The dark matter modern approach to the explanation of galaxies rotation has one drawback - it is still considers stars as equivalent to rocks (planets). In reality stars have one distinct difference from planets (for planets the third Kepler Law explains all the motion perfectly) - they are generating energy by themselves. If only a small fraction of that energy is transformed through any mechanism into the mechanical energy, that may easily explain any rotation curve of the galaxy without any new hypothesis about predominant non-observable matter. Let's consider the bright star with luminocity of 1260 Sun and total inertial mass of 5.4 Sun (Polaris star). The total energy release would be 5*10exp(+29) J/s and mass would be 1.1*10exp(31) kg. If only 1% of the energy released is somehow transformed into the mechanical energy, the star may reach the rotational speed of 230000 m/s (Sun surrounding) for only 1.8 million of years (estimation done from 1/2*mV^2 formula). This is smaller than life time of the star of such initial mass (10 millions of years).
Thus the difference between the star and planet is essentially inside the star. The idea of the strongly gravitating slow light [1,2], may not only explain the too fast rotation of the stars in the galaxy (the effective gravitational mass is higher compare to the inertial mass) but also the overall dynamic of the stars in the galaxy (origin of spiral arms) and the difference between the elliptical and spiral galaxy (why the elliptical galaxy stopped rotating).
According to the hypothesis of [1], the stars has a lot of trapped photons inside. Not only the gamma quanta from the nuclear reaction but softer light like X-ray and visible light due to bremsstrahlung scattering of electron and ions inside the fully ionized plasma inside the star. Those photons are inside the environment with enormous value of effective refraction coefficient (inside the fully conductive media) and thus are moving really slow and gravitating very strongly (similar idea is expressed in [3]). The gravity-like behavior of slow photons is demonstrated in [4] experimentally (polaritons are exactly what is expected for photons inside the stars).
The photons inside the stars are gravitating according to general relativity, of course, they are not creating the mutually reciprocal force like the baryonic matter. The slow photons are attracted to the galaxy center (and much strongly if calculated per energy compare to baryonic matter) but not creating the additional distortion of time-space themselves (except for the equivalent inertial mass they have in vacuum, from E=m*c^2). Thus they create the additional force to the bright stars, which forces them toward the center of gravity (center of galaxy). This force moves the star to the new position and according to the momentum conservation law the star is accelerating (new equilibrium position closer to the center of rotation needs higher velocity). This mechanism effectively transforms the energy of the thermonuclear fusion into the mechanical energy necessary for the accelerated rotation. Thus the energy of the nuclear fusion is transformed into the rotation energy of the whole galaxy (the effect is smaller for light stars like Sun, but stars are created and dying continuously). In this situation the rotation of the galaxy is more like dynamo phenomena than static rotation of planets around the star.
That additional force might be expressed in the following formula:
F=K*E*M/(R*R)
The force is concentrated in the star, so for the outside space it will be the central force. The 1/(R*R) law follows from the attraction formula for light and from geometry of space-time (should be similar to Newtonian law in the weak gravitational limit). The force is proportional to the inertial mass of the object which attracts the star (or to the curvature created by the inertial mass in the weak gravitation limit of general relativity), since light is "attracted" due to the curvature of space-time (similar to the deviation of light near the star). But the force does not proportional to the inertial mass of the star which attracts, but rather to the total energy of trapped light inside E (and the coefficient K depends upon the type of star, upon the effective refraction coefficient inside, which makes the whole force non-universal). When the E of trapped light is zero the force is zero only the usual gravitation exist,
For the evaluation it is possible to assume that the value of F will depend upon the luminosity I of the star (it is an idea that the amount of light still trapped inside the star should correlate with the light emitted by star every second).
F=K*I*M/(R*R)
For evaluations it is possible to assume that the force from light matter should be at least equal to the gravitational force:
K*I*M/(R*R)~G*m*M/(R*R)
and then for the stars like Sun K=3.3*10exp(-7) m*s/kg
for bright stars like Polaris K=1.46*10exp(-9) m*s/kg
and taking the average (geometric one):
K~2*10exp(-8) m*s/kg
With this force the origin of spiral arms would be the higher velocity of bright stars compare to the rest of stars: the bright stars are short lived, but they are the main driving force for the rotation of galaxy - the additional force accelerates them very much like the rotation of the skater is accelerates when he or she pulls the leg in. This acceleration of rotation transfers to the rest of stars and the galaxy starts to rotate.
The gravitational force only is seemingly not enough to sustain the rotation: the elliptical galaxies are contracting radially, not rotating. Only young galaxies, full of new stars have enough energy to start rotation and hold it at the almost constant for all galaxies speed (the energy originates from the drain of stars in the black hole, very much like the rotation of water in the tub originates from the energy of the drained water). The comparison is not really quite well because the friction is much smaller, but it was found that the vortex in bathtub also need some threshold discharge rate [5] - if the discharge is too small, water drains pure radially.
It puts the elliptical galaxies as the final evolution stage of galaxy: it starts from protogalaxy, starts to rotate around the central black hole (spiral galaxy), slowly uses all of the necessary molecular clouds - no bright stars any more - and turns into the elliptical galaxy with huge black hole and aging low luminosity stars.
References.
1. https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
2. https://tipikin.blogspot.com/2019/09/accelerated-rotation-of-star-because-of.html
3. https://arxiv.org/abs/0710.0273
4. https://funsizephysics.com/gravity-for-photons/
5.T.Kawakubo Y.Tsuchiya M. Sugaya K.Matsumura "Formation of a vortex around a sink: a kind of phase transition in a nonequilibrium open system" // Physics Letters A, Vol.68, No1, p.p.65-66, 1978
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