Modified dynamics (MOND) as a dark halo

We propose a form for dark haloes that embodies the fundamental aspect of Milgrom's modified dynamics (MOND): the discrepancy between the visible mass and the Newtonian dynamical mass appears below a critical acceleration. This is a halo having a density distribution, at least to several tens of kpc, of the form |$\Sigma_0/r$|⁠, where |$\Sigma_0$| is a constant of surface density which does not vary from galaxy to galaxy. To avoid rising rotation curves, such a density distribution must obviously steepen beyond some radius, and we have chosen the Hernquist model in which the density falls as |$1/r^4$| beyond a characteristic scale. We show that, assuming that the visible (baryonic) matter is some constant fraction of the dark matter, spiral galaxies with such haloes exhibit a Tully–Fisher law of the observed form. In a sample of 10 spiral galaxies with well-determined extended rotation curves this halo, combined with the observable matter, can successfully model the observed curves. Moreover, in the seven most luminous galaxies, the best-fitting models have about the same value of |$\Sigma_0$| and are effectively one-parameter fits as in MOND (mass-to-light of the visible disc). The one-parameter description, however, does break down for the three dwarf galaxies in the sample with the lowest internal accelerations.