Self-Similarity Of Hadrons, Black Holes And Galaxies
After 2 bone-headed mistaken attempts, I think I have got this straight now, or at least I hope so.
I just read a new paper in Astronomy & Astrophysics with the title “ The angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals”. Here is a link to the paper: https://arxiv.org/abs/1804.04663 .
The authors have found that for various types of galaxies there is a “fundamental scaling law” correlating a galaxy’s specific angular momentum to its mass. The law is j ~ M^.55. This applies to the Galaxy’s stellar content. There is also theoretical and observational evidence for the law being j ~ M^.67 in the case wherein dark halos are included.
The specific angular momentum is the system’s angular momentum (J) divided by its mass (M), so j = J/M. If we want to convert to the slightly different relationship between J and M, then we must write J/M ~ M^.67, and then J ~ (M)(M^.67), to get J ~ M^1.67.
From the standpoint of Discrete Scale Relativity it is very interesting that this law is roughly J ~ M². It is interesting because we know that subatomic hadrons (protons, neutrons, lambdas, etas, pions, kaons, etc.) obey J ~ M² laws.
We also know that Kerr-Newman black holes obey J ~ M² laws. Discrete Scale Relativity predicts that the dark matter is predominantly composed of stellar-mass Kerr-Newman black holes, often called primordial black holes.
So there is a definite potential for a universal J ~ M² law that applies to fundamental systems on all Cosmological Scales of nature’s discrete self-similar hierarchy. There is still some uncertainty in the galaxy law, but we can take advantage of this by predicting that in the future astrophysicists will eventually arrive at J ~ M² as the correct scaling law for galaxies.