# Why are there no known white dwarfs between 1.35 to 1.44 solar masses?

The Chandrasekhar limit for white dwarfs is 1.44 Solar masses, however the heaveist known white dwarf is only 1.35 solar masses. https://earthsky.org/space/smallest-most-massive-white-dwarf/ What's the cause of this gap in mass?

The "Chandrasekhar mass" of 1.44 solar masses is based on a pair of unrealistic assumptions, that are not met in practice, which means the true mass limit is more like 1.37 or 1.38 solar masses.

The two assumptions are: (I) that the white dwarf is supported by ideal electron degeneracy pressure. i.e. Point-like, non-interacting fermions. (II) That the structure of the star is governed by Newtonian gravity.

The first assumption fails because the electrons and ions do have Coulomb interactions that make the material more compressible. More importantly, at high densities (and the density increases with mass), the electron Fermi energy eventually becomes high enough to initiate electron capture to make more neutron-rich nuclei. Since the electrons are ultra-relativistic, the star is already marginally stable at this stage, and the removal of electrons causes instability and collapse.

The second assumption fails because more massive white dwarfs are smaller and General Relativity must be used. The General Relativistic formulation of the equation of hydrostatic equilibrium features pressure on the RHS. So the higher the pressure, the steeper the required pressure gradient. Ultimately, this also leads to an instability at a finite size and density that occurs at masses lower than the canonical Chandrasekhar mass.

For typical C/O white dwarfs, both of the instabilities discussed above occur when the white dwarf is at about 1.38 solar masses.

Note that white dwarfs of more than about 1.2 solar masses are not expected to arise from the evolution of a single star. If the C/O core of a star is more massive than this, then it will also become hot enough to ignite these elements. More massive white dwarfs will need to have been produced by accretion in a binary system or by a merger. Then, another factor comes into play, which is the possible detonation of the entire white dwarf, which may also occur at about 1.37 to 1.38 solar masses, possibly ignited by the fusion of helium from the accreted material or by pycnonuclear reactions in the dense C/O core.

Postscript - there actually are some white dwarfs with estimated masses of $$1.35-1.37M_\odot$$ in classical novae binary systems (e.g. Hachisu & Kato 2001). These may be systems that are about to go "bang".

• This also means the accreting versions tend to explode at a very consistent mass and result in consistent energy release, thus type Ia supernovae are used as standard candles. Sep 19 '21 at 6:10
• It seems a really odd coincidence that two effects of so fundamentally different nature both kick in within 90% of the non-interactive/Newtonian Chandrasekhar limit. Is there any known reason for why it plays out this way? Sep 20 '21 at 8:38
• @leftaroundabout - The reason is a survivorship bias. The Chandrasekhar limit was derived using some simplifying assumptions, like every result in physics. It would achieve little fame had it left a gap of orders of magnitude between the heaviest observed white dwarfs and the theoretical limit. That great fit left a thinner mass gap for the inevitable corrections to either the observational or theoretical side of the equation. Sep 20 '21 at 9:52
• @leftaroundabout the reason is that the dependence of density on mass becomes very steep as the canonical Chandrasekhar limit is approached. It is like $\rho \propto M^2$ at lower masses, but becomes much steeper as the electrons become ultrarelativistic. This means that the central density increases by orders of magnitude as you increase the mass up towards that last 10% before the Chandrasekhar mass. And it is density that is really the important parameter here. Sep 20 '21 at 10:05
• +1 for an excellent answer covering most white dwarfs, but what about the unusual ones (which is what we might be looking for at the limit of stability)? For example, does the rotation of a white dwarf affect its ability to remain stable at more than 1.38 solar masses? What if the rotation isn't uniform? What about the composition: some white dwarfs are ONeMg & others are He. I'm guessing that greater or lesser mass in the nucleus will change the constraints on relativistic uncertainty? Dec 13 '21 at 0:19