Rotating Love: The dynamical tides of spinning Newtonian stars

We carefully develop the framework required to model the dynamical tidalresponse of a spinning neutron star in an inspiralling binary system, in thecontext of Newtonian gravity, making sure to include all relevant details andconnections to the existing literature. The tidal perturbation is decomposed interms of the normal oscillation modes, used to derive an expression for theeffective Love number which is valid for any rotation rate. In contrast toprevious work on the problem, our analysis highlights subtle issues relating tothe orthogonality condition required for the mode-sum representation of thedynamical tide and shows how the prograde and retrograde modes combine toprovide the overall tidal response. Utilising a slow-rotation expansion, weshow that the dynamical tide (the effective Love number) is corrected at firstorder in rotation, whereas in the case of the static tide (the static Lovenumber) the rotational corrections do not enter until second order.