NIHAO - XVIII. Origin of the MOND phenomenology of galactic rotation curves in a ΛCDM universe

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 ΛCDM 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} M_{⊙ }) the simulated scatter is just ≃0.04 dex, increasing to ≃0.11 dex at low masses (10^7 ≲ M_star ≲ 10⁹ M_{⊙ }). 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 disfavouring 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 ∼ 10^6 M_{⊙ } MOND breaks down, predicting lower accelerations than observed and in our ΛCDM simulations. The assumptions that MOND is based on (e.g. asymptotically flat rotation curves, zero intrinsic scatter in the RAR) are only approximately true in ΛCDM. Thus if one wishes to go beyond Newtonian dynamics there is more freedom in the observed RAR than assumed by MOND.