Debated Models for Galactic Rotation Curves: A Review and Mathematical Assessment

Abstract

Proposed explanations of galactic rotation curves (RC = tangential velocity vs. equatorial radius, determined from Doppler measurements) involve dramatically different assumptions. A dominant, original camp invoked huge amounts of unknown, non-baryonic dark matter (NBDM) in surrounding haloes to reconcile RC simulated using their Newtonian orbital models (NOMs) for billions of stars in spiral galaxies with the familiar Keplerian orbital patterns of the few, tiny planets in our Solar System. A competing minority proposed that hypothetical, non-relativistic, non-Newtonian forces govern the internal motions of galaxies. More than 40 years of controversy has followed. Other smaller groups, unsatisfied by explanations rooted in unknown matter or undocumented forces, have variously employed force summations, spin models, or relativistic adaptations to explain galactic rotation curves. Some small groups have pursued inverse models and found no need for NBDM. The successes, failures, and underlying assumptions of the above models are reviewed in this paper, focusing on their mathematical underpinnings. We also show that extractions of RC from Doppler measurements need revising to account for the effect of galaxy shape on flux-velocity profiles and for the possible presence of a secondary spin axis. The latter is indicated by complex Doppler shift patterns. Our findings, combined with independent evidence such as hadron collider experiments failing to produce non-baryonic matter, suggest that a paradigm shift is unfolding.

Generalized Inflation Theory as a solution to Galaxies Rotation Curves And Variation of fine structure constant

“…This change rate is compatible with one of the related data was given by Shylakhter [2] and reviewed by Lipovka and Cardenas [3,4] which is reported as 4 × 10 −11 . This shows an amazing compatibility of BDM generalized inflation results and astronomical results of physical constants evolution.…”

“…The problem has been justified by assuming a hidden dark matter distributed in the galaxies with a certain pattern. The modified Newtonian dynamics (MOND) is also another approach to this discrepancy by suggesting a modification of Newtonian dynamics at very large distances and very low gravity accelerations [2]. The fine structure constant variation over large astronomical distances is somehow a similar problem observed at far galaxies.…”

“…Velocity (rotation) curves of distant stars relative to their galaxy's center do not obey the Newtonian dynamics. Based on astronomical observations, the orbiting velocities of these stars are approximately equal or slowly increasing over the large distances whereas the Newtonian dynamic predicts a lowering speed proportional to 1 √ with as the distance of star from galaxy's center [2]. The problem has been justified by assuming a hidden dark matter distributed in the galaxies with a certain pattern.…”

Thermodynamic Constraints on the Non-Baryonic Dark Matter Gas Composing Galactic Halos

“…Multicomponent fits are inherently ambiguous, so it is common practice to minimize the amount of dark matter [17]. This procedure is needed because 100% dark matter reproduces RCs in all cases [18]. The lack of independent and direct confirmation of either halo material or NBDM Figure 1.…”

“…Multicomponent fits are inherently ambiguous, so it is common practice to minimize the amount of dark matter [17]. This procedure is needed because 100% dark matter reproduces RCs in all cases [18]. The lack of independent and direct confirmation of either halo material or NBDM particles has fueled many challenges to the assumptions underlying NOMs (e.g., [17][18][19][20][21][22][23][24][25][26][27]; also see the recent Special Issue of Galaxies, "Debate on the Physics of Galactic Rotation and the Existence of Dark Matter").…”