The statistical signal for Milgrom's critical acceleration boundary being an objective characteristic of the optical disk
The various successes of Milgrom's MOND have led to suggestions that its critical acceleration parameter $a_0 \approx 1.2\times 10^{-10}\,mtrs/sec^2$ is a fundamental physical constant in the same category as the gravitational constant (for example), and therefore requiring no further explanation. There is no independent evidence supporting this conjecture. Motivated by empirical indications of self-similarities on the exterior part of the optical disk (the optical annulus), we describe a statistical analysis of four large samples of optical rotation curves and find that quantitative indicators of self-similar dynamics on the optical annulus are irreducibly present in each of the samples. These symmetries lead to the unambiguous identification of a characteristic point, $(R_c,V_c)$, on each annular rotation curve where $R_c \approx f(M,S)$ and $V_c \approx g(M)$ for absolute magnitude $M$ and surface brightness $S$. This opens the door to an investigation of the behaviour of the associated characteristic acceleration $a_c \equiv V_c^2/R_c$ across each sample. The first observation is that since $a_c \approx g^2(M)/f(M,S)$, then $a_c$ is a constant within any given disk, but varies between disks. Calculation then shows that $a_c$ varies in the approximate range $(1.2\pm0.5)\times 10^{-10}\,mtrs/sec^2$ for each sample. It follows that Milgrom's $a_0$ is effectively identical to $a_c$, and his critical acceleration boundary is actually the characteristic boundary, $R=R_c$, on any given disk. Since $a_c$ varies between galaxies, then so must $a_0$ also. In summary,Milgrom's critical acceleration boundary is an objective characteristic of the optical disk and $a_0$ cannot be a fundamental physical constant.