Tidal streams in a MOND potential: constraints from Sagittarius

Abstract

We compare orbits in a thin axisymmetric disc potential in MOND to those in a thin disc plus near-spherical dark matter halo predicted by a $Λ$CDM cosmology. Remarkably, the amount of orbital precession in MOND is nearly identical to that which occurs in a mildly oblate CDM Galactic halo (potential flattening q=0.9), consistent with recent constraints from the Sagittarius stream. Since very flattened mass distributions in MOND produce rounder potentials than in standard Newtonian mechanics, we show that it will be very difficult to use the tidal debris from streams to distinguish between a MOND galaxy and a standard CDM galaxy with a mildly oblate halo. If a galaxy can be found with either a prolate halo, or one which is more oblate than $q \sim 0.9$ this would rule out MOND as a viable theory. Improved data from the leading arm of the Sagittarius dwarf - which samples the Galactic potential at large radii - could rule out MOND if the orbital pole precession can be determined to an accuracy of the order of $\pm 1^o$.