  The phenomenological basis for Modified Newtonian Dynamics (MOND) is the
radial-acceleration-relation (RAR) between the observed acceleration,
$a=V^2_{rot}(r)/r$, and the acceleration accounted for by the observed baryons
(stars and cold gas), $a_{bar}=V_{bar}^2(r)/r$. We show that the RAR arises
naturally in the NIHAO sample of 89 high-resolution LCDM cosmological galaxy
formation simulations. The overall scatter from NIHAO is just 0.079 dex,
consistent with observational constraints. However, we show that the scatter
depends on stellar mass. At high masses ($10^9 <M_{star} <10^{11}$ Msun) the
simulated scatter is just $\simeq 0.04$ dex, increasing to $\simeq 0.11$ dex at
low masses ($10^7 < M_{star} <10^{9}$Msun). Observations show a similar
dependence for the intrinsic scatter. At high masses the intrinsic scatter is
consistent with the zero scatter assumed by MOND, but at low masses the
intrinsic scatter is non-zero, strongly disfavoring MOND. Applying MOND to our
simulations yields remarkably good fits to most of the circular velocity
profiles. In cases of mild disagreement the stellar mass-to-light ratio and/or
"distance" can be tuned to yield acceptable fits, as is often done in
observational mass models. In dwarf galaxies with $M_{star}\sim10^6$Msun MOND
breaks down, predicting lower accelerations than observed and in our LCDM
simulations. The assumptions that MOND is based on (e.g., asymptotically flat
rotation curves, zero intrinsic scatter in the RAR), are approximately, but not
exactly, true in LCDM. Thus if one wishes to go beyond Newtonian dynamics there
is more freedom in the RAR than assumed by MOND.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics