Abstract

I review the connection between dynamics and the baryonic mass distribution in rotationally-supported galaxies. The enclosed dynamical mass-to-light ratio increases with decreasing galaxy luminosity and surface brightness. The correlation with surface brightness appears to be the more fundamental, with the dependence on luminosity following simply from the weaker correlation between luminosity and surface brightness. In addition to this global relation, there is also a local relation between the amplitude of the mass discrepancy and the acceleration predicted by the observed distribution of baryons. I provide an empirical calibration of this mass discrepancy-acceleration relation. The data are consistent with the operation of a singe effective force law in disk galaxies, making this relation tantamount to a natural law. I further provide formulae by which the radial dark matter distribution can be estimated from surface photometry. The form of the dark matter halo depends uniquely on the distribution of baryons in each galaxy and, in general, is neither a cusp nor a core. It remains difficult to see how galaxy formation models can reproduce the observed behavior, which is uniquely predicted by MOND.

Highlights

  • The dynamics of galaxies clearly evince a mass discrepancy [1]

  • (1) Rotation curves attain an approximately constant velocity that persists indefinitely [6,7]; (2) The observed mass scales as the fourth power of the amplitude of the flat rotation [8,9]; (3) There is a one-to-one correspondence between the radial force and the observed distribution of baryonic matter [2,4]. These are statements of the empirically-observed behavior of galaxies and their rotation curves. It is an important question whether these are scaling relations that emerge from the process of galaxy formation in the context of the dark matter paradigm or genuine laws of nature that follow from a modification of known dynamical laws

  • 1560 has a corresponding feature in the total rotation curve (Figure 4). This is a dramatic example of the general rule in low surface brightness (LSB) galaxies, where the distribution of the baryons remains predictive of the dynamics despite their apparent dark matter domination [57,58]

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Summary

Introduction

The dynamics of galaxies clearly evince a mass discrepancy [1]. The observed motions of stars and gas in galaxies cannot be explained by established dynamical laws relating the force of gravity to the observed distribution of luminous matter. (1) Rotation curves attain an approximately constant velocity that persists indefinitely (flat rotation curves) [6,7]; (2) The observed mass scales as the fourth power of the amplitude of the flat rotation (the baryonic Tully–Fisher relation) [8,9]; (3) There is a one-to-one correspondence between the radial force and the observed distribution of baryonic matter (the mass discrepancy-acceleration relation) [2,4]. These are statements of the empirically-observed behavior of galaxies and their rotation curves. I review the third law, which is less widely appreciated than the first two

Galaxy Rotation Curves
The Global Surface Brightness Dependence of the Mass Discrepancy
The Local Relation between Mass and Light
The Universal Rotation Curve
Renzo’s Rule
The Mass Discrepancy-Acceleration Relation
Discussion
The Dark Matter Distribution
Neither Cusps nor Cores
Findings
Broader Context
Full Text
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