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We study the impact of out-of-equilibrium, dissipative effects on thedynamics of inspiraling neutron stars. We find that modeling dissipativeprocesses (such as those from the stars internal effective fluid viscosity)requires that one introduce a new tidal deformability parameter--thedissipative tidal deformability--which modifies the phase of gravitationalwaves emitted during the inspiral phase of a neutron star binary. We show thatthe dissipative tidal deformability corrects the gravitational-wave phase at 4post-Newtonian order for quasi-circular binaries. This correction receives alarge finite-size enhancement by the stellar compactness, analogous to the caseof the tidal deformability. Moreover, the correction is not degenerate with thetime of coalescence, which also enters at 4PN order, because it contains alogarithmic frequency-dependent contribution. Using a simple Fisher analysis,we show that physically allowed values for the dissipative tidal deformabilitymay be constrained by measurements of the phase of emitted gravitational wavesto roughly the same extent as the (electric-type, quadrupolar) tidaldeformability. Finally, we show that there are no out-of-equilibrium,dissipative corrections to the tidal deformability itself. We conclude thatthere are at least two relevant tidal deformability parameters that can beconstrained with gravitational-wave phase measurements during the late inspiralof a neutron star binary: one which characterizes the adiabatic tidal responseof the star, and another which characterizes the leading-orderout-of-equilibrium, dissipative tidal response. These findings open a window toprobe dissipative processes in the interior of neutron stars with gravitationalwaves.

Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neutron star binaries