The spiral shape of many galaxies is truly one of the more extraordinary mysteries of the universe. Most of the reason for dark matter comes from the constant rotation of all galaxies, however the constant rotation of a galaxy is simply a manifestation of gravitization in quantum gravity.
Gravitization is a vector force that couples moving star decays with each other. The product of a start matter decay, kg/s, and star velocity, m/s, is dimensionally a vector force and each star in a galaxy has a mass decay due to its radiation as well as a velocity vector from its motion. So each star has in addition to gravity an extra gravitization force due to its moving matter decay and those force vectors couple with other stars in the galaxy to make galaxy rotation constant. One manifestation of constant galaxy rotation is the spiral density waves that persist as fundamental modes in many galaxies long after the perturbation of colliding galaxies. Gravitization couples angular momentum of inner to outer stars and that coupling explains why galaxies rotate at constant velocity.
The persistence of spiral density waves of galaxies due to gravitization means that there is no need for the mystery of dark matter to hold galaxies together. The Whirlpool galaxy (below, M51a) has spiral features with reported pitch angles mA =
16.7°, mB =
15.8°, while the dashed rectangle has the proportions of the golden ratio, 1.62. The golden ratio rectangle is quite well known in the aesthetics of architecture and art and encloses a golden spiral with a pitch of 17.0°. Why average pitch of galaxies is the golden spiral pitch seems more than just a coincidence.
The asymmetry of the galaxy central bulge, the arrowed
circle, is the dynamo that drives galaxy spiral dynamics due to gravitization. With just Einstein's gravity science needs the mystery of dark matter to keep all galaxies from flying apart. The supermassive black hole at the center is therefore somehow tied to the destiny of both the central bulge and the outer spiral disk in a cosmic ballet of gravitization that science barely understands. The tens of thousands of light years across a galaxy are the time equivalents of tens of thousands of years separating events anywhere within the galaxy.