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

Department of Earth and Planetary Science, Washington University, St. Louis, MO 63130, USA
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Galaxies 2020, 8(2), 47; https://doi.org/10.3390/galaxies8020047
Received: 25 April 2020 / Revised: 26 May 2020 / Accepted: 27 May 2020 / Published: 1 June 2020
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. View Full-Text
Keywords: spiral galaxies; rotation curves; data analysis; gravitational models; non-baryonic matter; inverse methods spiral galaxies; rotation curves; data analysis; gravitational models; non-baryonic matter; inverse methods
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Hofmeister, A.M.; Criss, R.E. Debated Models for Galactic Rotation Curves: A Review and Mathematical Assessment. Galaxies 2020, 8, 47.

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