## Friday, August 06, 2021

### Hyperon problem of stellar cores in TGD framework

Hyperon problem is a mystery related to the physics of neutron stars (see this). In neutron star neutrons temperature is zero in good approximation and Fermi statistics implies that the all states characterized by momentum and spin are filled up to maximum energy, known as Fermi energy EF identifiable as a chemical potential determined by the number density of fermions.

The increase of density inside a neutron star increases the total Fermi energy. Above a critical Fermi temperature possible in the core of the neutron star, the transformation of neutrons to hyperons which are baryons with some strange quarks becomes possible. λ hyperon with mass about 10 percent higher than neutron mass becomes possible. In a thermo-dynamical equilibrium the chemical potentials of hyperons and neutrons are identical. Note that chemical potentials are in a good approximation Fermi energies at zero temperature.

If part of neutrons transform to hyperons, the total energy decreases since the Fermi energy scales like 1/mass. One therefore expects the presence of hyperons in the cores of neutron stars, where the density and therefore also Fermi energy is high enough. The problem is that the maximal mass for known stars is above the maximal mass expected if hyperon fraction is present. Hyperon cores seem to be absent.

If further neutrons are added part of them transforms to hyperons and eventually all particles transform to neutrons and one can even think of the doomsday option that all matter transforms to hyperon stars.

Can one imagine any manner to prevent the formation of the hyperon core? Could the Fermi energy in the core remain below the needed critical Fermi energy by some new physics mechanism.

1. Apart from numerical constants, the Fermi energy for effectively n-D system is given by EF= ℏ2 kF2/2, where kF is some power of number density (N/Vn)2/n, where Vn refers to volume, area, or length for n=3, 2, 1. Since zero temperature approximation is good, Fermi energy depends only on the density.
2. Could one think that part of neutrons transforms to dark neutrons in the transformation heff→ kheff such that neither mass, energy, and Fermi energy are not affected but that wavelength is scaled up as also the volume. For an effectively 3-D system, dark neutrons would occupy a volume which is scaled up by factor k3.
3. The Fermi energies as chemical potentials for both ordinary neutrons and their dark variants could remain the same in thermal equilibrium and remain below the critical value so that the transformation to hyperons would not take place? The condition that Fermi energies are the same implies that the numbers of ordinary and dark neutrons are the same. This would reduce individual Fermi energies by a factor 1/22/3 but is only a temporary solution.

One can however introduce phases with k different values of heff and in this case the reduction of Fermi energies is 1/k2/3.

4. Fermi statistics might however pose a problem. The second quantization of the induced spinor fields at the space-time surface is induced by the second quantization of free spinor fields in the embedding space M4×CP2. Could the CP2 degrees of freedom give additional degrees of freedom realized as many-sheeted structures allowing to avoid the problems with Fermi statistics?
See the article Solar Metallicity Problem from TGD Perspective.

For a summary of earlier postings see Latest progress in TGD.