Cooling off with a kilonova - Lower Limit on the Expansion Velocity of GW170817

GW170817 was the first detection of a binary neutron star merger via gravitational waves. The event was observed over a wide range of the electromagnetic spectrum, revealing a thermal kilonova dominating the optical signal during the first $\sim$15 days, and a non-thermal synchrotron emission that has continued to rise $\sim$200 days post-merger, dominating the radio and x-ray emission. At early times, when the kilonova is still dominant, the synchrotron emitting electrons can efficiently cool by up-scattering the kilonova photos through inverse-Compton. Yet, the cooling frequency is not observed up to the X-ray band. This can only be explained if the source is moving at least at a mildly relativistic velocity. We find a lower limit on the source's bulk Lorentz factor of $\Gamma > 2.1$ at $9$ days. This lower limit is model independent, and relies directly on the observed quantities, providing an additional robust evidence to the relativistic motion in this event at early times.