbers as in a star (a carbon white-dwarf of 1.44 solar masses contains 1.44E+56 nucleii .) Only extremely low probability states - of the order of 1 in 10^10^(56) - will show macroscopic quantum effects in a white-dwarf.