Milky Way and M31 rotation curves: $\mathrm{\Lambda }$CDM vs. MOND

We analyze the existing rotation-curve data of the Milky Way and M31 galaxies that extends to very large distances and low accelerations. We find a systematic downward trend in the weak acceleration (large distances) segment of the radial acceleration. A similar downward trend has been noticed in the $\mathrm{\Lambda }$CDM EAGLE simulation, while the deviation from the generic MOND prediction would need to be ascribed to an external field effect, or possibly a post facto selected acceleration function $\mu (x)$.