The shape of ‘dark matter’ haloes of disc galaxies according to MOND

Analyses of halo shapes for disc galaxies are said to give conflicting results. I point out that the modified dynamics (MOND) predicts for disc galaxies a distribution of fictitious dark matter that comprises two components: a pure disc and a rounder halo. The former dominates the true disc in regions of small accelerations, where it controls the z ‐dynamics in the disc (disc flaring etc.); it has a finite total mass. It also dominates the round component near the centre where the geometry is nearly planar. The second component controls motions far from the plane, has a total enclosed mass that diverges linearly with radius, and determines the rotation curve at large radii. Its ellipticity may be appreciable at small radii but vanishes asymptotically. This prediction of MOND differs from what one expects from galaxy formation scenarios with dark matter. Analyses to date, which, as they do, assume one component – usually with a constant ellipticity – perforce give conflicting results for the best value of ellipticity, depending on whether they probe the disc or the sphere, small radii or large ones.