  The gravitational waves (GWs) emitted by neutron star binaries probe the
physics of matter at supra nuclear densities. During the late inspiral, tidal
deformations raised on each star by the gravitational field of its companion
depend crucially on the star's internal properties. The misalignment of a
star's tidal bulge with its companion's gravitational field encodes the
strength of internal dissipative processes, which imprint onto the phase of the
gravitational waves emitted. We here analyze GW data from the GW170817 (binary
neutron star) event detected by LIGO and Virgo and find the first constraint on
the dissipative tidal deformability of a neutron star. From this constraint,
\emph{assuming} a temperature profile for each star in the binary, we obtain an
order of magnitude bound on the averaged bulk ($\zeta$) and shear ($\eta$)
viscosity of each star during the inspiral.: $\zeta \lesssim 10^{31}
\mathrm{g}\;\mathrm{cm}^{-1}\mathrm{s}^{-1}$ and $\eta \lesssim 10^{28}
\mathrm{g}\;\mathrm{cm}^{-1}\mathrm{s}^{-1} $. We forecast that these bounds
could be improved by two orders of magnitude with third-generation detectors,
like Cosmic Explorer, using inspiral data. These constraints already inform
nuclear physics models and motivate further theoretical work to better
understand the interplay between viscosity and temperature in the late inspiral
of neutron stars.
