A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form — dark matter — or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation — Milgrom’s law — involving an acceleration constant a₀ (or a characteristic surface density Σ_† = a₀/G) on the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.

We introduce SPARC (Spitzer Photometry and Accurate Rotation Curves): a sample of 175 nearby galaxies with new surface photometry at 3.6 μm and high-quality rotation curves from previous H i/Hα studies. SPARC spans a broad range of morphologies (S0 to Irr), luminosities (∼5 dex), and surface brightnesses (∼4 dex). We derive [3.6] surface photometry and study structural relations of stellar and gas disks. We find that both the stellar mass–H i mass relation and the stellar radius–H i radius relation have significant intrinsic scatter, while the H i mass–radius relation is extremely tight. We build detailed mass models and quantify the ratio of baryonic to observed velocity (V _bar/V _obs) for different characteristic radii and values of the stellar mass-to-light ratio (ϒ_⋆) at [3.6]. Assuming ϒ_⋆ ≃ 0.5 M _⊙/L _⊙ (as suggested by stellar population models), we find that (i) the gas fraction linearly correlates with total luminosity; (ii) the transition from star-dominated to gas-dominated galaxies roughly corresponds to the transition from spiral galaxies to dwarf irregulars, in line with density wave theory; and (iii) V _bar/V _obs varies with luminosity and surface brightness: high-mass, high-surface-brightness galaxies are nearly maximal, while low-mass, low-surface-brightness galaxies are submaximal. These basic properties are lost for low values of ϒ_⋆ ≃ 0.2 M _⊙/L _⊙ as suggested by the DiskMass survey. The mean maximum-disk limit in bright galaxies is ϒ_⋆ ≃ 0.7 M _⊙/L _⊙ at [3.6]. The SPARC data are publicly available and represent an ideal test bed for models of galaxy formation.

We explore the Tully-Fisher relation over five decades in stellar mass in galaxies with circular velocities ranging over 30 less, similarVc less, similar300 km s-1. We find a clear break in the optical Tully-Fisher relation: field galaxies with Vc less, similar90 km s-1 fall below the relation defined by brighter galaxies. These faint galaxies, however, are very rich in gas; adding in the gas mass and plotting the baryonic disk mass Md=M*+Mgas in place of luminosity restores the single linear relation. The Tully-Fisher relation thus appears fundamentally to be a relation between rotation velocity and total baryonic mass of the form Md~V4c.

We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.

▪ Abstract Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below a_o≈ 10⁻⁸cm/s²≈ cH_o/6 the effective gravitational attraction approaches [ ], where g_nis the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V⁴that forms the basis for the observed luminosity–rotation velocity relation—the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to superclusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extention of MOND to cosmology and structure formation.

We study the link between baryons and dark matter (DM) in 240 galaxies with spatially resolved kinematic data. Our sample spans 9 dex in stellar mass and includes all morphological types. We consider (1) 153 late-type galaxies (LTGs; spirals and irregulars) with gas rotation curves from the SPARC database, (2) 25 early-type galaxies (ETGs; ellipticals and lenticulars) with stellar and H i data from ATLAS 3 D or X-ray data from Chandra, and (3) 62 dwarf spheroidals (dSphs) with individual-star spectroscopy. We find that LTGs, ETGs, and “classical” dSphs follow the same radial acceleration relation: the observed acceleration ( g obs ) correlates with that expected from the distribution of baryons ( g bar ) over 4 dex. The relation coincides with the 1:1 line (no DM) at high accelerations but systematically deviates from unity below a critical scale of ∼10⁻¹⁰ m s⁻². The observed scatter is remarkably small ( ≲ 0.13 dex) and largely driven by observational uncertainties. The residuals do not correlate with any global or local galaxy property (e.g., baryonic mass, gas fraction, and radius). The radial acceleration relation is tantamount to a natural law: when the baryonic contribution is measured, the rotation curve follows, and vice versa. Including ultrafaint dSphs, the relation may extend by another 2 dex and possibly flatten at g bar ≲ 10 − 12 m s⁻², but these data are significantly more uncertain. The radial acceleration relation subsumes and generalizes several well-known dynamical properties of galaxies, like the Tully–Fisher and Faber–Jackson relations, the “baryon-halo” conspiracies, and Renzo’s rule.