## NASA Hubble Space Telescope Detects Ring of Dark MatterThe following catched my attention during this morning's webwalk.
"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 Z
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 v 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
hbar= GMm/v
equals to a ruler-and-compass rational which is ratio q= n The obvious TGD inspired hypothesis is that the dark matter ring corresponds to Bohr orbit. Hence the distance would be
r= n
where r
r
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 v 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. - From the
*Summary and Conclusion*part of the article the radius of the ring is about .4 Mpc, which makes in a good approximation 1.2 Mly (I prefer light years). More precisely - using arc second as a unit - the ring corresponds to a bump in the interval 60''-85'' centered at 75''. Figure 10 of of the article gives a good idea about the shape of the bump. - From the article the mass in the dense core within radius which is almost half of the ring radius is about M=1.5×10
^{14}× M_{Sun}. The mass estimate based on gravitational lensing gives M=1.5×10^{14}× M_{Sun}. If the gravitational lensing involves dark mass not in the central core, the first value can be used as the estimate. The Bohr radius this system is therefore r_{0}= 1.5×10^{14}× r_{0}(Sun),where I have assumed v _{0}=2^{-11}as for the inner planets in the model for the solar system. - The Bohr orbit for our planetary system predicts correctly Mercury's orbital radius as n=3 Bohr orbit for v
_{0}=2^{-11}so that one hasr _{0}(Sun)=r_{M}/9,where r _{M}is Mercury's orbital radius. One obtainsr _{0}= 1.5×10^{14}× r_{M}/9. - Mercury's orbital radius is in a good approximation r
_{M}=.4 AU, and AU (the distance of Earth from Sun) is 1.5×10^{11}meters. 1 ly corresponds to .95×10^{16}meters. This givesr _{0}=11 Mly to be compared with 1.2 Mly deduced from observations. The result is by a factor 9 too large. - If one replaces v
_{0}with 3v_{0}one obtains downwards scaling by a factor of 1/9, which gives r_{0}=1.2 Mly. The general hypothesis indeed allows to scale v_{0}by a factor 3. - If one considers instead of Bohr orbits genuine
solutions of Schrödinger equation then only n> 1
structures can correspond to rings like structures.
Minimal option would be n=2 with v
_{0}replaced with 6v_{0}.
The conclusion would be that the ring would correspond to the lowest possible Bohr orbit for v For more details see the new chapter Quantum Astrophysics . |