The light scattering is observed by JWST through blurring of far galaxies at z~10-14 [1], through 2-4 times larger than diffraction limit of telescope supernovas [2] and through analysis of little red dots [3]. In [1,3] the empirical formulas are discussed which depict the light scattering and it was possible to come to the conclusion that the energy loss on each step is proportional to energy (key assumption) with coefficient α=2*10exp(-12). From that coefficient it is clear that the particles scattering light are enormously light with approximate evaluations of total energies of femto to pico eV (only for such light particles the energy loss of say green photon would be so small as it is necessary). Heavier particles like today approximation of axions as particles with micro-eV total energies will drain the energy of photon much faster and thus created too strong scattering which is not observed.
However, application of quantum mechanics general ideas will allow to evaluate the properties of such "dark matter" (better be called almost completely transparent matter, because it is after all interacting with light). For total energy of 10exp(-15) eV the energy expressed in Joules would be 1.6*10exp(-31) Joule, for total energy of 10exp(-15) eV the energy expressed in Joules would be 1.6*10exp(-34) Joules. The effective mass may be estimated using the relation E=m*c2 (the relativistic mass, because such particles is moving with speed very close to c). For pico-eV particle it is 1.78*10exp(-48) kg, for femto-eV particle it is 1.78*10exp(-51) kg. The pulse may be calculated using E=p*c relation: for pico-eV particle the pulse is 5.33*10exp(-40) kg*m/s and for femto-eV particle the pulse is 5.33*10exp(-43) kg*m/s. Since pulse is known the important characteristic of the particle - de-Broglie wavelength may be easily found λ=h/p here h is Planck constant. For pico-eV particle de-Broglie wavelength is 1.24*10exp(6) meters and for femto-eV particle it is 1.24*10exp(9) meters (1/3 of Earth to Moon distance).
For such enormously large de-Broglie wavelength no doubt the light is not interacting with the particle easily, the cross-section of the interaction may be evaluated as the square of diameters of "particle" size. For photon it would be wavelength (500 nm for green photon) and for particle which scatters light it is de-Broglie wavelength. Then the cross-section for pico-eV particle would be [500*10exp(-9)/1.24*10exp(6)]2=1.6*10exp(-35) and for feemto-eV particle it would be 1.6*10exp(-41).
How frequently the photon is scattered on the route from supernova to the Earth to have the scattering parameter of 2*10exp(-12)? From the formulas outlined in [1] and assuming for z=1 supernova the distance between the star and Earth of 7.731 light years (7.314*10exp(25) meter) we may have: after N scatterings
EN/Eo=1/(1+z)=(1-α)N ln(1/(1+z))=ln(0.5)=N*ln(1-α)~-N*α
and N=3.47*10exp(11) for the distance traveled of 7.314*10exp(25) meters. Therefore the average distance traveled between the interactions is L=2.16*10exp(14) meter (approximately 8.33 light-days).
In order to evaluate the mass density of such axionic dark matter the assumption is as follows: during the travel of 8.33 days the effective volume of the photon has covered is V= π*λ2/4*L , here λ is the wavelength of the light and the mass of the axions in this volume is mass of one axion divided by the cross-section (because it is necessary to meet enormous amount of axions to interact with only one of them). V=42.4 cubic meters and mass density is 2.62*10exp(-15) kg/cubic meter for pico-eV particles and 2.62*10exp(-12) kg/cubic meter for femto-eV particles.
This value is comparable to the interstellar visible matter (mainly protons) of 1.67*10exp(-15) kg/cubic meter [4], less than the total mass density of Milky Way (2*10exp(-10) kg/cubic meter [5]) and larger than the calculated mass density of dark matter in the halo around Milky Way (0.2-0.4 GeV per cubic cm [6]) which would be 3.55-7.1*10exp(-22) kg/cubic meter.
The values obtained are reasonable and interestingly, the axionic dark matter interacting with light will be looking close to what astronomers are expecting - it must form halo. Because the particles are interacting with photons and so light, they are virtually pushed away by any photons (even microwave ones) from the stars, away from galaxy (full of photons) but due to some gravitational interaction they can not really lost the galaxy completely. They are indeed forming the halo around galaxy (and even more so pronounced halo around galaxy clusters) - an exactly as it is expected from gravitational consideration of light bending and too fast galaxy rotation. The estimated value of the mass density of those particles from light scattering is also reasonable - not really small and not enormously large (the distribution of them in halo is a separate and very difficult problem). However, the enormously small effective mass of them (energy of pico to femto eV) deemed the possibility of detection of them on Earth virtually impossible - they are sweeped out of Solar system by photons. Unless they are generated in the Sun itself (and in this case the stream of them directly from Sun similar to neutrinos stream is expected) they are only be possible to research using the light scattering from far-far stars, supernovas and galaxies.
References.
1. Tired light hypothesis possibly got confirmation by direct observation of light scattering
(PDF) Tired light hypothesis possibly got confirmation by direct observation of light scattering
4.Interstellar medium - Wikipedia
5.What's the theoretical maximum density of a galaxy? - Astronomy Stack Exchange
6.Determination of the local dark matter density in our Galaxy | Astronomy & Astrophysics (A&A)
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