A recurrent issue with the interpretation of Hi rotation curves is the argument that the dark matter interpretation is not necessarily correct, starting with a paper by Milgrom (1983) proposing MOND (“MOdified Newtonian Dynamics”). Begeman et al. (1991) made models for 10 galaxies, both for Newtonian gravity and for MOND, and pointed out that a common critical acceleration parameter can be found once some leeway is allowed for galaxy distances. Reviews about MOND and its relative success in reproducing rotation curves have been produced by Sanders and McGaugh (2002) and Famaey and McGaugh (2012). However, the applicability of MOND to larger scales, such as clusters of galaxies, is problematic, and Angus (2009) argues for the presence of 11 eV neutrinos to cure this. Such particles have not been found yet, but then, the nature of the dark matter remains unknown. The fate of the Vulcan hypothesis by Le Verrier (cf. Fontenrose 1973) is frequently quoted to illustrate the idea behind MOND (modifying the theory of gravity rather than searching for additional planets), but the history of dark matter detection resembles now more the discovery story of Pluto, rather than of Neptune.
My own contribution to this has been limited to refereeing some of the papers, and I will neither treat the debate here, nor discuss other alternative theories. What is of interest are the attempts to disprove MOND, by emphasizing the discrepancies with Hi imaging data. There are manifest problems with some galaxies if their Cepheid distance is adopted, the clearest case being NGC 3198 (cf. Bottema et al. 2002; Gentile et al. 2011, 2013). For late-type dwarf galaxies, the recent results of Carignan et al. (2013) for NGC 3109, and Randriamampandry and Carignan (2014) for DDO 154, IC 2574, NGC 925 and NGC 7793 — in addition to NGC 3109 and NGC 3198 — clearly bring out discrepancies as well. However, Angus et al. (2012) could reduce the discrepancy for DDO 154 by considering a thick gaseous disk, up to the point of getting a reasonable fit for most of the radial extent of this galaxy. Such thick Hi gas disks are not unreasonable for DDO 154 and IC 2574, in view of the discussion above, in Sect. 7, and further in Sect. 9.2, but less so for the Sd galaxies NGC 925 and NGC 7793. Finally, the often cited “dip” in the rotation curve of NGC 1560 (Broeils 1992; Gentile et al. 2010) poses a problem, since the curve determined from the data for the northern half of this galaxy does not have a dip, while the one for the southern part does, due to a local absence of gas and stars there; the mean thus has “half a dip”!?
MOND does not go away easily, and the recent result from 153 galaxies in the SPARC sample (12 galaxies too face-on and 10 galaxies too asymmetric were rejected, cf. McGaugh et al. 2016), i.e., a tight relation, with a scatter of ∼30% on a log-log plot, of the acceleration determined from rotation curves compared to the one based on 3.6 µm radial surface brightness profiles assuming a constant M / L-ratio for galactic disks, revived some interest in it. Ludlow et al. (2016) argue that the small scatter in this mass-discrepancy - acceleration relation is due to different feedback processes moving data points along this line, rather than deviating strongly from it, so that the ΛCDM theory does not have much difficulty explaining it. However, this leaves the core-cusp problem unsolved (cf. Fig. 12, inset of left panel).
The diversity of the 3.6 µm radial surface brightness profiles (e.g., Type I, II and III profiles — Martín-Navarro et al. 2012; Muñoz-Mateos et al. 2013; Kim et al. 2014; Laine et al. 2014), and the various physical processes invoked to explain these down- or up-bending profiles, cannot be ignored. Furthermore, in Famaey and McGaugh (2012), the two galaxies presented as examples for good MOND fits, NGC 6946 and NGC 1560, have a different K-band M / L-ratio (0.37 vs 0.18), i.e., a factor of two difference, which is just the order of magnitude difference discussed in Sect. 5. Moreover, data from the high angular resolution THINGS and LITTLE THINGS samples are not included in the SPARC sample, since, according to Lelli et al. (2016), their rotation curves are characterized by many small-scale bumps and wiggles thought to be due to non-circular components such as streaming motions along spiral arms. This exclusion is ironic, seen that when MOND is discussed, the capacity of reproducing such bumps is deemed very important. Anyway, these “details” seem to operate on a different level of complexity than the overall mass-discrepancy - acceleration relation. Perusal of the individual mass models of each of the SPARC galaxies confirms this: the limiting surface brightness of the 3.6 µm profiles used in those mass models is 23.8 ± 1.8 mag arcsec−2, i.e., faint surface brightness levels are not considered for every galaxy.