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 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.

We present rotation curve fits to 175 late-type galaxies from the Spitzer Photometry and Accurate Rotation Curves database using seven dark matter (DM) halo profiles: pseudo-isothermal, Burkert, Navarro–Frenk–White (NFW), Einasto, Di Cintio et al. (2014, hereafter DC14), cored-NFW, and a new semi-empirical profile named Lucky13. We marginalize over the stellar mass-to-light ratio, galaxy distance, disk inclination, halo concentration, and halo mass (and an additional shape parameter for Einasto) using a Markov Chain Monte Carlo method. We find that cored halo models, such as the DC14 and Burkert profiles, generally provide better fits to rotation curves than the cuspy NFW profile. The stellar mass-halo mass relation from abundance matching is recovered by all halo profiles once imposed as a Bayesian prior, whereas the halo mass–concentration relation is not reproduced in detail by any halo model. We provide an extensive set of figures as well as best-fit parameters in machine-readable tables to facilitate model comparison and the exploration of DM halo properties.

The strong equivalence principle (SEP) distinguishes general relativity (GR) from other viable theories of gravity. The SEP demands that the internal dynamics of a self-gravitating system under freefall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics. We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. Our detection is threefold: (1) the EFE is individually detected at 8σ to 11σ in “golden” galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than 4σ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies’ environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity. Tidal effects from neighboring galaxies in the Λ cold dark matter (CDM) context are not strong enough to explain these phenomena. They are not predicted by existing ΛCDM models of galaxy formation and evolution, adding a new small-scale challenge to the ΛCDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond GR.