  An excess in the X-ray emission from the neutron star merger GW170817 above
the predicted afterglow was recently detected t~3.4 years post-merger. One
possible origin for the excess is accretion onto the newly unshrouded black
hole (BH) remnant. While fall-back of the bound dynamical ejecta is
insufficient to generate the excess luminosity, L_X ~ 5e38 erg/s, fall-back
from the disk wind ejecta-due to their larger mass and lower velocity-remains a
viable possibility. We present hydrodynamic alpha-viscosity simulations of the
post-merger disk evolution which extend to an unprecedently long timescale t ~
35 s post-merger, as necessary to capture the end of photodissociation and the
asymptotic evolution into the radiatively inefficient regime. Due to
inefficient neutrino cooling, the BH accretion rate decays rapidly at late
times (Mdot_BH ~ t^(-\beta_BH), where \beta_BH ~ 2.4-2.8), seemingly
incompatible with generating the late-time excess. However, the rate at which
matter falls back to the inner disk from the equatorial regions (as inferred by
the rate matter is unbound in outflows by viscous heating at higher latitudes)
decays more gradually, Mdot_fb ~ t^(-\beta_fb) with \beta_fb ~ 1.43 in our
alpha ~ 0.03 simulations. By the present epoch, the fall-back rate has become
sub-Eddington and the disk can again accrete efficiently, i.e. Mdot_BH ~
Mdot_fb, this time as a result of photon cooling instead of neutrino cooling.
The predicted X-ray accretion luminosity at the present epoch is L_X ~ 0.1
Mdot_BH c^2 ~ (2-70)e38 erg/s for beta_FB ~ 1.43-1.66, thus supporting (with
caveats) an accretion-powered origin for the X-ray excess in GW170817. The
suppressed BH accretion rate prior to the radiatively efficient (sub-Eddington)
transition, weeks to months after the merger, is key to avoid overproducing the
kilonova luminosity via reprocessing.
