2.2. Rotation-curve analysis

Rotation-curve analysis is arguably the heart of MOND testing. It surpasses all other tests as regards the quality of the data, the freedom from astrophysical assumptions, and the range of acceleration values covered. About eighty disc galaxies with sufficient data (extended, two-dimensional velocity maps, photometry, and HI distribution) have now been successfully MOND tested by various studies [23] [10] [24] [11] [12] [13]. For each galaxy the analysis involves, in most cases, one adjustable parameter-the M / L value of the stellar disc (in standard dark-halo fits there are two additional free parameters characterizing the halo). A success of MOND for even a single rotation curve is most significant, because even full freedom to choose M / L is anything but sufficient to make MOND work in any given case. This is nicely demonstrated in ref [13] by analyzing a synthetic galaxy model taken to have the HI data (HI distribution, and rotation curve) from one galaxy, and the stellar light distribution from another. An attempt to fit this galaxy with MOND gives a very bad best fit, and the best-fit M / L value is unreasonably high. In contrast, a standard, dark-halo fit for this "wrong" galaxy model gives a very good fit (with reasonable M / L value). Another example serving to demonstrate the limited leverage of the M / L parameter: Many galaxies have high accelerations (a >> a₀) in their inner parts; MOND then predicts no discrepancy there, and the stellar M / L value is thus fixed by the inner parts. The rotation curve in the outer parts (its shape, whether falling or rising, and amplitude) then remains an unadjustable prediction of MOND that could easily fail.

In addition, note that the stellar M / L value is not really a totally free parameter. In must fall within some acceptable range, and, by and large, is constrained by theoretical models. The study of ref. [12], which is unique in its use of the infrared K' photometric band-arguably the best representative of stellar mass-shows that, indeed, the resulting MOND M / L values, for the sample of Ursa Major galaxies studied, are very narrowly distributed near one solar unit. The study also finds that the B-band, MOND M / L values are strongly correlated with the observed galaxy color, following the expected theoretical relation. All this shows M / L to be a rather tightly tethered parameter, which further heightens the significance of the successful MOND analysis.