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. 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 the free parameter. The model's average reduced chi square compares favorably with the dark matter model 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 the model's free parameter and galactic photometric quantities is observed, potentially removing the need for the free parameter.

Figures (6)

• Figure S1: Graphical Representations of Our Transformations (a) Curved 2-frame transformation $S(r)_1$ and (b) curved-to-flat transformation $S(r)_2$
• Figure S2: Physical Interpretation of the Model's free parameter $\alpha \propto L/R$ For $L$ the total luminosity in units of $10^9 M_{\odot}$ and $R$ the half-light radius in units of $kpc$. There is one $\alpha$ value per galaxy in the subset of the most reliable SPARC galaxy data described in Table \ref{['TSet']} and Sec. \ref{['sec:analysis']}. We report results with respect to the MW baryon model from (a) McGaugh-Jiao and (b) Xue-Sofue-Jiao.
• Figure S3: Normalized residuals for fits to SPARC galaxies assuming two different MW baseline models, each fitted by a Gaussian function. The means and standard deviations of the Gaussian fit are shown. (a) For the Xue-Sofue-Jiao Milky Way (b) For the McGaugh-Jiao Milky Way
• Figure A1: Declining Rotation Curves of high-surface brightness galaxies. Rotation curve data (blue points with error bars) and the input baryonic mass model (purple dashed line). This model's fits are shown by the red solid line, with respect to the Xue-Sofue-Jiao Milky Way. (a) NGC 2841 Blok1, (b) NGC 2841 2016Lelli, (c) NGC 3521 2016Lelli, (d) NGC 5055 2016Lelli, (e) NGC 5055 Blok1.
• Figure A2: Flat Rotation Curves. Lines are as in Fig. \ref{['N2841a']} (a) NGC 7814 Frat12016Lelli, (b) NGC 891 Frat12016Lelli, (c) NGC 3198 2016Lelli, (d) NGC 3198 Gent.