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Galaxies: Flat rotation curves a sign of dark matter or cosmic dust?
The flat rotation velocity curve of the M31 spiral galaxy is produced by the redshift of Nitrogen II in cosmic dust having nothing to do with dark matter
By: QED Radiations
Since the 1970's, dark matter was thought to exist because the rotational velocities found  in Andromeda M31 and other low-redshift galaxies (Z< 0.001) were higher than expected by Newtonian mechanics which suggested the galaxies could not be held together as they appear. Following Hubble's methodology, the M31 rotation velocities were inferred from the redshift of the nitrogen NII line, the consequence of which was flat rotation curves became the signature of dark matter holding galaxies together. However, high-redshift (0.6< Z <2.6) galaxies in the distant Universe were recently found  to have falling rotation curves suggesting the absence of dark matter. What this means is modern cosmology faces a dilemma as dark matter should not depend on whether a galaxy is in the local or distant Universe.
Unlike the data for M31 that shows flat rotation curves out to 24 kpc, criticism of the falling rotation curve in the high-redshift galaxies is the data  was only taken out to about 10 kpc - not long enough to verify the curve is indeed falling. Since extended data can be resolved by future work, the emphasis in this PR is placed on the critique of flat rotation curves in M31 and specifically, to the unanswered question posed by Rubin and Ford  as to what causes the decrease in intensity of the nitrogen NII line with increasing distance from the galaxy nucleus.
In M31, the redshift of the NII line occurs upon absorption in cosmic dust distributed throughout the galaxy, the submicron dust particles concentrated in the outermost spiral arms. For clarity, only three dust particles are illustrated in the thumbnail. The dust particles are located relative to the x-axis oriented in the direction of the observer on Earth by radius R and angular position θ. The galaxy radius y is, y = Rm sinθ, where Rm is the radius locating the outermost dust particle. Ultraviolet radiation from the stars within the nucleus is assumed to produce an intensity Ao of ionized NII nitrogen at 6583 Å. The NII emission is spherical moving radially outward from the nucleus shown by yellow arrows until absorption by a dust particle which then as a local spherical emitter re-emits the redshifted NII line having at intensity Ao cosθ in the direction of Earth. The velocity V of the rotation curve is determined from the redshift Z of NII which is nearly uniform across the galaxy, but the NII intensity decreases with increasing distance consistent with  observation.
The redshift in cosmic dust went unnoticed for almost a century because the light-matter interaction of galaxy light including NII was assumed to follow classical physics allowing the heat capacity of the nanoscopic dust particle to conserve the galaxy photon by an increase in temperature. But the heat capacity of the atom given by the Planck law of QM is not scale invariant being finite at the macroscale while vanishing at the nanoscale. QM stands for quantum mechanics. Conservation of the galaxy photon is therefore only possible by a non-thermal mechanism proposed here to be simple QED.
Simple QED relies on the high S/V ratios of cosmic dust whereby the NII photon of wavelength λ is absorbed almost entirely in the dust surface placing internal atoms under the high EM confinement necessary in the Planck law for heat capacity to vanish. S/V stands for surface to volume. A non-thermal EM standing photon having half-wavelength λ/2 = d is then created as the NII photon adjusts to the EM confinement bounded by the dust surface. The speed of light c corrected for the refractive index n of the dust gives the Planck energy E of the redshift NII photon, E = h(c/n)/λ. On Earth, NII is observed to have wavelength 2nd with redshift Z = (2nd - λ)/λ. Once the Planck energy of NII absorbed in the dust surface is expended in forming the redshifted NII, the EM confinement vanishes and the redshifted NII is free to travel to the Earth. See diverse simple QED applications in nanostructures at http://www.nanoqed.org/
Since the rotation galaxy velocity V curve is flat with increasing radius, the redshift Z of the NII line is given by the absorption at a dust particle at distance y from the nucleus is, V(y) = cZ. Since Z depends on dust material and diameter d, the velocity V(y) fluctuates about a mean, but otherwise is constant with distance giving the flat velocity curve, but the intensity of the NII line decreases with distance.
The low-redshift M31 galaxy having a flat rotation curve is the consequence of redshift of the NII line in cosmic dust particles which requires the intensity of the NII line to decrease with the distance from the nucleus.
High-redshift galaxies showing falling rotation curves are more compact than M31, but otherwise mostly transparent and void of cosmic dust.
Flat galaxy rotation curves depend solely on cosmic dust having nothing to do with dark matter allowing galaxy dynamics at both low and high redshift to be governed by Newtonian mechanics.
 V. Rubin and W. Ford., "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions ", Astrophysical J., 159, 379, 1970.
 R. Genzel, et al., "Strongly Baryon-Dominated Disk Galaxies at the Peak of Galaxy Formation Ten Billion Years Ago", Nature, 543, 397–401, 2017.