The tightening of wide binaries in dSph galaxies through dynamical friction as a test of the Dark Matter hypothesis

We estimate the timescales for orbital decay of wide binaries embedded within dark matter halos, due to dynamical friction against the dark matter particles. We derive analytical scalings for this decay and calibrate and test them through the extensive use of N-body simulations, which accurately confirm the predicted temporal evolution. For density and velocity dispersion parameters as inferred for the dark matter halos of local dSph galaxies, we show that the decay timescales become shorter than the ages of the dSph stellar populations for binary stars composed of 1 $M_{\odot}$ stars, for initial separations larger than 0.1 pc. Such wide binaries are conspicuous and have been well measured in the solar neighborhood. The prediction of the dark matter hypothesis is that they should now be absent from stellar populations embedded within low velocity dispersion, high density dark mater halos, as currently inferred for the local dSph galaxies, having since evolved into tighter binaries. Relevant empirical determinations of this will become technically feasible in the near future, and could provide evidence to discriminate between dark matter particle halos or modified gravitational theories, to account for the high dispersion velocities measured for stars in local dSph galaxies.