Modified dynamics (MOND) as a dark halo

• Published in: Monthly notices of the Royal Astronomical Society 1994-01, Vol.266 (2), p.360-366
• Main Authors: Sanders, R. H., Begeman, K. G.
• Format: Article
• Language: English
• Subjects: Astronomy; celestial mechanics; Characteristics and properties of external galaxies and extragalactic objects; Earth, ocean, space; Exact sciences and technology; galaxies: kinematics and dynamics; galaxies: spiral; Kinematics, dynamics, and rotation; stellar dynamics; Stellar systems. Galactic and extragalactic objects and systems. The universe
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/266.2.360

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.