  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.

Astrophysics