The details of Einstein's rings as a support for the TGD view of dark matter?

There was an interesting popular article in Science-Astronomy.com with the title "Einstein rings says dark matter behaves more like a wave,not particle" (see this). The article told about the article published by Amruth and his team published in Nature Astronomy as an article with title "Einstein rings modulated by wavelike dark matter from anomalies in gravitationally lensed images" (see this). Unfortunately, the article is hidden behind paywall.

Dark matter is known to exist but its real character has remained a mystery. The models assume that its interactions with ordinary matter are very weak so that it makes itself visible only via its gravitational interactions. Two basic kinds of particles have been proposed: weakly interacting massive particles (WIMPs) and light particles, of which axions are the basic example. WIMPs behave like point-like particles whereas axions and light particles in general behave like waves. This difference can be used in order to find which option is more favoured. Axion option is favored by the behavior of dark matter in dwarf galaxies and by its effects on CMB.

The study of Amruth and his team found further support for the axion option from the study of gravitational lensing.

1. As light passes by a massive object, it bends both by the visible and dark matter associated with the object. This leads to a formation of Einstein rings: as if the light source would be a ring instead of a point-like object. If dark matter particles have some interactions with the photons , this causes additional effects on the Einstein rings. For instance, in the case of axions this interaction is known and corresponds to the electromagnetic analog of instanton term.
2. The effect of point-like particles on light is different for WIMPs and light particles such as axions. From the abstract of the article one learn that WIMP option referred to as \rho DM option leaves well documented anomalies between the predicted and observed brightnesses and positions of multiply lensed images, whereas axion option referred to as \psi DM option correctly predicts the level of anomalies remaining with \rho DM lens models. Therefore the particles of dark matter behave as if they were light particles, that is having a long Compton length.

What TGD allows us to conclude about the findings?

1. TGD predicts that dark matter corresponds to phases of ordinary matter labelled by a hierarchy of Planck constants h_eff=nh₀. The Compton length of dark particles with given mass is scaled up by factor h_eff/h. Could this be more or less equivalent with the assumption that dark particles are light?
2. Gravitational Planck constant is an especially interesting candidate for h_eff since it plays a key role in the TGD based view of quantum gravitation. Gravitational Planck constant obeys the formula ℏ_gr=GMm/β₀ for two-particle system consisting of large mass M and small mass (β₀ ≤1 is velocity parameter) and is very large.

   The gravitational Compton length Λ_gr= ℏ_gr/m = GM/β₀, which does not depend on the mass m of light particle (Equivalence Principle), is very large and and gives a lower bound for quantum gravitational coherence length. For instance, for the Sun it is rather near to Earth radius, probably not an accident.

3. Gravitational Compton length for particles at the gravitational magnetic body, which for stars with solar mass is near to Earth radius if the velocity β₀ in ℏ_gr has the same value β₀∼2^-11, makes dark variants of ordinary particles to behave like waves in astrophysical scales.
4. What happens in the scattering of a photon on a dark particle in the TGD sense. It seems that the photon must transform temporarily to a dark photon with the same value of h_eff. Photon wavelength is scaled up h_eff/h but photon energy is not affected in the change of Planck constant.

   Suppose that the scattering takes place like in quantum mechanics but with a modified value of Planck constant. In the lowest order in expansion in powers of α_em= e²/4πℏ_eff the scattering cross section is the same and whereas the higher corrections decrease. This provides actually a good motivation for the dark matter in TGD sense: the phase transition increasing the value of Planck constant reduces the value of gauge coupling strength and makes perturbation series convergent. One could say that Nature is theoretician friendly and takes care that his perturbation theory converges.

   In the lowest order of perturbation theory the scattering cross section is given by the classical cross section and independent of ℏ_eff. The Nishijina formula for Compton scattering (see this) indeed shows that the scattering cross section is proportional to the square of the classical radius of electron and does not depend on ℏ_eff. The result is somewhat disappointing.

5. On the other hand, for large values of ℏ_eff, in particular ℏ_gr, one can argue that the scattering takes place on the entire many-particle states at the flux tubes of the magnetic body so that superposition of scattering amplitudes on different charged particles at the flux tube gives the cross section. This can lead to interference effects.

   If the charged dark matter at the flux tube has a definite sign of charge this would give rise to amplification of the scattering amplitude and it would be proportional to the square N² of the number N of charged particles rather than to N. Scattering amplitudes could also interfere to more or less zero if both signs of charges are involved.

   One can also argue that only particles with a single value of mass are allowed since ℏ_gr is proportional to m so that particles would be like books in the shelves of a library labelled by ℏ_gr.

6. The effects of axion Bose-Einstein condensates have been indeed studied and it has been found that the scattering of photons on cold axion Bose-Einstein condensate could cause what is called caustic rings for which there is some evidence (see this). Could the quantum coherent many-particle states at gravitational flux tubes cause the same effect?

The optimistic conclusion would be that astrophysicists are gradually ending up with the TGD view of dark matter. One must of course that the above argument only suggests that the effects of scattering on Einstein's ring could be large for a large value of h_eff.

For the TGD view of the formation of astrophysical objects based on TGD based views of dark matter and dark energy see this and this.

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