The following catched my attention during this morning's webwalk.
NASA Hubble Space Telescope Detects Ring of Dark Matter
"Rings" puts bells ringing! In TGD Universe dark matter characterized by a gigantic value of Planck constant making dark matter a macroscopic quantum phase in astrophysical length and time scales. Rotationally symmetric structures - such as rings- with an exact rotational symmetry Zn, n very very large, of the "field body" of the system, is the basic prediction. In the model of planetary orbits the rings of dark matter around Bohr orbits force the visible matter at the Bohr orbit (see this).
TGD based model for dark matter inspires the hypothesis that it corresponds to Bohr orbit for macroscopically quantum coherent dark matter with gigantic value of Planck constant predicted by the model. The article about finding is now in archive and contains the data making possible to test the model. I am grateful for Kea for providing the link. The ring corresponds with a good accuracy to the lowest Bohr orbit for v0= 3×2-11, which is 3 times the favored value but allowed by the general hypothesis for the favored values of Planck constant.
I add the little calculation here to give an idea about what is involved. The number theoretic hypothesis for the preferred values of Planck constants states that the gravitational Planck constant
equals to a ruler-and-compass rational which is ratio q= n1/n2 of ruler-and-compass ni integers expressible as a product of form n=2k∏ Fs, where all Fermat primes Fs are different. Only four of them are known and they are given by 3, 5, 17, 257, 216+1. v0=2-11 applies to inner planets and v0=2-11/5 to outer planets and the conditions from the quantization of hbar are satisfied.
The obvious TGD inspired hypothesis is that the dark matter ring corresponds to Bohr orbit. Hence the distance would be
r= n2 r0,
where r0 is Bohr radius and n is integer. n=1 for lowest Bohr orbit. The Bohr radius is given
where M the total mass in the dense core region inside the ring. This would give distance of about 2000 times Schwartschild radius for the lowest orbit for the preferred value of v0=2-11.
This prediction can be confronted with the data since the article Discovery of a ringlike dark matter structure in the core of the galaxy cluster C1 0024+17 is in the archive now.
The conclusion would be that the ring would correspond to the lowest possible Bohr orbit for v0=3× 2-11. I would have been really happy if the favored value of v0 had appeared in the formula but the consistency with the ruler-and-compass hypothesis serves as a consolation. Skeptic can of course always argue that this is a pure accident. If so, it would be an addition to long series of accidents (planetary radii in solar system and radii of exoplanets). One can of course search rings at radii corresponding to n=2,3,... If these are found, I would say that the situation is settled.
For more details see the new chapter Quantum Astrophysics .