Single Parameter Model for Galaxy Rotation Curves

Abstract

One key piece of evidence for dark matter is the rotation-curve problem: the disagreement between measured galactic rotation curves and their luminous mass. A novel solution to this problem is presented here, in a model that predicts observed Doppler-shifted spectra based only on the luminous matter estimates and one free model parameter 𝛼. This model is applied to fit the rotation curves of the SPARC sample of 175 galaxies, yielding mass-to-light ratios, goodness of fit measurements, and 𝛼. The measured average 𝜒2 𝑟 =2.24 compares favorably with the Navarro-Frenk-White dark matter model’s average of 𝜒2 𝑟 =4.19 for the same data, and more galaxies are successfully fit by this model. The model provides a useful formulation linking luminous matter to the observed rotation curves, with the dark matter contribution to galaxies encoded in two transformation terms of the luminous mass. It also offers a lower-parameter characterization of the rotation curve problem, and a power law relationship between 𝛼 and galactic photometric quantities is observed, potentially removing the need for the free parameter.